Using Diagrams to Represent Addition & Subtraction: IM 6.5.2
[url=https://im.kendallhunt.com/MS/teachers/1/5/2/preparation.html]“Using Diagrams to Represent Addition and Subtraction”[/url] from IM Grade 6 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 6.5.2
- IM 6.5.2 Lesson: Using Diagrams to Represent Addition and Subtraction
- Practice 6.5.2
- IM 6.5.2 Practice: Using Diagrams to Represent Addition and Subtraction
IM 6.5.2 Lesson: Using Diagrams to Represent Addition and Subtraction
Here is a rectangle.
What number does the rectangle represent if each small square represents:
1?
0.1?
0.01?
0.001?
Here is a square.
What number does the square represent if each small rectangle represents:
10?
0.1?
0.00001?
[size=150]You may be familiar with base-ten blocks that represent ones, tens, and hundreds. Here are some diagrams that we will use to represent digital base-ten units. A large square represents 1 one. A rectangle represents 1 tenth. A small square represents 1 hundredth.[/size][br][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAggAAADVCAYAAAAywwi7AAAgAElEQVR4Ae2dh3cUV5pH5z/Z3ZmdneDx2B4nbBwwwYDB5AwmI3IGk6NEjiYnISREBtsEk2yiwUQFokkCTEbkHAT89nwPd1utAAKVWqJ065xWq6urXtW7Xf292y/Vn8QCAQhAAAIQgAAEMhD4U4bXvIQABCAAAQhAAAJCELgIIAABCEAAAhDIRABByISEFRCAAAQgAAEIIAhcAxCAAAQgAAEIZCKAIGRCwgoIQAACEIAABBAErgEIQAACEIAABDIRQBAyIWEFBCAAAQhAAAIIAtcABCAAAQhAAAKZCGQrCA8ePNDt27d18+ZNHjAoFNfArZs3df/+/UxfEla8OIFHjx65+HH+3Dldu3ZNDx8+zHEi9+7eVerFi3r8+HGO98nNhhbrbt26VSiuceI55ZldA3a9371z57lfm2wFYcmiRRoxbJgGRUVqUFQUDxj4/hqIioxU3KxYXbxw4blfHDbInoD9sEjYvVuTJ07UuLFj9c2YMfphxQpdOH8++50kpaWl6XhKiqKnz1Dvnj2dYDx58uSZ++T2TTvm2jVrZJ89cY44X1iugcFRURo1YuRzvz7ZCkLdWrX1SbGiKv7FpypdqQQPGPj+Gni/6DuqVLGCkpOSnvvFYYPsCfx68KDatm6tvr17a+uWLZodG6dmTZpo7pw5sl/rWS0mAseOHdOgyCiVK1NWRd55V1evXFFeC8Ldu3fVq3sPvf76P31/fRPHKcfsGvi8QnF9VKyI/vo/f87qqxiyLltBqFW9hlr1iVD01ila+OscHjDw/TXQZVR71a5bw/36DfmW8OKFCPTt1Vvdv+6m1NTU4H4zpk9Xl46ddOb0meC6wD8mAdYE0apFCw0bMkRxs2bpoyIfhEUQrKq1R7duTg6Ic8T5wnANzNsXp37RvfSX//rvwFcw22cEgYLf9wV/Tr/0CEK2cSLHbzxKS1Ozxo0VNTDSNRkEdkxKTFSbVq21aePGwKpMz0cOH3b9FdavW6ei7xdBEIhNxKY8uAYQhDyAmtNChu1e3V8hCEKmMvuFVjx5/FgXLlxQ4wYNXf+D9Dvv27dP7du01epVq9KvDvnfOjZax8TNmzYhCMQw5CCPrgEEIY/AUvi/uoV/Tj47BCGkvH7hF1a4p6SkqEnDhoqdNStk//379jtBWLZ0acj6rF4gCP7+nuXku8g2eXcNIAgIAvb9EtcAgpBVcZ3zdSYIJ46fcDUIs2JiQnY0QWjXuo2Wff99yPqsXiAIeVc4UPDCFkF4icKBLw5fHAQhq+I65+uss+HVq1edIIwdMyZkx317nzYxrFm9OmR9Vi8QBL6LxOO8uwYQBASBGoSXuAYQhKyK6xdbZ7UIEU2bKmrgwJCJjnbu2KHWLVtq86bNz00QQci7woGCF7YIwksUDnxx+OIgCM8tu3O0QUz0THXu0FEHDxxwknD1ylUNHTxY3bp01bmzZ10ap06d0sYNG3X299fpE0YQ+C4Sj/PuGkAQEARqEF7iGkAQ0hfTL///byd/09hRoxU5YIBWrVyp2JhZ6ti+g77/7jvZSAVb1v30k9q2aq3VK1dmOtC2X35RmZKldP3atTyfKIl5EPKuIKKQL5hsEYSXKBy4mAvmxRzOzwVByFRWv/SK06dPa+H8Berft6+b0jUxIcFNnRxIcPu2bercsaNMBjIuR48e1eiRI3Xnzh0EgVjGjx2PrwEEwWOg4SykOFb+iQqCkLGo9v9rahDy7/tGrMsf9ggCgoB1v8Q1gCD4Xwgy5hBByJ9CCjnIP+4IwksUDlyw+XfBFhT2CELG4jM8r61fgt2YyW7zbKMgwrkgCHzvC0r8Cdd5IAgIAjUIL3ENIAjhLJr/OJbdHnr61KnavWuXk4Q/3sn7/xAEBCFcBXNBOQ6C8BKFQ0H58DiP/AtYCILcDZauXL4ScqMlL4vptLQ0Xb58OST91IsXVa5MGcXHzXY3a/LyeM9LC0HIv+8bsS5/2CMICAI1CC9xDSAI0qXUVNWpVUvnzp17Xtn6Uu9fvHBBtWvUlD0HFgQhfwoKCujCyR1BeInCgS9L4fyypP/cC7MgWNv/ubPnNDM6WiWKFdOqlau0Jzk5OLGRFeZWs3Dw4EHt2rlT+/ft053bd4J9Bm7evOnW3b17VzbEMTkpSQm7E9y9GR48eOC2O3PmjGZMm+7StymXXfrnzikgCHGzYnXo11+1J3mPO8axo0fdUMeASOTFc6AGoWT5YordNYMHDHx/DcRsn6aeE7vqL//138/9Sv0puy1qVa+hVn0iFL11Cr9GEY5CcQ0UakF49FiJCYn6unMXffDee4oaGOlk4cD+/Xr48KGssB4zarQG9OuvsaPHqF+fPho9cpQTCLsHw8mTJ9Wofn199+23mjhhgiZPnKThQ4eqS8dOMhm4dvWadu3c5V4XefddDY4apJjoaCccAUEYHBXl5kyYPHGimwfBZmNctHCha5LILk7ldr0Jjc3V8P4H76h2ixo8YOD7a6BWRHWVq1ZG/37tX8/9+iAIFP6FovBPX1OQ3f+FWhAeP9al1EtaMG++ypQqpeSkZNfcYB0IrXZg2JCh6tiuvbZv264TJ064CY6+/KKcfli+Qrdu3tShQ4dU8rPP3K2et27Zot9OnnRTLQ/o28/NmHjs6DGlXkzVvDlzVbpkKe3ds9cdz9IPCEKlLyto2fdLdfLECaUcO6ZJEyaoUYMGSkpMfG4ge9kNrE/EiuXL1aFde7Vr05YHDArFNWDfZfsR8LwFQUAQEITfr4HCLAgWKKywXrtmrb784gtZc0Bgsf4C77z5ljZv3Kgrly/rxo0bOn/+vKIGDHSFf0pKihOEz0uU1DdjxujSpUtuV/t1vvXnLapRtZrsZk23b93W6pWrVL5s2ZA+DgFB6NWjh86cPu32tVoLq72oV7u2lubgFtGBc+UZAhDwjgCCgCAgCAiCiyhZCYLNUWDNC6/97e+qW6u2WjSLUIuI5opo0lTlSpdRvdp1nBxYDYLVPKz8YaWsXd+W+/fvKzkxSVUqVnI1Ds8ThFkzY9x8CLbvo7Q0HU9JUZ2atbRk8WKXHn8gAIHwEkAQEAQEAUFwUScrQbDOi0cOH3aCsHb1Gh05ckRHjxzRkcNHXBPCyRMnXc3DU0H43NVAWDq2OEFISlaVihVzJAjxcXHBYY4mJieOH0cQwlsecDQIhBBAEBAEBAFBcEHBbo7049q1ro/A6VOn3DrrgHjBmhje+o9+2bpV1myQ1ZITQbhz+7ZWr1ql0iVLhtzmOdDEkH4eBAQhK8qsg0B4CSAICAKCgCC4qGPDEW02ww/fL+JGHFjfA+tvcP36dbVr00bdunZ1QxOt/8GF8+ddZ0W7JbMV5jkRBKtR2LF9u4q8+54SEhLcXAjWARJBCG/Q52gQyCkBBAFBQBAQhGC8sMLaOhW2btlSNuzwpx9/dLMeWkfEDm3bqUnDRhrQr58G9h+g1i1aaNOGDa5WwZodKleooHU/rQvOXWDCYaMVbGIk66Roi8mF9Ulo06qVG+q4ft1616mxWuXKmj93npMR286kw0YzNKrfgE6KwU+HfyAQXgIIAoKAICAIwahjw/4uXrioTRs3avOmTa4pwJoZrMC+eeOGm8how7r1Wr9unSvA79+7J3vfagI2btjgBMDSsMX6L1y7dk0/b/45OJeBvWdNFratpW8zNlrNgh3PhODhgwduX0vz9q1brlnDJl5igQAEwk8AQUAQEAQEISTyWMFufQ3u3rnjJkkKvGmFttUKWF8F64hohb2ts8UEwvZJv87es7Tu3bsXcu8Fl/6dO257G84YeJ328GEwPUvT1puA2DYsEIBA+AkgCAgCgoAghD/ycEQIQKDAE0AQEAQEAUEo8IGKE4QABMJPAEFAEBAEBCH8kYcjQgACBZ4AgoAgIAgIQoEPVJwgBCAQfgIIAoKAICAI4Y88HBECECjwBBAEBAFBQBAKfKDiBCEAgfATQBAQBAQBQQh/5OGIEIBAgSeAICAICAKCUOADFScIAQiEnwCCgCAgCAhC+CMPR4QABAo8AQQBQUAQEIQCH6g4QQhAIPwEEAQEAUFAEMIfeTgiBCBQ4AkgCAgCgoAgFPhAxQlCAALhJ4AgIAgIAoIQ/sjDESEAgQJPAEFAEBAEBKHABypOEAIQCD8BBAFBQBAQhPBHHo4IAQgUeAIIAoKAICAIBT5QcYIQgED4CSAICAKCgCCEP/JwRAhAoMATQBAQBAQBQSjwgYoThAAEwk8AQUAQEAQEIfyRhyNCAAIFngCCgCAgCAhCgQ9UnCAEIBB+AggCgoAgIAjhjzwcEQIQKPAEEAQEAUFAEAp8oOIEIQCB8BNAEBAEBAFBCH/k4YgQgECBJ4AgIAgIAoJQ4AMVJwgBCISfAIKAICAICMILRZ4nT57owYMHunr1qm7evKmHDx/maP+HDx7oxo0bbj/bx9LJarG0r1+7psePH2f1NusgAIEwEUAQEAQEAUHIcbixgj01NVVbfv5ZC+bN05JFi7V3715X6D8rkSuXL2tPcrIWLVighfMXaPu2bUq9mKq0tLTgbo8ePdLly5e1fdt2RU+frnv37knZSERwp1z+YxJy/tw57du7V3v35P5xYP9+nT93Ppdnxe4QKBgEEAQEAUFAEHIcjS5evKhRI0aoZrXqmjZligZFRimiSVPNmT0721/8j9IeuQK/4Vf1NWLoME2ZNFm1qtfQhHHjdeXyleCxr127pqmTp6hEsc/0/tvv6OqVK9nWMgR3yuU/9+/f19DBQ/T2m2/qnbf/k8vHW/rgvfc0KDIyl2fF7hAoGAQQBAQBQUAQchyNFi9aJCvoExMSdOvmTd26dUvz5sxV4wYNdeq3U7JagPSL/ULfv3ef2rZqrdmxcW77O3fuKCkhUR3attOaVaudBDxKS1PPbt3VtVNnTRw/QUWLFAmLINj59+zeQ8U+/1ijvh+Wq8eQeQNVplJJl6/0DPgfAq8qAQQBQUAQEIQcxS8r7K32oEG9r2SFfKAPwb69+9SiWYS+W/Lt02aBdKmZMPy4Zq1aRjR3UhF46/atW+rVo4eTAkvH0l730086duyYVq9apaLvh08QenTrplIVimvu3thcPWZum6oKdcqpXes2gWzyDIFXmgCCgCAgCAhCjoKYFeoD+vZTuzahBaAV6lYbMGP6dCcO6ROzmoEZ06br6y5ddPTo0fRvqXePnq5mIVDrYP0b7P/NmzaFXRBKVyqR6+9B3O5oVapXHkEI+ZR58SoTQBAQhFwHxoU+YdhlVHvVrltDCbt3v8rf6Tw7d+t/YM0AgwaGtrGnHEtRx/YdXJ+EO7dvhxzfOiFG9h/g2uVPnz4d8l6fXr3UplVrNyIi/RsIQnoa/A+B/COAIPikcPNLIZ2f+UAQnh2ILly44ARhcFRUyIYpKSnq0K69xo0dq9tZCMKAfv01ODJKZ86cCdmvT6/eatW8RaZaBwQhBBMvIJBvBBAEBIEahN+vAQTh2XHI5jDo27u3unbuErJhyrFj6tiuvaZPnZqpsLcahInjxrvmBKtpSL/07vm0iSHjPAoIQnpK/A+B/COAICAICAKCkKMIZIX98KFD1ah+g5DRCocPHVLrFi0VHxenu3fvhqRlfQqWL12mtq3byOYICCwmBT27d1eHdu0yDY9EEAKUeIZA/hJAEBAEBAFByHEUmhsfryYNGurXgwfdDIo2mmH5smVOGnbt3OnWnTl9Wod+/dXNmmijE/bu2aM2rVpp2dKlTiBMGmx/6+w4Y9q0TMdGEDIhYQUE8oUAgoAgIAgIQo6Dz4njx9Wvdx/X8dBGL5gUdOnU2c0lYLUCNmRx5PDhbnSC1SzYYjMijho+Qp06dFBycrKOHT2qfn36umYH+z/jsnXLFhX/5FNdu3o1OJQy4zZevbZ5EGyYI6MYvCJKOn4igCAgCAgCgvBCMe3s2bMaPXKUGtWvr4imTRU3K1ZXrvwxI2L/Pn1Vp0ZNJSUmBtO1WRLnz53rZl38qk5dJxFZyYHtYDUONpeA3echMNdCMCGP/0EQPAZKcr4igCAgCAgCgvBCQc36Ily/ft3dk+HSpUtudsTAXAaWkP3yt3sqpO+PYO/bCAfbPvXiRbd/xs6JgZOw6Y9NOKx5Iq8XBCGvCZP+q0wAQUAQEAQE4VWOYbk6dwQhV/jY2ecEEAQEAUEIoyDYr2/7hWy3NM7r6vPnxS77VW9DF9P/+n/ePi/yvuXPagmsJsHynd1iNQU2S6PdDjoctQbpzwNBSE+D/yEQSgBBQBAQhDAKglXNb960WUePHH1moRn6Nc2bV9bGP3/uvEyTG3l1NJMD69Ro91iwJofsFuvEuGrlSh09ciTTrIrZ7ePVegTBK5Kk40cCCAKCgCCEURCsZ3+blq00N35OSBt9fgQXK7z/8df/yzTDoVfnYoXvd0uWqH7dekpOSs422dTUVFUoV05z4uN1/dq1bLfLizcQhLygSpp+IYAgIAgIQhgFweYHaN2ihebMjtfdO6GTCoU7qBxPSdH//fkvsnkL8mKx20F/u3ix6tWuo6SkJHcI63xokyOlH/VgnRbLlSmj+LjZstEO4VwQhHDS5livGgEEAUFAEPJBEGbHxunUb7+52xsfOXxE586d0+NHf/Tav3r1qqueTx9QrCr+Uuol97Dqe3tt29nIAOtLcOLECR05fNgV+PZe+j4OgZEHdkfFI0eOyO6rcPjQ4RBBsDROnTrlmj7sxkomEJdSU4OnYO//dvI3NwmSHcsd4/GT4PvWf8CaEmzqZRvCaFMrf7tkiROExIQEd542q2LpkiVlcx3Y+yYKAUGIi411x7R7Oxw6dEg2nNL6a+TlgiDkJV3SftUJIAgIAoIQZkFo1rixhgwapJkzZshufGQ3LRo5YoQSdycEC8T169apedNmIfHFCt+xo8fI5MIKNhODKZMm6dvFS9xshqNGjJTNQTBsyFDXph8oXK1DpBX4dtvlvn36aGD//u7YK5YvDxGEX7ZuVdfOnbV7125NHD/eTatsBbl1YrRmgBXLlitywAD17d1HUQMH6ocVK5ygmIjYsY4fP+7ux2D3a7CbM02eOEkTx09QrepP75C5besvatEsQu+89ZY6te+g4UOHubkSAoIwZtRoxc2apWFDhjgmxsjOxfKaV4sNvbQpnz/6rIii4vvn6tFvRk+VLF9M7du0zavTJV0IhJUAgoAgIAhhFoS6tWqrxKfFtGDefCUmJOrnzZtdIVW9chVdvnTJBYCFCxbos08+DQkG1hTQ/etuGjFsuPvlbTUQdvvliuW/dOKwe9cuV6BOmzJFxT7+RHZ7ZvtVb7UFUQMjVaNqNW3asNH1B/ju229Vs1r1EEFY9v1Svf3Gm+5mTJs2bnI1DFevXHE3YLLJkOrXqSvbz2oDrGagVPESribgwf37unD+vLuRU5OGDfXjmrWu4LeplatUrKgqFSspYXeCTp86rejpM1Tys+JPaxBSUtycCQFBsO2mT5umxMREWV769OzlJOnggQMhHLx8YWJj95d4/513VfTDIrl7fFBERYsUUeSAgV6eImlBIN8IIAgIAoIQZkFo3rSpxo4e7SYLsl/n1lywf98+/fNvf3dNDRYNcioIXTt1VtlSnwfTsvSsQK1WubLWrlnrRihs3LBBtWvU1HdLvg1OamQFv9VgpO+DsPS77/XBe+9r+7ZtTgpMLqx2wJoZPv7gQ23euCl4LwUbjdG3V2917/q1Tp44qX179+m9/7yt5KQk1/QQqHWw2gyrQUhKTNKtm7e0csUPKl+2rOsYGUg/IAg2e6J1nLR979+7p4Tdu13zxMoVK/IsQFr+rJnGml4OHz6c64c1y9joEBYI+IEAgoAgIAhhFoRWzVu46YntRke2WCFlnRf//r9/1bmz59y6nAqC3TK5S8dOrlAOBCS7R0LDr+q7poebN25oZnS0GyVgv/Kt8LXF+iTYDZMyCsInHxZ1BZwV3rbY88kTJ/T6P/6pbl26umYBq8EYMmiwK7wb1PvKCcn2X7bpjdf+5WorLD+2WJ+F2XFxshoT66R4+9ZtrV65ygmC9bkILAFBsNtFW7OJLXZ+1o+hbq1arrYisG1ePFse7Xgmarl9WDoBdnlxrqQJgXASQBAQBAQhzIKQcRTDU0E49FKC0K9PH/dL3joMBhbr5Ne4QUMtXrTIFdLTpkzVF6XLuF//gcLbts04isFqED796OOQuQgeP3okG5r52t/+rjGjRmnB/PnuMX/ePNdfwJoRLl64oPXr1uvf/3wtWMBb+vZL2kQnp4Jgt4sOjGIwkbHahDo1a2nJ4sWBrPEMAQiEkQCCgCAgCK+IIFiBbnMojBg2LNgHob8JQu8+ITUIGQXB5heoXKGi+0Vuv3BtsY6Le5KTM9UgZBQEEwr7tf/m6/92Vf4222HGxX4x242Z3nz9ddcZMlBLYXMa2O2crZB3NQi3n9YglP38c507ezaYTKAGIf0wRwQhiId/IJBvBBAEBAFBKICCsGTRYpUo9pluXL/ufvlbc4T9Si9XpqyGDxn6QoJg/QKs82BsTIyu/H4TJRtCaKMEMjYxZBQEi0w2FLFa5SquBuHsmTPufO7dvev6N1iVvEnErwd/dR0vly9b5ra36ZXPnD7jbutsnSFNEGyfTRs36sP3i7ihkFbrkfYwLTjMEUHIt3KAA0MgSwIIAoKAIBRAQdi5Y4fq1a7tbo8cEz3TdWps3qyZGxFgwwOt0LZRDDmpQbhx/YbmzZmrUsWLa/TIkYqJjtagyEi1iIjIkSBYbcOObdtl/Q1seOKsmBjXvGDHDnRctE6LNvyy0pcV3DDF6BkzNLD/ALd99SpVnSCYSNhwy0+LfqT+ffu62SQtn9QgZBmbWQmBfCeAIBQgQYjbHa3BcweoasOK6jW5m+ITYyi8w/j5dBnVXrXrPh2zn1ffTJvLwNrt9+7Zo7SHD4OHsfXjxn4THPNvY/9tsqCF8+e7WRfXrFrl9rF+Alt+3uJ+xVsnwPU//SSbMyHQdGAJ2u2WbTjigf373fwEVl1vPfVtdMLC+Qu0YN487di+3aX/zZixwV731lHSCvZAE0Hg5KxgtxoBm9DJ7qswb+5cJxw2R4KJim1vx7f+AzY80Y5h/QYSEhJ0POW4Fi1c6IZBWnqWzs4dOzU3Pt6tP3b0mBsxMWf2bNfkYaMXbLFmC8vHogULdfDAwcCp8AwBCISRAIIQxgJo4TOONePnyeo2rrPK1yyjj0t8oDaRLRS7awaC8Axmz+L5Mu+FQxCsSt6aCzLOdGjrA4Vt4PtvBa9JgK2/c/uO6zdg0zPbI9Dz3gpcuxOiFeKBxQprm+bYxvgHetTb+5ae/dK3h6veT0vTlctXgnJhhbO9l90SEAUruE043B0pfx/tENjHjm3nbA/3/pMnwaYI2yar8wicV/rztW1tvYlSQBoCx+AZAhAIDwEEIYwF0LMKrQExvVW1UUVF9GqscjVKq21USwQhzJ9NOAQhPF9rjgIBCEAg9wQQhDAXQtlJwtSNEzRt80SNWzVKVRpUQBDy4XNBEHIfUEgBAhDwDwEEIR8KoqwkYf7+2VpwIF4T1o5FEPLpM0EQ/BPYyAkEIJB7AghCPhVGWUmCrZuIIORbvwsEIfcBhRQgAAH/EEAQEIR8K5Czk6T8Wo8g+CewkRMIQCD3BBAEBAFB+P0aQBByH1BIAQIQ8A8BBAFBQBAQBP9ENHICAQh4RgBBQBAQBATBs4BCQhCAgH8IIAgIAoKAIPgnopETCEDAMwIIQgEThOhfpqrzyPaKiu+vOcmzKLzD+PnQB8GzuEJCEICADwggCGEsgPKrdz7HnZMj0UIQfBDRyAIEIOAZAQQBQchR4VkYJANB8CyukBAEIOADAggCgoAg/H4NIAg+iGhkAQIQ8IwAgoAgIAgIgmcBhYQgAAH/EEAQEAQEAUHwT0QjJxCAgGcEEIQwCcL8A7M1b1+c5u2N04KD8ZkKZXvPbtZk79mNm+bujZXts/Bg5g52z0urMPQXyIs80sTgWVwhIQhAwAcEEIQwCIIV+jO3TdXopcM1etlwxe2OdjKQvpAbt2q0Zu2YrjlJs9wNm0YsGazoX6Y4WUi/nf0fs32aS2f00mFZppVxe15nlqysmCAIPohoZAECEPCMAIKQh4JgYhC7a4baDWqlctVLu9s4V2lQQWWrlHLzHJgoWEFl21WsW04t+zVTo85fqWrDiqraqJJKfvmZOo1o54TAbXcgXgNieqty/S9VsU4591y2aikNXzRIsxNnZqqVyKoQZF32soAgeBZXSAgCEPABAQQhDwXBmhN6TOiqSvXKq9s3nTV+9WiNXTHCCUPl+hU0aE7/oCAU/+JTla5UQj0mdNG4laM1fvUYtYlsoYp1y2vEkiGuecJqDCrU+UJtI1to7PIRrkaiydcNnHiMWTYCQcjlZ4kg+CCikQUIQMAzAghCLguVZ/0in50Yo7JVP1er/hGuucDVAhyM14wtk/Vl7S/UqEt914RgNQjFy36qWs2racqGCcGCfuyKka4mocvoDrK0Wg9sri+qfa7Bcwdq2uZJmrJhvPrP7K3Pyn7iahqedS68l33NQYANguBZXCEhCEDABwQQhDwUhFk7p+uNN/+l/jG9NW9/XLDgNyGwGoRqTSprdtJM18RggtCyX4Ridz1tdrBCa9JP36h6k8rqMKS14nZFq3bL6ipe9hNVa1xJX7WrrXrtajupKFqsiNoPaR1MP1Dg8fx8KUjPCEHwQUQjCxCAgGcEEIQ8EgSTgJgd0/XvN17TwLi+T0ckpDtWFdfPoOLTToa/1yC0HtDcvQ4UWukFwfoymFBYE0O3cZ0UGdc3+BgY29fJRGA/nl9MDAK8EATP4goJQQACPiCAIKQrtAMFhVfP1nHQqv87DG3jRii4dA/OUezuaNfEYLUANqQx0MTwLEGIS5gp629gnRnHLBuu+MSYPx5JMa6PglfnXVjTQRB8ENHIAgQg4BkBBCEPBcHmMtUrfMwAAAe3SURBVOg4rI0bbWC/8qf/PEnTN09Sj4ldVb5GGfWe0t01C+REECytQfH9VbpySZfm5PXj3NDJQF8Eq2EorAW7V/lGEDyLKyQEAQj4gACCkIeCYBMfmRA07lpf1ZtWcTUJrQdEqFyNMq5TYfTWKUFBKF+zrDoOaxsyXHHqxgmq17aWvh7bydUy2O2fbchk5a++VLOejdR5ZDvXAbJp94aamq5zo1cFZmFLB0HwQUQjCxCAgGcEEIQ8FIRAAWvzHYxYPFjdxnVW93Fd3CRHNioh8L7NlmgdGb/5YaSbQTGw3moFhi2M0riVo4Lb2oyL9rrXlG6y0Q09J32tb1aMVHxSuvTCkKfAOfrpGUHwLK6QEAQg4AMCCEIYClNrQrCCfe6eWM3ZExvsd5C+cHVTK+8PnVo5sJ/1Uwhue3CO29+llTzLpRnoxxDcJgx58uOxEAQfRDSyAAEIeEYAQaAw/UM+CjkLBMGzuEJCEICADwggCIW8UPRjTcDL5glB8EFEIwsQgIBnBBAEBIEahN+vAQTBs7hCQhCAgA8IIAgIAoKAIPgglJEFCEDAawIIAoKAICAIXscV0oMABHxAAEFAEBAEBMEHoYwsQAACXhNAEBAEBAFB8DqukB4EIOADAggCgoAgIAg+CGVkAQIQ8JoAgoAgIAgIgtdxhfQgAAEfEEAQEAQEAUHwQSgjCxCAgNcEEAQEAUFAELyOK6QHAQj4gACCgCAgCAiCD0IZWYAABLwmgCAgCAgCguB1XCE9CEDABwQQBAQBQUAQfBDKyAIEIOA1AQQBQUAQEASv4wrpQQACPiCAICAICAKC4INQRhYgAAGvCSAICAKCgCB4HVdIDwIQ8AEBBAFBQBAQBB+EMrIAAQh4TQBBQBAQBATB67hCehCAgA8IIAgIAoKAIPgglJEFCEDAawIIAoKAICAIXscV0oMABHxAAEFAEBAEBMEHoYwsQAACXhNAEBAEBAFB8DqukB4EIOADAggCgoAgIAg+CGVkAQIQ8JoAgoAgIAgIgtdxhfQgAAEfEEAQEAQEAUHwQSgjCxCAgNcEEAQEAUFAELyOK6QHAQj4gACCgCAgCAiCD0IZWYAABLwmgCAgCAgCguB1XCE9CEDABwQQBAQBQUAQfBDKyAIEIOA1AQQBQUAQEASv4wrpQQACPiCAICAICAKC4INQRhYgAAGvCSAICAKCgCB4HVdIDwIQ8AEBBAFBQBAQBB+EMrIAAQh4TQBBQBAQBATB67hCehCAgA8IIAgIAoKAIPgglJEFCEDAawIIAoKAICAIXscV0oMABHxAAEFAEBAEBMEHoYwsQAACXhNAEBAEBAFB8DqukB4EIOADAggCgoAgIAg+CGVkAQIQ8JoAgoAgIAgIgtdxhfQgAAEfEEAQEAQEAUHwQSgjCxCAgNcEEAQEAUFAELyOK6QHAQj4gACCgCAgCAiCD0IZWYAABLwmgCAgCAgCguB1XCE9CEDABwQQBAQBQUAQfBDKyAIEIOA1AQQBQUAQEASv4wrpQQACPiCAICAICAKC4INQRhYgAAGvCSAICAKCgCB4HVdIDwIQ8AEBBAFBQBAQBB+EMrIAAQh4TQBBQBAQBATB67hCehCAgA8IIAgIAoKAIPgglJEFCEDAawIIAoKAICAIXscV0oMABHxAAEFAEBAEBMEHoYwsQAACXhNAEBAEBAFB8DqukB4EIOADAggCgoAgIAg+CGVkAQIQ8JoAgoAgIAgIgtdxhfQgAAEfEEAQEAQEAUHwQSgjCxCAgNcEEAQEAUFAELyOK6QHAQj4gACCgCAgCAiCD0IZWYAABLwmgCAgCAgCguB1XCE9CEDABwQQBAQBQUAQfBDKyAIEIOA1AQQBQUAQEASv4wrpQQACPiCAICAICAKC4INQRhYgAAGvCSAICAKCgCB4HVdIDwIQ8AEBBAFBQBAQBB+EMrIAAQh4TQBBQBAQBATB67hCehCAgA8IIAgIAoKAIPgglJEFCEDAawIIAoKAICAIXscV0oMABHxAAEFAEBAEBMEHoYwsQAACXhNAEBAEBAFB8DqukB4EIOADAggCgoAgIAg+CGVkAQIQ8JoAgoAgIAgIgtdxhfQgAAEfEEAQEAQEAUHwQSgjCxCAgNcEEAQEAUFAELyOK6QHAQj4gACCgCAgCAiCD0IZWYAABLwmgCAgCAgCguB1XCE9CEDABwQQBAQBQUAQfBDKyAIEIOA1gWcKQvMeTTRl/XjFJ8XwgIHvr4EOw9qoVp3qSti92+vvGelBAAIQeOUIZCsI9evWU42GVdVxWFv1mNCVBwx8fw3UiqimmjWra0/ynlfui8wJQwACEPCaQLaC0LtHT3360cf6zxtv8oBBobkGWkU017Gjx7z+npEeBCAAgVeOQLaC8MrlhBOGAAQgAAEIQMAzAgiCZyhJCAIQgAAEIOAfAgiCfz5LcgIBCEAAAhDwjACC4BlKEoIABCAAAQj4hwCC4J/PkpxAAAIQgAAEPCOAIHiGkoQgAAEIQAAC/iGAIPjnsyQnEIAABCAAAc8IIAieoSQhCEAAAhCAgH8IIAj++SzJCQQgAAEIQMAzAgiCZyhJCAIQgAAEIOAfAgiCfz5LcgIBCEAAAhDwjACC4BlKEoIABCAAAQj4h8D/A1Jys8HnK8mSAAAAAElFTkSuQmCC[/img][br]The applet has tools that create each of the base-ten blocks.[br][br]Select a Block tool, and then click on the screen to place it.[br][img]data:image/png;base64,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[/img][br][br]Click on the Move tool when you are done choosing blocks.[br][icon]/images/ggb/toolbar/mode_move.png[/icon]
Here is the diagram that Priya drew to represent 0.13. Draw a different diagram in the applet below that represents 0.13. [br][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXAAAADkCAYAAACBmX/eAAAegklEQVR4Ae2d+3MVVZ7A8zftT7NVW7sztTOjKMysijCCioK8RBAJEAJ5EsgLJAFCAANBfKwPnFEkgIzi1IyO89AhCDgzNVO1q+6qVVsS8rr35j6S79Zp0njS3fQ5relMzs3nVnX1Od/z9dL9Od/z6XN7pioVwgcCEIAABJwkUOHkVXPREIAABCAgCJwigAAEIOAogVsCn5iYkHI5ZmouyoWXuo+Z+kwIdZaUNcySEpOycZlpbVaohFKpJIVCQQqFvONHQQrFgnc/phtPXhLf/Be3mBUVM9e53bwHVQMzwazoMXO9zvIzV2fjJSkWi46vy8n59tZmUcYnxr9ZTNPcUjU8Pj7uzY/7a1NxK3jzfztmFWrh5sZyMjw6dPPIDMuww8dIZkSyuaw3idNcG97X+QWSG8vKyKjbrG7N8+iwjI3lPGZpSVzVmZoXNT+3/l1X62x0SEYywzKWz0mxVEztwaeYjeXHZDQ7WjZrM5PNiHqIp/VR8s4X8jfrrBzW5+iwZLKjnsSj1maFkvdv//i+PLT+AVld+6isqV/h7lG3QlbvWCFbaiu9G06jSPyn+5m33/SYralzmJea67oVsnzLw3LsuR7vaa/uL41PPj8mx55/RtbuWOlufU2uDbVOlm9+SJ579aQMjw6nJvDhkSF55fRL8uimh2RVzaOypm65u+zqlsvqHcul+3iXKImn8VGCU7/Aj518RlZULZPVtQ7zmqw15eVX3nzptpvSimw2I2ffOSPzHv+B1Lz+lNS/WensUXe6Ura/slHuWnyHN5FpFIn/hD/28lG5b/PdUvfGJmd5qblW179y/1Jp2tso+Xw+tV8uaqOwvWmbPHlkpdO8FDO1Th5t+5nsOdoqA0PXU2N2ffBr6TyxV5bU3is1v9godafdrTV17U8cXS6VtRtlNDOSxtL0HqRq911Vt1VWdz0ktY77TNXaPZXzZP/Jp71deGm8FOJWoZ6G537VJ/fXLJCu/hY5crXd2ePwlTbp/KBJ5i+dl7rAe1/rkUdaF0v3x63O8lJz3X25VapeXSfNnU3pCjyfk5rmamk8vdVpXoqZWiebTq6RjhN7ZGBoIEWBX5euFzpk7YFl0nWpWVR9u7g+D19tk+4rbVJ/ZpNsrt/kvd4ImWgaAmoHrjYh2xqqZNvP10vXJcd9drVNlrUskkMv7ZdMbtT73/aCmG4JfFHtAjl0uUWOXGt39vjHCLzNWV5qrtUDqOpU+gJX74tvCdzhGlPM1DqpnEmBH1wmXf3NokTo6vpU117fVzkjAq9uqJLqn6+XQ2pD6nKtXW2XZS2LEXjwqfVd+v4rlG924O4uKgT+7TYrCDw5NwSenJn6tYXAv4utI/5bBB4BxSLEDtwCUiDl+uDkKxR24AEy0V3/FQo7cEd/dvAKJflTnlcoyZmxA0/OjB14cmbswKMf1N8pyg782+FjB56cGzvwZMzYgfM/YhorBoEbEUUmIPBILLFBBB6LJzSIwBF4qCiCAQQeJGLXR+B2nPQsBK7TMLcROAI3VgkCNyKKTEDgkVhigwg8Fk9oEIEj8FBRBAMIPEjEro/A7TjpWQhcp2FuI3AEbqwSBG5EFJmAwCOxxAYReCye0CACR+ChoggGEHiQiF0fgdtx0rMQuE7D3EbgCNxYJQjciCgyAYFHYokNIvBYPKFBBI7AQ0URDCDwIBG7PgK346RnIXCdhrmNwBG4sUoQuBFRZAICj8QSG0TgsXhCgwgcgYeKIhhA4EEidn0EbsdJz0LgOg1zG4EjcGOVIHAjosgEBB6JJTaIwGPxhAYROAIPFUUwgMCDROz6CNyOk56FwHUa5jYCR+DGKkHgRkSRCQg8EktsEIHH4gkNInAEHiqKYACBB4nY9RG4HSc9C4HrNMxtBI7AjVWCwI2IIhMQeCSW2CACj8UTGkTgCDxUFMEAAg8SsesjcDtOehYC12mY2wgcgRurBIEbEUUmIPBILLFBBB6LJzSIwBF4qCiCAQQeJGLXR+B2nPQsBK7TMLcROAI3VgkCNyKKTEDgkVhigwg8Fk9oEIEj8FBRBAMIPEjEro/A7TjpWQhcp2FuI3AEbqwSBG5EFJmAwCOxxAYReCye0CACR+ChoggGEHiQiF0fgdtx0rMQuE7D3EbgCNxYJQjciCgyAYFHYokNIvBYPKFBBI7AQ0URDCDwIBG7PgK346RnIXCdhrmNwBG4sUoQuBFRZAICj8QSG0TgsXhCgwgcgYeKIhhA4EEidn0EbsdJz0LgOg1zG4EjcGOVIHAjosgEBB6JJTaIwGPxhAYROAIPFUUwgMCDROz6CNyOk56FwHUa5jYCR+DGKkHgRkSRCQg8EktsEIHH4gkNInAEHiqKYACBB4nY9RG4HSc9C4HrNMxtBI7AjVWCwI2IIhMQeCSW2CACj8UTGkTgCDxUFMEAAg8SsesjcDtOehYC12mY2wgcgRurBIEbEUUmIPBILLFBBB6LJzSIwBF4qCiCAQQeJGLXR+B2nPQsBK7TMLcROAI3VgkCNyKKTEDgkVhigwg8Fk9oEIEj8FBRBAMIPEjEro/A7TjpWQhcp2FuI3AEbqwSBG5EFJmAwCOxxAYReCye0CACR+ChoggGEHiQiF0fgdtx0rMQuE7D3EbgCNxYJQjciCgyAYFHYokNIvBYPKFBBI7AQ0URDCDwIBG7PgK346RnIXCdhrmNwBG4sUoQuBFRZAICj8QSG0TgsXhCgwgcgYeKIhhA4EEidn0EbsdJz0LgOg1ze04KPJvNyrl3+2Rh9Xw5+OFuOdTf6u5xqUU6f7tLFiydJ4ViwTzj3yLjlsBP9ciy5sXS9acWd3n1t0rXRy1S9fI6ae5oknw+L+r+0vjcFPh2aXx9q9O81Po48OFueap3tXT07pEbQwMyPpEOs4HB69L1Qqes6Vzm/ZtdlxyttUstoq699vQm2VJfKaOZ0TRKTJTAC4WCVDdUybZT6+Xgh81u19qlFnl41yI59J/7JZMbldJ4KcStIpfLydlfnpHv3fNPsqTxHnmw6V6nj6X198pd992RqsALhbw888Jh+bcH/tlpVt5c77xX5m/4oTS01HnFn57Ax2R7U7Xcv2WB88zUOpm3+gfSemB36gJ/+pl2+dGj/yZLGv9Dljq8NtW137P5Lqms2SSj2ZQFXl8lCzb+SJbudNtlan3+68++Jx3H9komm4kWeLFYlC++/ELOXuiT8++ck7cunnf7eOe8vPf+e6ntJNVTfny8JH//r7/LuQtn3Wal5vqd83L+7XNy7ZNrHjN1f2l8SqWSXPnkily4+JbzzNQ6Ucz+/NdPJJ8f83Z+aTAby4/JX//2F3nr7fOTa9Pl9XnOm/vLV/pT21ypOVAbkGt/vuYxe6sMfKYc85e/feIxi1qbFeqm1YBaYOVwqAmMutHpXmDq31D/luvM1D3MBDOfVzkwU3M+U8x8bq7Xmc9spriVU53FMfME7ktcFUs5HNMt69t9Xzmw8u/hdvc4nXH/3yqX83SyifuucuHl30fcvU7XmP9vlcv5dlxuCfx2CcQhAAEIQGB2EkDgs3NeuCoIQAACRgII3IiIBAhAAAKzkwACn53zwlVBAAIQMBJA4EZEJEAAAhCYnQQQ+OycF64KAhCAgJEAAjciIgECEIDA7CSAwGfnvHBVEIAABIwEELgREQkQgAAEZicBBD4754WrggAEIGAkgMCNiEiAAAQgMDsJIPDZOS9cFQQgAAEjAQRuREQCBCAAgdlJAIHPznnhqiAAAQgYCSBwIyISIAABCMxOAgh8ds4LVwUBCEDASACBGxGRAAEIQGB2EkDgs3NeuCoIQAACRgII3IiIBAhAAAKzkwACn53zwlVBAAIQMBLwBK7+8Of4xM2/Tq7+ArKzx4T6i/Qz+FfpFTPXuU3eg6qBtD/+H5h1tr70tTGDdeatT/3fdrTtr80JSbfW1PeXl9Nuz6uiVCrJyOiwfPrFf8tnX34qn3/l8vGZfP7VZ/LV/33lPYTSEJK/mIaGB+Wz/1Ws1L/pOLMvP5PrN772mKn7S+MzPl6S6zeuy/989bnjvD711slnX3wqA4MDotZPWkJS3z04PCiff/lZGazNT725/3rgaymWimmUmPedanNwY3DAY1YOa1PVmbofr84i1mbF2NiY/O7DD+TRDQ/LutrV8kTdGqeP9bVrZXtjtRSL6RSJKpBCsSB9b5+R5RuXOc3Kn+vVVSvk2Rd7PWbq/tL45At56X3huGyofdx5ZmqdrNqyQl489bwMjw57u700mA2PDMurp1+R1ZtXyLqaVfJEnavrU133anlixxo50tst2Vw2DVzePKh13/v8cVlbvVKeqHXbZWp9rti4TE69+YrkxrKRm9IKBfPcxT6Z/8QPpf50pTT2bXH3OLNFal+rlPlL5nmSTaNKlOA8Gb3aI/dvnS8NbzrMq2+LNLy5WdZ0PSy7n94p+Xw+skimg+NYfkxqm3fIpp417tbX5NpQ6+SxPUvk6Z52uTE04L1Gmw5Gwe8YGLwuB5/rkAcbFkrdG5XScGazs+zUtW/oWSFb6zfLaGY0eKvT0le/HguFgmxv3CaPdy+T+tPu8vI9vHDrfOl6fr9kchkpjZdCnCoy2Yyc+1Wf3F8zX7r6W+Tw1TZ3jytt0vlBk8xfemf6An+tRx5pXSzdH7e6y+tqmxy63CpVr66T5s6mlAWek5rmamk8vdVpXmp9dPU3y6aTq6XjxB4ZUAJP6VfLdSXwFzpk7YFlcvBSs3RfcXdtdl9plbozm2Rz/SYZyYyERDQdASVwtQnZ1lAl236+XrouOe6zq22yrGWRdL2kBD7qvUYJcrol8EU1C+TQ5RY5cq3d2ePwLYHPwA5cE7jLzLqVwE/NrMBd5qWu/VB/i1SeXDMjAu+aFLh6aKiHh5PsrrZ7117fVzljAq9WAu933GdX2z2BH7ISeC0CDz7dovq3XqHcEriji2ryQa1+QSDwZJsWtdGZUYEfXObt+p0V+LWZFXh1Q5UogasHrZMPPH8T7Ql8sSDwKBN/yxgC/3bgxvLfvEJxelGpHTgCTyxG9fCZqR04AvefAI6d/zGvUNiB2ygdgdtQmpqj3oF7r1DYgU8Fc5ue/w4cgTsmbn9Hh8CTvQpQ3HiFkpwZO/DkzNiBJ2d2hFcot3lUf4cwr1C+HTx24Mm5sQNPxowdOP8vFGPFIHAjosgEBB6JJTaIwGPxhAYROAIPFUUwgMCDROz6CNyOk56FwHUa5jYCR+DGKkHgRkSRCQg8EktsEIHH4gkNInAEHiqKYACBB4nY9RG4HSc9C4HrNMxtBI7AjVWCwI2IIhMQeCSW2CACj8UTGkTgCDxUFMEAAg8SsesjcDtOehYC12mY2wgcgRurBIEbEUUmIPBILLFBBB6LJzSIwBF4qCiCAQQeJGLXR+B2nPQsBK7TMLcROAI3VgkCNyKKTEDgkVhigwg8Fk9oEIEj8FBRBAMIPEjEro/A7TjpWQhcp2FuI3AEbqwSBG5EFJmAwCOxxAYReCye0CACR+ChoggGEHiQiF0fgdtx0rMQuE7D3EbgCNxYJQjciCgyAYFHYokNIvBYPKFBBI7AQ0URDCDwIBG7PgK346RnIXCdhrmNwBG4sUoQuBFRZAICj8QSG0TgsXhCgwgcgYeKIhhA4EEidn0EbsdJz0LgOg1zG4EjcGOVIHAjosgEBB6JJTaIwGPxhAYROAIPFUUwgMCDROz6CNyOk56FwHUa5jYCR+DGKkHgRkSRCQg8EktsEIHH4gkNInAEHiqKYACBB4nY9RG4HSc9C4HrNMxtBI7AjVWCwI2IIhMQeCSW2CACj8UTGkTgCDxUFMEAAg8SsesjcDtOehYC12mY2wgcgRurBIEbEUUmIPBILLFBBB6LJzSIwBF4qCiCAQQeJGLXR+B2nPQsBK7TMLcROAI3VgkCNyKKTEDgkVhigwg8Fk9oEIEj8FBRBAMIPEjEro/A7TjpWQhcp2FuI3AEbqwSBG5EFJmAwCOxxAYReCye0CACR+ChoggGEHiQiF0fgdtx0rMQuE7D3EbgCNxYJQjciCgyAYFHYokNIvBYPKFBBI7AQ0URDCDwIBG7PgK346RnIXCdhrmNwBG4sUoQuBFRZAICj8QSG0TgsXhCgwgcgYeKIhhA4EEidn0EbsdJz0LgOg1zG4EjcGOVIHAjosgEBB6JJTaIwGPxhAYROAIPFUUwgMCDROz6CNyOk56FwHUa5jYCR+DGKkHgRkSRCQg8EktsEIHH4gkNInAEHiqKYACBB4nY9RG4HSc9C4HrNMxtBI7AjVWCwI2IIhMQeCSW2CACj8UTGkTgCDxUFMEAAg8SsesjcDtOehYC12mY2wgcgRurBIEbEUUmIPBILLFBBB6LJzSIwBF4qCiCAQQeJGLXR+B2nPQsBK7TMLcROAI3VgkCNyKKTEDgkVhigwg8Fk9ocM4K/OzFM3Jv1Tzp+P1OOfDRLmeP/R/ukr2/bpC7l9wphWIhNMHTEfAFfvzUM/JQ00LZ/8cmZ3mpue78Q5NUvrhadnXslHw+L+r+0vjkxnKyY/c2qX1tk9O8FDO1TjYce0z2HW+XgaGB1JgpgR98vkNW7XtQ9v2uUfZ/6Gat7f9ol3ft23+xQTbXbZKRzEgaJSa+wLfVV8mWl9c67zNVa0t33icHX+yQ0eyolEqlELeKbC4r5y+ekx+v+L5sOPqYbDy2yt2jZ5WsP/SY3PPgT1IX+IlXj8lP1t0hT/Y4zOvYKnmyZ6U8uPM+ad63K1WBqx14fWutrGx7yN36mlwbap08UHOP7Htmj9xQAp9I56E3oAT+bIcsrFwg648+5s2Vq+tT1dnytgdkW+NWGc2MhkQ0HQEl8EKhILW7auThXffLk0dXOl9r8x//sXQ91ykZJfDxCIGrG/7L3/4se7vbZX/vPtl/wt3jwIkOOdDbIc++eCLyaTVdRaKehH/s/8NNZg7z8ua6d5909OyVt9/9pcdMLYI0PsViUS68e0EO9u53usYUs87efbLv6F55972LojZAaTHL5jLym9/9WvYd2Sudx592nptam30XzshYfiyNEvPmQa3NCxffkv3H9jnvM1Vre7vb5L0//EbyhXzkRqFC/WRWP2/V0947hq7LgLPHgNwYviEjo8OpLSq1WNWRyylmA95PaHd5qbke8HaR2WwmNWZqtao6y2QzMjh8w+H6mlwbaq0MDXjyTuuVk89MrU21y3d/bV731qbafUe9Cpguo6u1qR6qN+tMrU+3fabmXT3I1e47aqNQocCpAVWI5XJE3eh0FYj/PTDzSdify5HZhKTzi8WnWm7M1OumtNfnXGLmCdwvFs4QgAAEIOAOAQTuzlxxpRCAAASmEEDgU3DQgQAEIOAOAQTuzlxxpRCAAASmEEDgU3DQgQAEIOAOAQTuzlxxpRCAAASmEEDgU3DQgQAEIOAOAQTuzlxxpRCAAASmEEDgU3DQgQAEIOAOAQTuzlxxpRCAAASmEEDgU3DQgQAEIOAOAQTuzlxxpRCAAASmEEDgU3DQgQAEIOAOAQTuzlxxpRCAAASmEEDgU3DQgQAEIOAOAQTuzlxxpRCAAASmEEDgU3DQgQAEIOAOAQTuzlxxpRCAAASmEEDgU3DQgQAEIOAOAQTuzlxxpRCAAASmEEDgU3DQgQAEIOAOgQr1l+jH8mNyY+iGDKpj2OVjUIaGB2U0M5raX75Wf4Vc/dXr3Fhukteg88wGhwclm8umxkwtB1VnmWxGhoaHHOflr5ObzNR98YHAP4pARaFQkI+vXZbatu3ScrhJWo64fOyStiO7pfNwh5RKpVSYKnmr737v97+W2vbt0nJkl/PMmvbXyxt9r3v3pe4vjU+xWJTXz/5CWg/vdpxXkzQfbpLGzjo5+/aZ1B98acwF31k+BCrUTvL8xXNyx8rvy+bnHpetL65z93hhnVT2rpUFP7tLlDDS+KgdV6FYkN5XeuSnG+6Urc87zOvFdbLl+XXySOti2bV3p6iHeVo7ynx+TGqbd8jajkfcra/JtbH5ubXyYONC2Xu0TW4M30j1l0saNcx3lg+BCvWz9uzFM7Jw+91y4E+75dDlFneP/hbpeH+n3L30Tk+yaUyTEly+kJfjp56Rh5sXSdelZnd5XW6Rg39qli0vPy67O3ZKPp9PTeBqo7Bj9zZpeH2L07zU+jjw0W556sQq2dfbLgND11Njlkb98p3lRcAT+Ll3++T+mvnS1d8sh6+2OXt0f9wqnR80yfwZEHjvaz2yrGWxdF9udZaXmutD/S1S9eo62d3ZlK7A8znZ0VwtjW9sdZqXYqbWyaZnV8u+3j0yMDSAwMvLiU7dzU2B/6pPFtUu8HZGR661i6vH4SttkwKfl/oOXAlcvXro/rjNWV5qntVDr+rUOmlOWeBj+ZzUKIGf3uo0L8VM7cIrT66RjhMI3CnbleHFIvCEk+q/QkHgycAh8GS8yIaADQEEbkNJy0HgGowETQSeABapELAkgMAtQflpCNwnkeyMwJPxIhsCNgQQuA0lLQeBazASNBF4AlikQsCSAAK3BOWnIXCfRLIzAk/Gi2wI2BBA4DaUtBwErsFI0ETgCWCRCgFLAgjcEpSfhsB9EsnOCDwZL7IhYEMAgdtQ0nIQuAYjQROBJ4BFKgQsCSBwS1B+GgL3SSQ7I/BkvMiGgA0BBG5DSctB4BqMBE0EngAWqRCwJIDALUH5aQjcJ5HsjMCT8SIbAjYEELgNJS0HgWswEjQReAJYpELAkgACtwTlpyFwn0SyMwJPxotsCNgQQOA2lLQcBK7BSNBE4AlgkQoBSwII3BKUn4bAfRLJzgg8GS+yIWBDAIHbUNJyELgGI0ETgSeARSoELAkgcEtQfhoC90kkOyPwZLzIhoANAQRuQ0nLQeAajARNBJ4AFqkQsCSAwC1B+WkI3CeR7IzAk/EiGwI2BBC4DSUtB4FrMBI0EXgCWKRCwJIAArcE5achcJ9EsjMCT8aLbAjYEEDgNpS0HASuwUjQROAJYJEKAUsCCNwSlJ+GwH0Syc4IPBkvsiFgQwCB21DSchC4BiNBE4EngEUqBCwJIHBLUH4aAvdJJDsj8GS8yIaADQEEbkNJy0HgGowETQSeABapELAkgMAtQflpCNwnkeyMwJPxIhsCNgQQuA0lLQeBazASNBF4AlikQsCSAAK3BOWnIXCfRLIzAk/Gi2wI2BBA4DaUtBwErsFI0ETgCWCRCgFLAgjcEpSfhsB9EsnOCDwZL7IhYEMAgdtQ0nIQuAYjQROBJ4BFKgQsCSBwS1B+GgL3SSQ7I/BkvMiGgA0BBG5DSctB4BqMBE0EngAWqRCwJIDALUH5aQjcJ5HsjMCT8SIbAjYEELgNJS0HgWswEjQReAJYpELAkgACtwTlpyFwn0SyMwJPxotsCNgQQOA2lLQcBK7BSNBE4AlgkQoBSwII3BKUn4bAfRLJzgg8GS+yIWBDAIHbUNJyELgGI0ETgSeARSoELAkgcEtQfhoC90kkOyPwZLzIhoANAQRuQ0nLQeAajARNBJ4AFqkQsCSAwC1B+WkI3CeR7IzAk/EiGwI2BBC4DSUtB4FrMBI0EXgCWKRCwJLANwKvWSCHLrfIkWvtzh6Hr7RJ5wdNMn/pPCkUC5YIkqWFBd7qLC81192XW6Xq1Dpp7mySfD4v6v7S+OTyOalprpbG01ud5qWYdfW3SOXJNdJxYo8MDA2kxiyNeeA7y4vATYG/2ycLd8yXg5eapftKq7vH5Vbp+K0S+J0zIvBlLYvkUH+Lu7yutHoy2vrK47J7BgS+o7laGt7Y4jQvtT7UOtn07GrZ14vAy0uH7t1NRTaXlbPv9Mm/P/ovsuH4Y/LUs6ucPTaeWCVPHF4hdy1KX+A9Lx2Vu9b+UDb2rnSWl5rrJ3tXypKme2Vne0OqO/Cx/Jjs2LVNVrQtdZqXYqbWyeKan0r74ZabO/CJdH61uKcTrnimCVSon80ff3JZatu2S0NHrezsrHP76KiXrmMHpVgqpsJyfGJcisWifPDh+7KjpVoaHefV2FEndXt3yOnzr3v3NTExkQq3QiEvZy68Kbv373S7vjrrvHVSv2eHnL94VjLZjKTFLJWJ4EvLikBFqVSU3FhOhkYGJ48hGRpx9xgeHRb1qyKtd7lqsarvVv/GsMOc9DlW96FqQN1XWjIqlUqSzWZkZHTY6fq6yW1QhkdvMlMbhbSYlZVpuJlUCFSob/WlpHaX5XDMxILymJUJLzXnM8VsAmapLGS+dG4S8AQ+N2+du4YABCDgNgEE7vb8cfUQgMAcJoDA5/Dkc+sQgIDbBBC42/PH1UMAAnOYAAKfw5PPrUMAAm4TQOBuzx9XDwEIzGECCHwOTz63DgEIuE0Agbs9f1w9BCAwhwkg8Dk8+dw6BCDgNgEE7vb8cfUQgMAcJoDA5/Dkc+sQgIDbBBC42/PH1UMAAnOYAAKfw5PPrUMAAm4T+H/MPTGz4tLNVwAAAABJRU5ErkJggg==[/img][br][br]Explain why your diagram and Priya’s diagram represent the same number.
Here is the diagram that Han drew to represent 0.25. Draw a different diagram that represents 0.25 in the applet below. [br][br][img]data:image/png;base64,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[/img][br][br]Explain why your diagram and Han’s diagram represent the same number.
Draw or describe two different diagrams that represent 0.1.
Draw or describe two different diagrams that represent 0.02.
Draw or describe two different diagrams that represent 0.43.
Use diagrams of base-ten units to represent 0.03 + 0.05 and find the resulting value. Think about how you could use as few units as possible to represent each number.
Use diagrams of base-ten units to represent 0.06 + 0.07 and find the resulting value. Think about how you could use as few units as possible to represent each number.
Use diagrams of base-ten units to represent 0.4 + 0.7 and find the resulting value. Think about how you could use as few units as possible to represent each number.
Here are two ways to calculate the value of 0.26 + 0.07. In the diagram, each rectangle represents 0.1 and each square represents 0.01.
[img]data:image/png;base64,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[/img][br]Use what you know about base-ten units and addition of base-ten numbers to explain why ten squares can be “bundled” into a rectangle.
Use what you know about base-ten units and addition of base-ten numbers to explain how this “bundling” is reflected in the computation.
Find the value of [math]0.38+0.69[/math] by drawing a diagram in the applet below. Can you find the sum without bundling? Would it be useful to bundle some pieces? Explain your reasoning.
Calculate [math]0.38+0.69[/math]. Check your calculation against your diagram in the previous question.
Find each sum.
The larger square represents 1, the rectangle represents 0.1, and the smaller square represents 0.01.[br][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfgAAACkCAYAAAB7EzxHAAAdg0lEQVR4Ae2da5BU5Z3G830rm2yFGEZkGJA7AwzDXGHoud+cGwPMpQcBRQUUZsCtym3VbLKWMVy9oeAliaXGTaLJBqO7KaOiCAy7uSBM/JLsVir7IZv9kq1yFVxJfLZOjw0Ee/r8T5/untOnf1a9NczpPue85/k/7/M773R73k+I/1AABVAABVAABUKnwCdCd0VcEAqgAAqgAAqggAA8JkABFEABFECBECowIeB/eOQHOvTYI3r0iUN69InDNDRI2QOOj3bv+YYePnRQh9ExZR0Zh04OHYrl0v0P3qcHDt6vw497y6dHHn1Yd99ztw497mSbt1x76OEHdeC+/XKO4WXfw08c0sFDD2nv/r0fZar9vM717TuwTw8cfECHPF5rXJt//4/f6MMPPwwhvi5d0vvvv69Xjr6iw48dkqO3p/o8fkj37r5XB2P5ZN/X0fehRx7S/vv2xX7G9bae28nFH7/4gi5cuHDpQtL8rwkBv3qoS0va56luW4XqtpXT0CBFD1RoxcYSFS65WstWL1DtVrzEeErdA45/Vt5Qqlll07W4fa4it5SZfensW9ZXrM9O/4xWbFzmwYsVqru1Qks7Fuja8kJVb1xmP+e2ckW2lGlRy2zNWDot1ncv9V91S5lmlk5XSef82HHs+1aoekOJFq6aoxd/8mP9+c9/TjM6gnW48++f1/YvbtPiFodZ3vwV2VKuwsXTVBldqtot9n2dupb2LtKMkmlavrbYU32c81RFS9Q/1Kfz589nTMwJAb9uS49av1al20+t165TQzQ0SNkDN/+4V/OvK9Lqg3UaORHVrlH8xJhKzQOOf7b+ZK2WDsxR69ertOPYgNmXO0eHNPDtZk2Z+2nd/GKvdp609+H2f1uvrj21Kh1aIMfP1vo55xx+c1CNXynTgq5Z2vIva837OucYPjagJWvmqHtPbew4XsbOjT/qUuXGYr30yguhB/y58+9p5Gu3quGLZZ70dTQeeXNQ81tmatN3uzRyPGre36nr2kONmt89Q/1PNI/Xx8gJ5zwbn+1S38a1McBn6i8sSQHf8veV2jka1c6TNDRI3QM3HenR/PYi9TwY0fDxQfzEeErZA06o3vJSr5b0z1brPZXa/nq/+VjOzUH/N5s0Zc6ndNMLPRo5YfeiA4LOb0S0bHC+Nh/p8XTOHW/0q+Gu5VrQOTPWdy9Z4lzf4t456tpdG7uZ8bLvph90qmJDsV7MA8C/d/49DX91m+q/UGauTVzLHW8MaF5zkTY826HhNwfM+zv7rXm4XvO7CtX3WKOc3+PHdPs5fGxQG77TEQDAE0bmorkVNV9f/wvAOwPoROo3C/mqIdc97pnLAd/iGfCDlwB/xCPgR8cBX+IZ8IPaHgd8R6qAnz0OeA8AcfwC4G058xeAP2aHdAzwB1MF/IA2PAPggWsIbrAAvC1ogLi7TgDeXaO4jwC8TSsAHwLIxE3PT5vp06kTgM++5umsX5COBeDtXgLwNq0APIDnLwk+PADgbUETJJAGtS8A3u4lAG/TCsD7CPegBgX9spk/HToB+OxpnY56BfkYAN7uJQBv0wrAA3hm8D48AOBtQRNksAalbwDe7iUAb9MKwPsI96AEA/2wmT0TOgH4ydM+E/WczGMCeLuXALxNKwAP4JnB+/AAgLcFzWSCM1fODeDtXgLwNq0AvI9wz5XgoJ+2wZCKTgA+c9qmUo9c3gfA270E4G1aAXgAzwzehwcAvC1ochm82eo7gLd76SLgf3pEf/rThdiCM84jUb20jD0kPc0HTtuT7HjQjd1g2Rr0nCfYNQHwwa5PLo0fAG/3kgP48usX6Qf//JzeefcdvXvuXXN779y7OnfuvZx5hj2AT3zH5P4seh8zt1wKDvpqDw6vWgH4zGnrtRa5/n4Ab/fS+mfbNbvxGkW6V6h/yxr1b12jAVNbq8Gtfdr1+Z363X/+LjE5ArYVwCcuCIDnBibjHz8AeHso5zqAM91/AG/30tDTrZoRmarKrQvVua9GXfuN7UCNevbWqqm7XmNvjyUmR8C2AvjEBQHwAB7A44GMeyBd4AfwHgD/TJtm1hWoa28ktuqe82UyZ3ldU3tlUG19zQA+STY4eq5hsRm7IdMVAhwnWJozgw9WPXJ5fAB4u5eGPgJ8975ajXhZpnk0qpGjQ2rvB/DJxgqAT3L3k0w4XrMP4lzQCsCHq56T6TkAb/dSyoA/6QA+CuBd+AXgXQSazKDg3Pag8KsVgM+e1n5rFfT9AbzdSwDeppUD6nnNRdrwbIeG+d/kbKIFPSjoX/bqCOCzp3XYfQ3g7V4C8DatADwz8Zz5ElIQAx7A24ImiLULWp8AvN1LAN6mFYAH8ADehwcAvC1oggbTIPYHwNu9BOBtWgF4H+EexJCgTzbjp0snAJ9dvdNVtyAeB8DbvQTgbVoBeADPDN6HBwC8LWiCCNSg9QnA270E4G1aAXgf4R60gKA/NtOnUycAn33N01m/IB0LwNu9BOBtWgF4AM8M3ocHALwtaIIE0qD2BcDbvQTgbVoBeB/hHtSgoF8286dDJwCfPa3TUa8gHwPA270UB7zzqFrn8bSOdq7t+GDsqXfDrw6qjSfZJZ3YOTcGPKqWm4OkJglymKarbwDeHsrp0jysxwHwdi8NPd2motoCNd1RoY3f79DG521t0/MduuG7XWpZ06CzvzqbeBWTgG1lsZnEBWGxGW5AMn4DAuDtoRxWMKfrugC80UujUQ0+2aLplVdpbut0ld24QOWbnbbQvd20UBWbilXbukqnz5xOTI6AbQXwiQsC4AE8gMcDGfcAgF+uBR0zdctLvZ603v56vxb3zlbX7lo5fxI26zgaVfSpVs2omapVwyVa90ij+g41qu+wW2tS3+Em9T/Uoqaeep0dO5OYHAHbCuATFwTAE+720EhRK2bwxllXivqaQz8Ex2cGb/fSxc/g90RiNwfOc9aH37S0QQ07y8XyGXzSbOQz+BAESj6FZ6auFcDbQzlTNQjLcQG83UtxwHteLpbV5JKCPT6WADyANxklbpiw/gTw9lAOqwfSdV0A3u4lAG/TygE1q8kBa2CdogcAvC1o0gXBMB8HwNu9BOBtWgH4FIM9zEHDtdkGj6MTgLdrha+SawXgk+tzuX8AvE0rAA/gmb378ACAtwXN5eHMvxNrBuAT65LILwDephWA9xHuiYzHNpvxwqITgM+vemfStwDe7iUAb9MKwAN4ZvA+PADgbUGTSTCG5dgA3u4lAG/TCsD7CPewBAvXYRssiXQC8Klrl0jPfN4G4O1eAvA2rQA8gGcG78MDAN4WNPkMbuu1A3i7lwC8TSsA7yPcrQOX99nMmIs6Afjw1jbbfgTwdi8BeJtWAB7AM4P34QEAbwuabMMyF88H4O1eugT4SGwJ2JETUe20NOdJdq9F1c6japPmvnNjwHKxPsCQiwFEnz8eQAD+45rgk9Q0AfB23YaebtWMyFQ13VGpTd/r1Kbvd2nTc+7thue6dOP3etS8ukFnx1gudqKxCuCBe9I7wImME7btAN4eymGrfbqvB8DbvTT4rRZdXTpFfzPzk7pq4ac9tauLp6iqplI//+XPEy9TFrCtrCaXuCCsJsdNSMZvQgC8PZTTDcSwHQ/A273k/Im+KDJVNbuWat2jDVr3WIPWPe7e+h53lpZtUvPqeo29PZaYHAHbCuATFwTAA3gAjwcy7oF03WgAeG+An1lXoO59kdgysSPHBzVywthei7JcrEsu8Cd6F4HSNeg5jn3QT4ZWzOCDXZ/J8ESq5wTwdi9d+pJdbexLdl40HznKl+zc9ALwAD5nZkZuZvbzOoC3h7IfnfNhXwBv9xKAt2nlgJrlYoE1sE7RAwDeFjT5AGi/1wjg7V4C8DatAHyKwe53MLO/zaBB1wnAh6OOQfAZgLd7CcDbtALwAJ7Zuw8PAHhb0AQBoEHvA4C3ewnA27QC8D7CPeiBQf9sg8CPTgA+8xr7qU8u7Qvg7V4C8DatADyAZwbvwwMA3hY0uQTayeorgLd7CcDbtALwPsJ9soKA89rMnQ2dAHxwapGNemfyHADe7iUAb9MKwAN4ZvA+PADgbUGTSTCG5dgA3u4lAG/TCsD7CPewBAvXYRssiXQC8Klrl0jPfN4G4O1eShnwo1HxoBt3nZ0bA1aT4+Yg72f/AN49LPIZ2l6uHcDbvRQHfM+B2tgjamM6j0a109BGXh9iuVgXdgF4F4G8DGzeax/YQdMKwOdu7YLmJQBv91LUWS62ZqoqtxWr60CNuu9bZW49++rU2FWns2NnEq9iErCtLDaTuCAsNsNNSMb/wgDg7aEcNKAGrT8A3uil0aic5WILSqboU9P/Sp+59q81xUObOm+KqmuqdPqtXyYmR8C2AvjEBQHwAB7A44GMeyBdNwoA3gj4k1E5f6Ivqi1Qx7012vbyOt36U2N7ZZ1u+8mAWtc1sVxskmzgT/RJxEnXgOc49gE/WVoxgw9+jSbLG17PC+DtXop/Bt+93+NqcrEv2fEZvJs3ATyAz5mZkZuZ/bwO4O2h7EfnfNgXwNu9dBHw+1IBPMvFuo0nAA/gAfzJqAC8PZTdQiXfXwfwdi+lDPiT/G9ylnEG4AE8gAfweCCNOQDgAXyir5PxJbtEqkh8yS6N4WO568vH9zCDt4dyPvrDyzUDeLuXmMHbtHJm4vOai7Th2Q4NHxsw35AzgweeZrN4Cblcey+AtwVNrtV1MvoL4O1eAvA2rQA8oAbUPjwA4G1BMxnAzLVzAni7lwC8TSsA7yPccy1A6K9tUHjRCcCnX1Mv+ofpvQDe7iUAb9MKwAN4ZvA+PADgbUETJhBn6loAvN1LAN6mFYD3Ee6ZGugc12beIOgE4HOnVkHwS7I+AHi7lwC8TSsAD+CZwfvwAIC3BU0ysPHauIYA3u6lGODrC9TNg26S5jeA9xHuBJN9QIZVKwCPB9LlbQBv91Ic8M5ysbtGo9p1aki3/6ut7XpjvdoHmnkWfRL2OTcGrAefRKB0DXqOYx/0k6EVgA92fSbDE6meE8AbvTQaVfSpVhWu/Jyqbi5W956IuvdGYrN5Z0afrPU4r399fLnYt86eTvwElYBt5UE3iQvCg264AUn656tUg/jy/QC8MZTxoqsXAbzRSx8Bfnr1VZrdco1KN861t03zVHb9QtW21gjAT6w3M3gCyzWwLgdhWP8N4CcOibDWPFPXBeDtXnL+RF9UV6Dmr1Tqhn/q0o0/MrYjXdr8fI9a1zbyJ/okDAPwScTJVABwXHsAZEsrAB+8mmSr9uk+D4C3e+nSt+gjGjk+qJETUe10ax9l9shrrCbn5l0AD+CZwbPYDB5IYw4A+FQA73G5WFaTM41ZAJ/Gge12N8Xr9oGfba2YwQe3Ntn2gt/zAXi7ly7N4AF8Mt85oGaxGWBtuqtLZqR8fQ3A20M5Xz1ivW4Ab/cSgLdpBeCBO3D34QEAbwsaK+Ty+X0A3u4lAG/TCsD7CPd8DiOufXyAAXhb0OAXd50AvLtGcR8BeJtWAB7AM4P34QEAbwuaeDDzc2K9APzE2lzpGwBv0wrA+wj3K03H7zbThUknAJ9/Nc+UfwG83UsA3qYVgAfwzOB9eADA24ImU1AM03EBvN1LAN6mFYD3Ee5hCheuxTZgrtQJwKem25U68ntUAN7uJQBv0wrAA3hm8D48AOBtQQPA3XUC8O4axX3kD/BDau9nNbm4lol+OjcGrCbnAwyJRGWbfYAHRSsAn3s1C4p3ruwHgLd7yQG88yz6zt2rdNurfbrtNUM72qftTnt5QK19TTyLPgm/AHwSca4cuPxuH7i5phWAD29ts+1FAG/3Umy52BWf04LVM1S9Y5G9DS/Syu1LVNe6Sm+dfSvxOqQB28pysYkLwnKx3IRk/OMHAG8P5WwDM9fOB+DtXoo+2aLplVdpbmuhKm5cqIrNi1RpbRuLVdcW0ZmxM4nJEbCtAD5xQQA8gAfweCDjHkjXjQSAtwM+9hl8fYF6DtTG6rvrVFS7Tg25tttPDWnnG0NqH+Az+GS+5U/0BGfOBGcyI/t9jRm8PZT9ah32/QG83Uspf8luNKqRoywX6zaWADyAB/AsF4sH0pgDAD4LgGe5WNOYBfBpHNhud1O8bh/42daKGXxwa5NtL/g9H4C3eynlGTyAB/B+Byr72wdqrmsF4POn1pn2KoC3ewnA27RyZuKsB89s3HRXl+mAy8XjA3hb0ORibbPdZwBv9xKAt2kF4IE7cPfhAQBvC5pswzIXzwfg7V4C8DatALyPcM/FEKHPtoFh1QnAp1dPq+5hfB+At3sJwNu0AvAAnhm8Dw8AeFvQhBHI6b4mAG/3EoC3aQXgfYR7ugc4x7OZNkg6Afjcq1mQ/HN5XwC83UsA3qYVgAfwzOB9eADA24LmcpDx78SaAfjEuiTyC4C3aQXgfYR7IuOxzWa8sOgE4POr3pn0LYC3e8kf4Fku1s3Hzo0By8Vyc5D3s38Abw9lt1DJ99cBvN1LDuAvXy52+9F+mdvLA2pjudik2Q3ggXtSg+RLWAN4eyjniydSvU4Ab/TSaFQD32rR1aWf1dTiz2hGdYGKPLRrV05XdaRKP/vFzxIvUxawrawml7ggrCbHTUjGb0IAvDGU8aKrFwG83UvRp1tVuPJzWjo0W/VfLlXD3y03t6YvV6i+fZXOsB78hJ5kBk9gTWiOVGcwubgfgLeHci7WN5t9BvB2L8U/g3eWix05MWjOol2jUe08ymfwbr4G8ADePKjczJTLrwN4eyjncp2z0XcAb/dSHPDd+2s1ctwO+J2x5WIBvJufATyAB/AsF4sH0pgDAD4FwO/zCHhWkzONWQCfxoHtdjfF6/aBn22tmMEHtzbZ9oLf8wF4u5cuzuABfFJgO6BmNTlgndQkfoMrzPsDeHsoh9kH6bg2AG/3EoC3aQXggTtw9+EBAG8LmnQAMOzHAPB2LwF4m1YA3ke4hz1wuD73QQTg3TXCRzaNALxNJ8dPAN6mFYAH8MzgfXgAwNuCBsi76wTg3TWK+wjA27QC8D7CPW42ftrMFkadAHz+1j7dfgbwdi8BeJtWAB7AM4P34QEAbwuadMMwjMcD8HYvAXibVgDeR7iHMWS4JtvAiesE4L3pFdeNnx/XDcB/XJOJfALgbVoBeADPDN6HBwC8LWgmCmq2X9IPwF/Sws0XFwG/N6LhYwOxp9k5T7SztOFXo2rvb9bY22OJVzEJ2FYWm0lcEBab8QEutwHG6+NhBODtoYxnkmsF4JPrc7l/hp5uU1FtgZrurNDG73do03Md2vS8e7vBec8/dqllTaPO/upsYnIEbCuAT1wQAA/gM/7XCQBvD+XLA5p/f1w3AP9xTSbySfTJVl1TcZWKIgUqXjtLxetsbfG6WVq6dq4iTTU6feZ0YnIEbCuAT1wQAA/gATweyLgHJoKQ1+0A3gPgnxpfLrbylmJ17l6lrj3GtneVenbXqaGzTmfGziQmR8C2AvjEBQHwhHvGw50ZvD2UvQIv394P4O1ecj6DL6oriMF9+9F+bX+9Xzss7Y1+7Xh5QG19fAafbHw5X85bc7Be87sK1fdYo5zfk73/8tec70RseKZDfRvX6vz58/rwww8TE9rnVgAP4M2mvNygXv4N4O2h7EXXfHwvgLd76eKX7FhsJmnG8S16IJjUIPkYtF6uGcDbQ9mLrvn4XgBv9xKAt2kF4AE8gPfhAQBvC5p8BLbXawbwdi8BeJtWAN5HuHsdwLzfZspc0gnAh6+mk+U/AG/3EoC3aQXgATwzeB8eAPC2oJksaObSeQG83UsA3qYVgPcR7rkUHvTVNiC86gTgM6Or1zqE4f0A3u4lAG/TCsADeGbwPjwA4G1BEwYAZ/oaALzdSwDephWA9xHumR7wHN9m4snUCcAHv0aT6Q8v5wbwdi8BeJtWAB7AM4P34QEAbwsaL6DL1/cCeLuXALxNKwDvI9zzNYi47kuDC8Bf0gJf+NMCwNv1A/A2rQA8gGcG78MDAN4WNMDfXScA765R3EdxwHftiWjH6wOxJWOdR6Ra2o5XBnlUrUvmOTcGfh9Vu/b6Xr3zv+/ogw/+Tx988IG5XbhwQU5z+49H1boUMT5Y+GkPliu1AvCpa3ellvn+O4C3e2no6VbNiExVy1ertflHPdr8gq3d9EKPbv5hb2y52DGWi51wcucX8Nc/06GOvuv029/9Vr//r997an/47z/oj//zRze+C8AD+AkNnC6YAHh7KKdL87AeB8AbvTQa1eC3WzSt7LO6etkUXdtwzXhrnK5rXdrsxumaW1+omvoV+sXpn7tCJAhvyMXV5IaebNOMpdMUGahWXXSl6ofsrbq1XF+5905X6QE8gAfweCDjHkjXDQeANwL+ZFRDz4zP4FfdXqK+JxrV/02nNZnawKPNalpdr7PM4CccG35n8ENPtWluU6HWf6dNG77brg3fs7brVLl5kbbfsQXApytYOI49WK7Uihl86tpdqWW+/w7g7V66+Bn83khsKdPYZ+9vDmjY0l4dVFs/y8UmG2/+Ad+uRZ0ztf1on60mF+s2qNpdy7Tjrq0APlmBeM0eFn60AvDZ0dlPjXJlXwBv91Ic8N0sFzvhLNzxvQPqec1F2vBsR+wLiNaxkBbAd83ytI58vG91t5dq+K5tAD4uCD/twZBurQD85Gmf7lpO9vEAvN1LAN6mFYDnM8qkd4CTHXpBPz+AtwVN0OsYhP4BeLuXALxNKwAP4AG8Dw8AeFvQBAGgQe8DgLd7CcDbtALwPsI96IFB/2yDwI9OAD7zGvupTy7tC+DtXgLwNq0APIBnBu/DAwDeFjS5BNrJ6iuAt3sJwNu0AvA+wn2ygoDz2sydDZ0AfHBqkY16Z/IcAN7uJQBv0wrAA3hm8D48AOBtQZNJMIbl2ADe7iUAb9MKwPsI97AEC9dhGyyJdALwqWuXSM983gbg7V4C8DatADyAZwbvwwMA3hY0+Qxu67VPGuBPDanzGxGVDM7X5iM95jwYOTGoHW/0q+Gu5VrQOVO3vNRr3tfRZPvr/VrcO1tdu2s9PxAFwNvGnS/AP1yv+V2F6nus0VN9nKcKDj3VrkU86MZWJGtA8L7s6xkH/OoHI7FHMjqhRx2yX4cwaO48ZtWB5JL+2Wq5pzIGQOt1jRwfjD2HfcqcT8nxpPO7dd9do+OAXxZNEfB3LteCjhQAfzQO+PHHzY6csPsmBvj6AnXvr41dq5d9R16Lqj3HHlU78tVtavhCmbmmTu0dTS4BvtPjk+z6tcYBfGcc8P3mc+84NqD1DuA7x59k56U2Tr99P8mud1OXym9YpNUP1NHQwJcH2u6u1ozKAq3YsUQ999Vq9f14inGVmgcc/1z39ZWaVTtNZTctUPf+iNmbPffXqu7zy/XpaZ9U290r5PxurUPvg3Wqunmx5jQUqu0fqs37OefoPhDRsuvnaEZ1Qazv1nM673Oub1bNtNi5uw94GzsNXy7T1aVTtOLWpeq9v15rHmgwt7UHGtXS06ixt8dcH4cahDecO/+ett+xVcujC8y1idehZ3+tCpdPVdOdleP5ZMx7p66rRkpUWDVVkb8tjdU5fky3n04tG79UrqKqq7X6QJ25LvEalvYv0G1f8rHYzJbhm1XVVKGVnZU0NPDlgaqWMi2tWKyKxuVa0YGfGFOpe8DxT1VrmZatWKqy+mVacZ23jKpoKFXxsoWqbiv36OkqldeVqqRqiapave3r9LGsdpmWVC72vG91e7lKqpeMjx2P11rZvFzFyxepvL5UKzsqVWNtnZWq7Vqp9RuH9Ovf/DoI/Hbtw7lz53T3nq+pOhVmdVRoaeViVTSVeconp67lDaVaGqtPqScvOj6ubFqukqrF3mrzUQ2rGyt01z13uOoy4XKxrnvyBhRAARRAARRAgcAqAOADWxo6hgIogAIogAKpKwDgU9eOPVEABVAABVAgsAoA+MCWho6hAAqgAAqgQOoKAPjUtWNPFEABFEABFAisAgA+sKWhYyiAAiiAAiiQugIAPnXt2BMFUAAFUAAFAqsAgA9saegYCqAACqAACqSuAIBPXTv2RAEUQAEUQIHAKgDgA1saOoYCKIACKIACqSsA4FPXjj1RAAVQAAVQILAK/D/a3gmNrM6/bAAAAABJRU5ErkJggg==[/img]
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dIyuTVU45UoIxXtV6IZn18JshZ3/lef6icieXbOaDN8OrILio0+caS4IBe/fTsCns6aY6tsBU5wa/sZcgss37YZezcS7UUVzo58gtpj1e6bz4f3jF9T4h5iWNdAiPhsRsQk7v54+5XbXFO18uUKGVLjHuLroV3gKNH4b2GxOHD3Ccbe26kollm6iaxqfaz1f1S0rbXljCi3ZsnfFP2SP6GjO3p+vgAFxQb6kK6Ul7QwH3sWToSfm6NmxMVzhGOLUcjOt3zRTnr8AANa+ULI0witm299zPrzaKXaGfpVjYSHkegTIoSAozETufuGYN6f+wxNwGqvk5UWIurwn/D10mzUIm9u9k5umLbqDLIL6Lrt2mhYKtq1QdnMeZDNNSsWzYOndnMN38EN7T+ai4Ii40W7rCgfhxdPhr+bZs23jRWJdnpKAsYM6QOJSLMhRuLmh6Fz/ja6dchhEo8izqIBv2JLvH9wK2zcd9notKwtglpVjvLCFLQI9NebmSR2zhjz1XqkZxVaW3WssrxUtK2y2YwrtLS4CAd++wX+Hu7M6JgtdoZf+GSNecS4pEBG2gcWPSHaLT9DjhWYR7Iz0zFt0uewt9NMyLLFbgh7ZwaIO3FjLPvKsnxcPbAS/EorUUKa9cKhV9w1q6arqAG1HIODAyGx0azvFkuc8OmXfyIt4/U4TMPIW6baL6eiXe1ILS/BcrkUCVd2o36wn8akYcuDo3Nz3EgkE5HGlZfYtNfMGAEvF41N20bgBMeOY61CtEtzs3B0yTS4OmjLbsuDf9AbiM5XGnQ+pI5UUUYsNs56T8NSu3ywffhQRCQV6S55hT9VgLIEA4IDIdbWnYj2qAlrqWjXUqtT0a4l0ObMhvhClhdlol2jBszokJwiLpI4Y+Y/F5BppMOf/JwMTHmnCZzEGhedYid39B33PQpNsI/XNhOlXIr0u2cR4O6q9T9iC3evIPx9NBZFpQqDi5Nw7wqGd2laIdocRwwZNQf5r4GbW5VCiqK4s2jg76334SKxd8H4/21FhhWcSG9wI1vwhVS0LbhxqrVoahV+HjVIvxWdwxOgee9Pcf1+AhQG+tZUykuReO8cmnpLwNdOwLl5B2HByl0oMfGE72qt44sSU6tQVpyLYR1CYS/ULFkU27vi/c+XIzWrwCATCRGtY+tXoJ6ns160HT3rYdZv+6zIedaLQD3799KCbBxe+Q28XLUT0TY2cHR2x5KtN5FXZNop78/Ojf7yNAJUtJ9G5RX9W+T5g+gYFqI1kbBAvP1NX74DSZmFLxYstRK5abH467sPwONqfEjb2LIRHNYOey88hsyEHZEqlQrFRYV4HP0QN25cx+3bkUhOSYVMUW70UkRDm6xcIce25TMQ6OXCcGBzBLB37YCj1+6hyIAHT2bCA3w9sj9EWtMAWT0R1nYATt0wzcWroeV+uevUIBOIckU5lCpjD1eryFkhkyLuXgSGdA7Uu6Rls3nwCWiIiMR8lJWbnnZFLvTbiwhQ0X4RoVfo99KceEwaNRBcNks/SnQL6IxF644zgvWsI6OIeaWsOA/H/12FRr4uet8jbL4Dur07AVKF+sWi/xSOZVIpDu/fib49OsPVxQlBwSH4aNTnuB2badJD4ClZ/OdPpC5Jty6jV/uWYLMqOHT9YDwu3YmForz8KXVRQ6VSQiYtxl8zxyLUQ7tyhvjkYHMxet4aJGZb7nI3UmdFUSYu3XqE9Ow8lEqlkMsVIA9NQ1zGqFUqKOQypERHYcH4ofq+Qx5YEnsPDPhoPsrkhpuX/tMo9A9GEaCibRQu675YrSzH+Z2/o0OI9gQbckArhw/P0NaYvvQvxKXnP3U7cmFWAtYtn4PQQO8qgh8Y1h6bj1w36Mb/Lzk1ctJTEN7IA/ZCHiOgHA4Hjk4u+HDMEiSmZv83SjX9RSmXYfk3k+HrUmHi4AvFCP9wPI5ejoLsiRGjqlyBnNQ4rJ43AXV9XfUMiO9xn4Y9cfhcJBRG7iytpqoYlIxKUYbC2Mto3jQMgS0748sZP2D34ZOIT85AmfxpD6mKZMlOyKKcdBzfuRFDwzvDTlzhf4R5y2jSBWcuPH6Ko7GKNOi36iVARbt6eVp8agXZadj1x08IcHPSjzS5fCFcPX3R8Y0emDJrCTb9uxP79u3Dzq3rsXj2WPTt1QUBvp4Q8DV2YHKzOjp7YOrsn5GRY+LaXJUCqTHX4SURgKM9/oukS2ztYT0/xK2HiTXKMiX2IaaPGwIHkdbUw2wScUWDFu3Q75MvsGLteuzYvRubN/6N76ZNQrfOHeDn7gQBT3M9i8OFxMUbi9YfQ0auZa8aIWeEFsVfQ1CAL7gCIRxd3RFSvyE6dOqCvuFvYdLUmVixei22bd+FAwcP4tChA9i5YxtW//YTJo4cjt7du6JBcAAc7MRVRtkhDRpjxca9KCySm/jgrtEmfmUTp6L9yjbtMyqmViEzNRE/zfsfgr09IeBVCDE55MDJ1QMBQcGoW68ugoP84eEiBpdTYUYgfrQd3YLx6fhvcC86/immhGfk++SfVXKkPLoCZ4FA73VPJ9oNu32AiAfxT8ao1v8TIbt3/RQ+fu8NOEg0J/SQ/G1YbHCEEvj4ByAkJBSBAX5w0fohZ34nDxYuHx5+wfhs5jKk5hSg3MCJ3GqtgBGJqZUKSLNjERzoX0V0SX1Ie9o7OsHH1w/BIaGoV68+6tevh5CQIPh4ecJeKNCbw8j15O2CePhr3LQ9fvvnX6RmGeAh0oiy0ktfTICK9osZvXpXqJUoLczFhiXfo2WD+nBzcYZIoPFWpxOmJz95fAEcnV0QGNIAn3y7Egmp2Xgpi4C6HGmJD+Hh7AQOW7OtnOTJF4gwYMR4xCal1zh3hawECdFRGDX0LQT6+cBOLAankr2/CgNbW63AOSO4fiNMXrgWKbmlTzUn1XjBjc1ArQJZ9dKtaxf4envD2dEBQgG/ysOySl0rTbJq/s5i2oWYrnz9g9Cp3xCcvxKJPCvYUGUsKmu4noq2NbRSDZbxQdQ1LJo7A2+0DAOxKZPAZrP1Qfe3ek1aYvL0+ThxPqra7Jf5OTmYMuAduNjbgcViMcHBwQl/bzqF/ALjt9ibhkkNMhLds/YPfDggHC6O9v9hQHhweTy4+Qbis8nTcejCTYu2YT+LQ2lhHo79uxnfThqPzu2agcfjPbXNK9pf0x84bAc0a9kdE7+ZhR0HT0OhVJn+hvWswtG/G0yAirbBqF7NC+WyMhTk5yE9LRWPY6Jx+dIF7Ny5E5s3b8bu3Xtx+ep1REfHICU1Dbl5+ZCWyarNfqksL0dOehpWLZmFwYMGYthHn2LbkXPILyyptgeDYa2mRmlxMXMqeXx8HG5cv4LNGzfgl19+wW8rV2L3vgOIvHMPiUnJyMrJq1YGhpWveq4iK2CkJSXIy8lh2js+Ph6PHj7EjWtXcezoEWzfthXr1q3Dhg0bsHPXXpw+ex5Rd+8hNi4BqWnpyMnNQ0mplAp29TSHyalQ0TYZ3asXkawUkMtlKCkpQVFREfMpV5ClYcZ45jCWixo52ZlITExg1mjnF0vNenQZYaBQyFFUWIjc3Fzk5eejpISYQZTV9rAyllBNXk+W/SkUCkilUhQXFaGwsACFhYUoLilBmUwGJal3TRaApm00ASraRiOjESgBSoASMB8BKtrmY09zpgQoAUrAaAJUtI1GRiNQApQAJWA+AlS0zcee5kwJUAKUgNEEqGgbjYxGoAQoAUrAfASoaJuPPc2ZEqAEKAGjCVDRNhoZjUAJUAKUgPkIUNE2H3uaMyVACVACRhOgom00MhqBEqAEKAHzEaCibT72NGdKgBKgBIwmQEXbaGQ0AiVACVAC5iNARdt87GnOlAAlQAkYTYCKttHIaARKgBKgBMxHgIq2+djTnCkBSoASMJoAFW2jkdEIlAAlQAmYjwAVbfOxpzlTApQAJWA0ASraRiOjESgBSoASMB8BKtrmY09zpgQoAUrAaAJUtI1GRiNQApQAJWA+AlS0zcee5kwJUAKUgNEEqGgbjYxGoAQoAUrAfASoaJuPPc2ZEqAEKAGjCVDRNhoZjUAJUAKUgPkIUNE2H3uaMyVACVACRhOgom00MhqBEqAEKAHzEaCibT72NGdKgBKgBIwmQEXbaGQ0AiVACVAC5iNARdt87GnOlAAlQAkYTYCKttHIaARKgBKgBMxHgIq2+djTnCkBSoASMJoAFW2jkdEIlAAlQAmYjwAVbfOxpzlTApQAJWA0ASraRiOjESgBSoASMB8BKtrmY09zpgQoAUrAaAJUtI1GRiNQApQAJWA+AlS0zcee5kwJUAKUgNEEqGgbjYxGoAQoAUrAfASoaJuPPc2ZEqAEKAGjCVDRNhoZjUAJUAKUgPkIUNE2H3uaMyVACVACRhOgom00MhqBEqAEKAHzEaCibT72FpezWq2GQqGATCaDXCaHUqm0uDLWRoHUKhXkcjlkZTLm83XjQOpL+oGivBwqtbo2kFtMHqTtleXlKC8vZ/o/uScs7R8VbUtrkVouT25OFu5F3cKOLeswf/48zJo5E9OnT8e3387AnLnzsPTXFTh+5gISktNQIpXVculqL7uszHRERlzDpnVrMW/ePMycMQPTp03HjG9nYO787/HLyrU4e/EKUtKyIJUpaq9gNZyTWqVETmYG7kTcxM5tm/DDDz9gznffYebMmZg1axbmzf8ey9ZtxsXrt5GWkQ2VyvJEzFRERKCLCwvw4E4Ujh7cg9W//ITv583Fd7Nn47vvSPgO8xb8gF//+BvHTp3D3UexKCqRmv1BRkXb1Ba34nhqtQryslLExcZg3apf0LVTe/j7eMLGxqZKsGWxwRVK0KBREwz/bDJOXriBlIzcV+bGJYJVWlKERw/v47fFc9GxXSt4e7hVYUCYsNgcCO0d0bhZC3w2aQ7OX4tERnYBrFm+VColigrz8fBuFH6Z/S06tm4Ff18vcNjsKvW3tWXB3sMbYa3aY8Ksn3D7zgPkFxRZ/VsYafe4x9HYteUf9OrQHvVCAuAgFoH9xD1gw+ZA4uSKeo2aoGP4IOw4eAKxCckoKZWaTQGoaJsNvbkyVkNeVoxHEcfRu1sniMWiKjepja0tbLXhSRF3862Lj6euQl6xFEqrH3GpUVZagGuntqFVszAI+DyDOfjVb4XJP2xBqUxh9lGXKb1IxYww87F74x9oHugPnq1tlbrr2p98Vu4Dtmw+PENaYtW6f5GbXwiSjtX9U6tRrlDg2pm9CO/TnenrFXW0hS2LBTabrQ2sJ363gY3ADm++PwLnb9xFuZnMh1S0ra7XvVyBlQopbl8+hi6tQiASCsBisSrdmLbgCkTw8PCEu5MTuE+MOtgcLhzdfDBgwgokpue+XEHMHFspL8Wp/evQpJ4veFxulZuTjC55Igm8vbzhYmcHzhMcOFweyANszPwtyC0sNXNNjM8+MzkGf8wdDXdXF/C4HNg+UT++vSOc3N3h5ORQqW/YgDzQSd0dnZwxZt4fiE7KND5zM8eQl0lxfMMatGpUH0KBoEr9OFwBvHyD0Lpte7Rr1w4tm4XB5T8MWBCKxGjethMOnLsNmbz2TWVUtM3ciWo7+we3ruG9Pm9AJODA1lZjDhHZu6Be07aYtWg5du7Zh5MnT+HEkSP4d8M6TB0xGMF+XhAKNCNRFpsLO48QzFpzEKnZBbVd/GrLL+LiKfTu3AZCPkd/40qcPNC8Yy8s/PUP7D1wEKdOncaxQ4ew6c8/MO7tvvD1dAWfp7mewxPAxb8xlu28gOyC4morV00nlJeTgc2rFyLIxxUslnYkzRHA2SsA7w4bhTV/b8SeQ0dw7MQJHD1yCBv/WYMxQ/shyMcFAm6F+czdJxDzfv0b6VnW0wfkUini70SgY7NGEAs1gm3L5oBv74LOvfpixZp1OHn6PG5G3EJERARuXLuCwwd2Y/HsiWjfLAR8Nkv/gBNLHNGu8zDEpOZCVl67bxxUtGv6LrGg9Itzs/DDlC/g5mCvFyqRoxfeGPQlDp2PQFZ+McqV2g5IVuPbDzYAACAASURBVJKUSZEZ/xi7N6xAh9ZNIRLy9fGCm7TD9hPXIVdal2WXrAYoyEzGF4PehbOdRF8fiUsA3vpsJk5du4PcwhLoVw2o1SgrKUZy9AP8s+IHhDUIgYDPZeIRW3fTLm/h7M1HUFgFBzUun9yJVk3r6+vN4gkR0qITpvy0HvdiElBaJtebfMjch0ImRULMXWxaMQM9OzaGWKCpOzEphDRoh7/3nEMta5bJd1ROegoWThgNsUioqT+LC0cPP4yYugA37jxEQVExnlwsoipXIDczBRcPb8HIXp3gaCfWsmNBLHHFrJWHkJ1fYnKZTIlY66KtVimQk52JmJgYPH4ci4SUDJSWvbqrEkxplJqK8/DaGXRv1kDb6WzB4vDQsM0XOHUz9rmTauryMhzdsQYNQvz0Iw0bjgQff70IaXnmm5AxhRNZznV5/1Y0Dw3QcLAlHPho0/M73HiY8hwOaqjLpdixdiGC/Ty1HGxhw3XAt8u2IquwzJTi1GocWUkBpowdAXthhUnMxa8+Fm04hJyS59+DirIiXDyyCa0bBTCTdYxJhStBj3c/REouETvLf3g/jLyK7s38weNoJlv5dq5oMWA60grKUP6COZpymRQpN4+hRcMg8Dkafjy+EF3fGYMHsam12o61Ltqq0jR8PW4wc8OwuXz4dhiAa/dia7XSr2tma6cPhZ+rZnRJVoZIvOpix6nrKDNglFhWkIa/F06CoJL9s167d3Ho6mOrwqmQyzD/055wd9CMtohgOwQ2w4V7iQa9NUhzEzH3i6HgVeLQtNconItKtHgOcdfPok+bJtqHtsbUMfzrTXicZph5R16cjYvbF8PFpo5+lYVv3Sb4c885KMotfE2/WoULJ4/CwaaOfuAR2PQNbDkTZUS7qbFu1tvwd9P0HVs2D+J6vXHu5iMj0nj5S2tdtJUlqfhq7KAK0W43ANfuUtF++aZ8TgpqJZTSbPRt2QRC3ShBIEafjxbiQWIWXjDIYBJWKRWIvHwMb7QIAls7eWnvVRfjf979nNHpc8pkhp/UqnKU5CaidaAPY58kr/gSJzcMm/43UrML//Nq/LQiqsrlOLf/H4SFeOnFz8m/MX7YcPJpl1vU347t3oB6wf5MuYngCJ3b4fiNR5DKDRNctbIcWUmx+N/7XeEo1giXwM4D7Yd8jzILX7uuVslx6sgusCo9bNu99TGuP842qo1uHViJzsHatmdzYevXBaeu3TcqjZe9mIr2yxK0gvjk1S7h0g40DNKZN2whtnPBot0RyC56/mtx5eplJjzCd4P7gqt9vWQLHNHlrcnIK1MZJPyV0zLHd3lJAe4cXAEvFyftaIsFd+9grL+QgCKp4asAkh5E4PMuLfWizRG6YOSEpSiUWbaJYPnUYfB2tmPKzRNI0Dp8LKIT0o166MpKChGxezV8PTXr2W3ZAngHtEVSbskLTQzmaHNdnoxoH95RZSVQp4FjcDupUHeJQZ+3j6/HG6F+mrZnc1HHpwtOXqWibRA8epHhBKTFhdi34gf4e7pqOhuLDwfX1rgUn2OQaUSXkzQ3HSdXTQWfp5uM4iCsZVdcflxgFRNxBdkZ+PPbL+Bkr52AZAnhF/omogvLoTDkdUMLojgjEVvnjdCLto0NB13f/ggPUg0zM+h41vbnZ43rwYmrsceK7Jww5Ku/kJJp3OoPtVIBeUEi2oX6g8/SmFhc3Dyx7Xw8iqTltV0lw/NTl+PS8YOMaUc32m7SfQjO3k0xPA0Apzf/gAb+7kzbkzkhhyZ9ceF2tFFpvOzFdKT9sgStIH5hYT4WzfkKbi5Oms7Gd4Rb+8+RXlAMYxYrqeTFiLuxC/ZCPlja5YI+Ic3x14G7KJNZ8A2rbaOM9BRMGDMcEolmQxFL6I66b88BedcwZoysLMvH9cOrwWPZ6O2jdVv2xZGrCRbcG9T4IDgIEps6TB+QOLpi7PIzSDdpIlmNGf1C4SbQLBm0c3DFpHlHkZlryWvW1bh97gyaCvngaDcNeQY1xYJNZyFXql7Y/sxKmrJiLBzVFZ5OmuWCZCKy23uj8CDOOOF/2U5CRftlCVpB/IK8bEz7pDecHTRiJXLywJsTFqOw2MibTK1EVup9dPPiQcjWjLI8vELx48qDKJXKLZ5EauJjfNS/NcRCzZpzew9/jFiw0fhyq8sRE3UOzR3+jxFuYhsPCG6NLXuvGp9WrcVQY0gV0XbD+GXnkGGSaANrvx0IX1fN8jeJnQPGTvwB6Rk5tVYbUzJKjn2E0e/2hlC7+9WWK0HdDkMRmV7ECPfz0iwvK0X0iU1oEOQLllb0xRJ7zP/5KLJr+WFFRft5LfWK/JablYYRrZ1hL9C8Gju6+2HM/L9RXGrsMjU1crOSMKyNgz4tJ3cfTFiwBsVm9MVgaDMlPrqLvvWEEHA1I0R3v3qY/edRQ6NXuk6NhOhb6FOfr0/Lwy8UP/xzsNI1lvd1cBXRdsXYFaaOtIE/Z7wPPzeNmUkkscPwsV8hJd2yd0hKi/JwYdtiuNmJNROStmyIHd3QfciXuB6TgqKyp89rlBbm4e6F/ehbNwASgWavgkBoh/oN3kFCcjYUCmPeV1++X1DRfnmGFp9CdloKurnxIdLaIF0962LmsqMoMWF0nJ+TgckDw+Ak0di1xWTUPm6h8aN2M1B7fPc2WojrgKc17XgHtsPvO6+bVJKUuAcY+oYfRHzNml8HD398OHedSWnVVqSPGteHY2Wb9v/+QYrROxrVgFqGBSPbw81O0wcEYgn6j/wCiakZtVUVk/IhK6AKspIx9bPhelMh2REpsHNC2/4j8fv6/YiOT4NMoVlNQ1YbpcU/xrbVS9GDbC5jsxixF4jEaNqyHXYfOocyWe2/YZpftNuTJX9xJjUCjWQYgczUFLQW8MHXLndy922MhX9fQ+kzRhbPS5WYWmZ+2hUu2nXOXIkrmg2agfyi2t0V9rwyPuu3R5G3ULdOHf0KAv+63bH+6MNnXf7cv6clxWDUW80gFmqEi+/ojV5frnhuHHP/+NMX78HTUTM65gnEaBk+Go8S0oxa+aNUlCEv+SbeqOsDEUdjIuMJxWjz9ijEJqWZu4ovzF9ZrkBidCQGv9cfLs6aOR6NwygOfPwb4P3h3+LIycuIjonGjcunMffToajnV7G8UyB2QNNWHbDlwElm+7oxcyEvLJyBF1SraBPH6WVlZfoglUrxZCjOicOk0QM1E2JcPnzavoPzEff/c92T8aQyecUWawMrRy8jBNTISElCfQFf7wDKK7QFfjv0AFK58ZOHhQW5WDT1A7hpl47Z8B3h2HoUci3e/4YaD25HwKfSxpCg1uHYdS3JpG6SkRqPCSN7QCLWTErVEbohqO8Mk9KqrUgHt/+N0EDtcjUWF3WcGmLP5fso1Y4sX1QO4n+6IDsNfy8eB3eXCmdSXIEYjft9guhEyxdtXR3jo6Pw+acfQiQUgq3zwcIMargQi3zQ680+CPYUga99MLFsWRAIRajX9gPsPXbVoI1Yuryq+7PaRJtsTz9+7DBWrlyJ33//Hb/99huWLVuGn3/+GUuXLsXixYuxYMECfD9nGjq20vg+ILvyxD71MXby11jwwwLmd3LN08LSletwJ856OkV1N5TJ6anVSE1KgFgg0K90eDnRzsHCqYPg5qxdNsdzhGOLUcjNt+zlbmTnTGTEjSqbK15WtL8c2R0SscbGWUfghqDeli3asdcvoFerpsyAycbGFjYsDlqNmovr0YatfijNTcPZTT8jWCwAt5J3SI5AjKAeI/Awvna3c5t8TwAoL1cgLSEWSyeOQ4CXAzhszXwP4WJrywaPz2fEnGzXZ9mw4WPviwmzlyImMZUxiZhjhK2rbzWJthoqeQE+/WgYvL294eXlpQ+enp4gwcPDA+7u7nB3c2ZcgjKvJMTvA1fAuHp093DX/E6ueUqo36EfDly6pys3/TSUgFqNlKR4CCq5ofQMaoZlu+5AasIyvcICItrvV4i2wAmOHcda/khbrcLtiOtawdK81gc2fxM7zptmmiMj7SqiLXZH0DtzDG0Vs1wnLcjF9DGfwFmidZhkYwN7N298OHkOIqMTnmkmUZbLkRh7D2sXTkXLQB/GvFTZnStfJEHH9z9HbHK6WeplWqZqpCfGYvdfPyMs0KWSaGv6hsZkovlua2MLkcgJA8d9h2v3HqOw1PANaaaV7fmxqke01WooS9IwoH/PKjdF5Yq/7HfXBh2x6/St59eG/vpfAk8T7cBmWLYjqppE2xGOnaxUtJv0wY7z8f9lZsBf/iPaIncEDZhrQExzXqLGzTOH0adFU73vEHJfunj6ouegUVjxxz/MsVrENWlUVCQibl7DqWP7sfKnJfj4gzcR5OsBPocHO4/6aBjsAZFAMwkrFEsQ/vEEi5+I1JEnE4zRdyOxeNpENGkQzHguZJbxEbfDTq7wDwiAl5ujfucvYcTmcODo7oM2/T/Emi17EZec+cK13br8qvuz+kS7OBmjPx6EoKCg54ZAfx846HakkZG2QAIPL5/nxiFpNu82AIevPKju+r8G6amRmpwAyZPmkYOm2rSfGGlrzSM51mAeuXWjwkOdjQ2CWoVj11XTbdpVRtpa84g5X5sN6cylebk4sGkj6vn6QMDj6Nccs1hsCMUOqNsgDK3atEWH9u3RpnULNKwbADGPy5iVOBw+XDwCMXzSr5gysBHcHTTr3cmSv0GjpyDZwpf8ERNZuUKG+Jh7eK9vL7g5auzy5IQekcQJviEN8e64mdi+Zxd+nDUGTcMawMvDTe97Wzfw9Aqsj0Ff/YaEpCyUm8EvbfWINuktKjkS4x4jMjISUVFRzwy3Lh/ByIFdmRG5LYcH+ybdsGH3oWder0sr8v5D5FnhKSGG3Eg1fU16SjKCBHz9qgnP0BZYTkS7OswjRLRbfmb55hGocf/2LbjZ1NHbtQNb98Ouq6Z559OMtLvpbdo2jGjPNNvoy5g+VFpYgJM7/kWHxgEQk92trKccq1XJsZLmCC4OXFzr4fOJPyNXqsSMd0PhJtaYD8QSB4z6chHSMiz7NCOy5C8zKQbhvbpAovWpTQSbxxeg28CJOHbxLsoqTcoWpMdj4+qf8GaXFuBwyKEhFceviSWe6PvWTKTnFNX6manVJ9pQM8fOy+VyPC+U5cdj8piK1SPebd/BxduPnhuHSU9Rbp1n0hlzN9XQtWTJX6vKS/4Cm2DxthsmLvnLwnefddcv+WNLXOD71tfIK7SGJX+3EVrn//QPL/8mPbHxtGluNcmSv9HvNNcv+eM4eKHJpz/WUAtWb7IqpRJlpSVITYrH3EkT0aldGzhWOhhDN6Ikn0TQ6zdugfcGT8K+41eRk1sAlUqBYXWDYKdd9y+xd8GEb/chI9uyJ6MTHkdjcP++sJeItcfsseHiHoiJC1YhPjkd0jJ5Fb/g5ACEkqJCJMfdx8afJ6BugLv+5CIWiwM7B3d88PEviE82zlPgy7ZmNYq2YUVRlqbj6/FDmJE240+bumY1DNxLXJWdlopeDpU213jXx+yVJ03eXPP1oOZwkmhejQWO7mj7yTwUGLsl/iXqY2rUx3ci0YpfsbnGJ7gDVu01bZ4kJf4hhncPgkh7XJnIzQ/h09eaWjSzxCMHF2RlpCPy1k3s2rUTGzasx6pVK5lVX8uX/4a1f/6FzZu34OzFK4hLTEVhsRRklZiiIJE5EFh3dqaDszuWbItEblHtbzQxFBw5tWnX2h/ham+nPxfVyz8MU5duRHxaznP9gSsVMhRkp+LE3vVo3riu3g0CObnIxasu9p28gmKZYe5tDS3v866rfdGWZuLrL4ZT0X5eq1Tzb3lZ6fikgx8cBJrzDZ3cA/DFwi2mbWPPTMFH7T1hr52EcnD1wiezVqCoxPJPsEmMvof+jZwh1O4K9PALw/z1p0ygrWY2aIQ3tIdAm5aLTzC+XbXbhLQsJYqaeZOVyWTMngmy30KhKK8y8iQlLS8rQfLlfxHg46lddMCCq7s/jt3JQKmBfrnNUePYO9cxqFMrbZltwBU5YuCYWYhJMdCko1ZBpSjFqV0r0KphYJWJ3CETFiExrfb8rtS6aKvKcvD1lx9R0a7FnluQl4OZ4wbARbsbTuzsgf6TTHQYlfIQ3VwqHEa5ewVhwW87USo17zIoQ3CmJcVh1MAujB2XvPqTreefLjLRYVTkBTQX1dE7jPILaoa/d583pBhWfU1pfjYOLv4KXtrNNbZsIXwCeiOrqAwGHIBktrof3vArGvhpXRPb2MA1sAXW7Lls9ByEvDAdSyd+BMdKB0I3b90Vl2/Wnk/tWhdttTwf30z8lIp2LXbfosICLF0wE26uLhruIicE956A7MJiozqtWlGKpMgjcBPw9ZN5Xv6N8PumS5CasCW+FhEwWWVmpGHy+FGwk2i803HsPNB6+AIY+2Krlhfh1skNENtUuGYNatgVe0/W3o1b2+x0+WVnJGPCoLZwkGg2FfEdPdB+1EKUyZ/ubEkXz9yfq/83Fa6VJleb9Z6GS/dNWVeuxqX9a9C8rsanNnn4BzZsie3Ha8/DoxlEuxDfTBpNRbsWe7GspAin//gZgV6ajmbL4sPJvT0ikvIgM2J4VFaQgfPr/geh/hAEG4Q0aYv9EWmQm2Hpk7EIi3IysWP2V3Bx0JzeYssWIbDeW0gsVhl1onhJdiJ2Lxmpf3CRG7dFr/dxNcbAV21jC24h1xPzQGzUedS344On3UHoGdAEy7da+BmRahWWTf2aOR+StBUJrQYvwo3HprVXxKlNaNPIh0mHpOUe2hxr9lyotVaqfdFWFOObyZ9T0a61JgbIRErmnbNoEqqzxbEgsXPDin13jJo8ykqKwfejwsHjamzjNmwRWncZjMR8OZRGnPxSi1WvkpVCWoy4C7vg6+aiFVwWPLxDsONSKorLDPfDkhJ9C1+Gt9bftDZsCd4bORUZxZY92qwCw4T/5KTEYvWEYcyhxpodkTy07PIWbsRk1fqyN6OKr1Yzou2kPQCCEe3hi3Ez1kTRPrMVbcJ89e3vFtocq19p0S6XYuqU8VS0jep1L3kxmUSRF2Fklxaw105G8gVivDPyVzxOyjHIREKOmbp76QR6NA3VH+wrdPDBO1/8btG2zCrk1EpICzPRr1EgxDzNbj57Rw+MnrYVGTmGmYrUSjku7duApkEVIy2RcxAmL9z2zG3gVcpgpf8hZ0Oe27seretpHU6RQ5HtvPDxmF9RWq42qA+Zr+pqrP72f/DQThoT0W7UexLO3k02vkjqcpzavgwNA5z1oh3QqDW2HLtmfFomxqj9kbZShpnTv4JIJIKdgxPqdh2CG/dN20psYp1f22h7fp+OEB9NZ2OxuXDx6YAD525DqnjxKLM0PwMbl06FY506esdT/vXa4Z+DptvyyJIzhVyOwoIC5OTkIDc3F8UlJVCqXnz8k6mNqJDLsGr2J/Bxs2duOg5XBI+gfrjxKAGy8hdbt4tzUrBwwkjYVbKPhjbtib3nokwtksXHK5fLEHfrDEb06awXKhtbNho2fQtHz9+1+PKTAu5dvRghLlonZ8SkEdwKv28/B7mRBxjIirKxYOpHcBBW+Chp2a4/rtw2bb2/KfBqX7RV5di1Yxs+HzMGoz8fiynzVyAutfaWy5gC6VWJk3z3Jt7r0lZ749mCbBDoOfJ/uPrgRVu5lTi/4w90CPHWCzYZrXQbMgl3k/JNxiOXyxBx4zK+HDUMocFBaNuuAxYu/RWJWUU1dlAw2Vjy8NxRdGzSQMOBuFJgc/He5KW4n/ACJ/5qJQ79sQDN/NyrcHh34o+ISTPuVG+TodVyRJVKiZibZ/DhG+1gV2kugyV0wZxf16OgxHLXZldGFXXtAt5oqfNwaMO0ee+Bn+N2rHH999r+1ejWhBw5ViHaA8cvQ2yKcQckVy6bsd9rXbSJf+eiwkKkpqYiNTUN6Vl5kFn4zLOxUC31evKKu3LWdPhUcv7u4OKOgaOm4Ma9x1CQA04rOc9Qq5SQlRTg0uENCG9fH3basxWJYDt51cOiNfuNsgVX5aJGXnYmPunRFO7ODuDxuBAIhfDxC8Skb/9GepZxN1PVtJ/zP7UaZYX5mD1yGDwcNaNtpj7u3vhs+mJExST+x2872RlXlJuOI5t+RPtGARDzNQcfENfCroGtsPXQZYteo/wcGs/8SS4rRUrCY2z78xe0bdEYTmQXIfN2QVyYCtHvrRl4EJNiFXMZpJIF2elY8/0E5iAQnYdCe0cfdOo2ASev3UFhaRlUlTt/JTLEy2F+VgoObViGdk1CYS/SrJwhm2sc3Zpi/7HrKDViTqRS0iZ9NYNom1ROGqmaCMQ/vIMJIwfATsiGrXa04OTmiXb9BmPW0uXYc/Aozl+8hLNnT2HHlnWYNuULtK7rDwets3/ih4IrssfgLxbifrwpS6a0FVGVIz0uEgF2AnArjVq4PCFa9/sEd2JMsDcawejhrav48J0eEGs3CRHhdvP2Q4+BIzF32WocPHoSFy9dwplTx7Hpnz8wZdwnaBroCbFAsxOUHFMldHDFF3PWIiHNtAktI4pbrZemJSZi+7adOHriNC5fvY6I25GMz6DbERG4fOEsdm/diMVzZ2Hk4HcQ7O9TMfFsw4ZE4oa33x2PO/cTUSq1nolXVbkM929dQZ8OLcHnah66NjYciCWuaNmlD6Z+twD/7j2Mqzdu4d69e7h//z7u3buLa5fPYcu61Zg4+kM0CfSGSNv+xDwkkLhiyJQfEZ/yim9jr9beRxMzmgA5Lurh7Yt4u1sTONiJ9JOKNiw2bIUSBIbUQ+OmTREW1gB+Ph4VNkzih4LNhtjBGa37DkdkTBJz3JLRBdBFUMmREn0F7gJ+FVMDm8dHaJf3ceO+aX6udcm/6FMpL8WVE9vRuWVdCAU8sHSnl7A54EocEFq/IZo2a4ZGDevBy6NiUwYRdzLCcnD1RPdhkxGXnmPWU0xeVM+n/X7h8GE09/VDg4ZhaN6yFdq2a4f27dujXds2aNG0Mfw83SDWnlhO6ksCjyeAm0cAunQdh5i4DMhk1iPYOgbFhXm4eHgDmjZuCDuRsNKSTVtwBCL4BoaiRas26NSpEzp37oROnTqiZbMw+Hi6VbkPOFwunFy90bL357iflA1pLe8EpSNtXYu+Rp/lslLERZ3HoPAucHawA4dDRt0VHsx0N6ruk/xG/AnbObrgjXdH4srDtJfvqCoFUmIjIRGLquRNPK71HPgxHsXV7EibNLdcWoTb5/eja7vGjBMhDvvFHDgcLhxcPPDOp1/jXnI+Y1Kytq5zZudOBNSp8Haoa+eqn7Zg3qq4XPAFAvj5N8a8n9ciMafI2qpbpbwKhRxXzx3DW61bwEEgAJfDqXhgV5pcrsqCPLjI3AcbPB4P7p4+GDt1PqJT85lJ8yoZ1MJ/qGjXAmRLy0KtVjF+hXOyMrBm7nfo1ak9M+r+b0fVjLJE9k7o0L0vZq/YgNTMHMjLlf/xSWF8HdXIzcrEyHZtYS+sOElFLLHD94u3Iiev5sWBcJDLpMjKSMXSyRPRuXVz2IkrylKZBxEwO2c3dOs3AMs37UNWrkawn2EGNR5HLcY4vXMn/CqtAqpcT9134szN3S8Y4W+/h2nL/sK9mHgUFZf8x95fi8WulqzIiiW5rAzZ6WnYumYl3uv3JoI93cBla5aA6ur/5CeXx0f9Zm0w9KPROHr2KvILCjVzQNVSKuMSoaJtHK9X62o1mQzMwv2o2zh08AA2bVyPBfPnYuLECZg4aRLm/7AI6zduxoFDRxB57yEjVM+arDEFjFwmw90b1/C/8R+hc8cOeKNHbyxYvhbJabmQV/JrbEraRsVRq5GdkY6oiBs4sH8f1v3zF+bMnoUvv/wSk776CguX/IjNW7fh8NETuPcoFrkFRc+ctDIqXzNdnJGUiF3/rMWPC+Zh6uTJGPf55xg/fjy++uobLFr8I/5ZtwG79+zDybMX8CgmFll5BZAZsCzUTNUxKVsyyV6Yn4fY6Ee4cOok9u7dgw3r/sFPS5di+rRpTNt//fU0LP3xF2zYuBn79h/ApWsRSExOQ3GpeZ2jUdE2qclfvUi6NdN5uTlIS0tDWno6cvPzISd+zGtyOMkch5aAe3ej8OBRNDLzi8zyyqlrUZVKBZmsDDnZ2UhLTUV6RoZmVMV4vNNdZd2f5FR1hUyKgrxcZKSlISU5GSkpKUhP19RVJpO/dr7rNW9dMmbPQFZmJrO6LSMjCwWFRZDLFdXwZll9fYaKdvWxpClRApQAJVDjBKho1zhimgElQAlQAtVHgIp29bGkKVEClAAlUOMEqGjXOGKaASVACVAC1UeAinb1saQpUQKUACVQ4wSoaNc4YpoBJUAJUALVR4CKdvWxpClRApQAJVDjBKho1zhimgElQAlQAtVHgIp29bGkKVEClAAlUOMEqGjXOGKaASVACVAC1UeAinb1saQpUQKUACVQ4wSoaNc4YpoBJUAJUALVR4CKdvWxpClRApQAJVDjBKho1zhimgElQAlQAtVHgIp29bGkKVEClAAlUOMEqGjXOGKaASVACVAC1UeAinb1saQpUQKUACVQ4wSoaNc4YpoBJUAJUALVR+Cpol1aWoqMjAzExsbi8ePHiI6OxsOHD3H//n3cvXsXUVFRiIyMxK1bt3Dz5k1cv34d165dw5UrV3D58mVcvHgRFy5cwPnz53H27FmcOXMGp0+fxqlTp3Dy5EmcOHECx48fx7Fjx3D06FEcOXIEhw8fZsKhQ4dw8OBBHDhwgAn79+/Hvn37mLB3716QsGfPHuzevZsJu3btAgk7d+7Uhx07doCE7du368O///4LXdi2bRsqh61bt6Jy2LJlC0jYvHnzc8OmTZvwZNi4cSNeFDZs2ABjw/r16/GisG7dOtBAGTzZB17Ub3S/G9snX9TPye9P3h+6/z/t3tLdc7r7j3xWvi8r37Pku+5+Jp+V73Xd/V9ZE3Q6odMNoiEkED3R6QvRGp3uEA0in+9Q6wAABIRJREFUWqTTJaJRRKuIZhHtIhpGtIxoGtE2onFE686dO8doH9HAS5cuMZpItJFoJNHKiIgI3L59m9FQoqX37t3DgwcP8OjRI8TExDCam5qaiqKiZx9s/VTRJoksWbIEI0eOxPDhwzFkyBAMGjQI7733Ht5991289dZb6NevH/r06YNevXqhe/fu6Nq1Kzp37oyOHTuiffv2aNu2LVq3bo2WLVuiefPmaNq0KRo3boywsDA0atQIDRo0QP369VG3bl2EhoYiJCQEwcHBCAwMREBAAPz9/eHn5wdfX1/4+PjA29sbXl5e8PT0hIeHB9zd3eHm5sYEV1dXuLi4MMHZ2RlOTk5McHR0hIODAxPs7e1Bgp2dHRMkEgl0QSwWgwSRSKQPQqEQAoGACbrvfD4fTws8Hg+6wOVy8WTgcDgwJLDZbDwtsFgsvCjY2trC2PDkidP0/5rT5y2dg7HtTK5/Uf8hvz+t7+n+Zkj/fbLfk//r7gvy+bR7h/xNd5/pPsn9RkLl+1F3j+ruWd19rLuvdfc5ued19z/RAhKINhCNIIFoBtEOoiFES4imEG0hgegM0RyiPSQQLQoKCmJ0iWgU0SqiWUS7GjZsyGgZ0TSibUTjWrRowWhemzZtGA0kWkg0kWgj0ciePXsymkm0k2joO++8w2gq0VaisURrR4wYgdmzZ+Pq1avPHJo/VbTJCJs8fWfNmoXp06fjm2++wZQpUzBhwgSMGzcOY8aMwaeffqoX9cGDB+P999/HgAED8PbbbyM8PBxvvvkmevfujR49ejCF7tKlCzp16oQOHTqgXbt2IBVr1aoVU9FmzZrpRb2yoNerV48BpRN0ApCANEXQdQ2oE/XKgk4avLKgkw6h6ySVP3WdSNepdJ+6zkY+dR2zcmfVfX+yUz/vRtDdLIZ+kpvO2JvZ0sWJlu/pDxFj25lcb2g/qnzds/rnk/1Y178rf+rug8r3hu5+0X3q7qfK95juOxHnysKsE2XyaaowE1Emg0CdMJPBIdEUEojGEGEmmqMTZqJFOlEmGkVEmWgW0S6iYUTLnhRmMogl2kc0kAgzGeQSbSQaOWzYMEaUP/nkE4wePRpjx45lTn2fPHkyo7HTpk3DzJkzsWrVKmYk/izVfqpoy+VyZniek5OD7OxsJmRlZSEzM5MJxHRCQnp6OhOY07vT0pgTjMnQnpzsTEJycrI+JCUlQRcSExOhCwkJCagc4uPjUTnExcXhyUAeKk8LxJTzrEBePYwJxCRU3YG8AtFAGbxqfaC67xOSnjH3Krn2Wfc9+fvTtIL87UldIf+vrD2675X1Sadb5FOnZ7pPnd7p9I9oIQk6fdTppU4/dXpKtFWns0RzCwoKIJPJnqXZeKpoP/Nq+gMlQAlQApSAWQlQ0TYrfpo5JUAJUALGEaCibRwvejUlQAlQAmYlQEXbrPhp5pQAJUAJGEeAirZxvOjVlAAlQAmYlQAVbbPip5lTApQAJWAcASraxvGiV1MClAAlYFYCVLTNip9mTglQApSAcQSoaBvHi15NCVAClIBZCfx/vaIpsAxV7VcAAAAASUVORK5CYII=[/img]
[size=150]A distant, magical land uses jewels for their bartering system. The jewels are valued and ranked in order of their rarity. Each jewel is worth 3 times the jewel immediately below it in the ranking. The ranking is red, orange, yellow, green, blue, indigo, and violet. So a red jewel is worth 3 orange jewels, a green jewel is worth 3 blue jewels, and so on.[br][/size][br]If you had 500 violet jewels and wanted to trade so that you carried as few jewels as possible, which jewels would you have?
Suppose you have 1 orange jewel, 2 yellow jewels, and 1 indigo jewel. If you’re given 2 green jewels and 1 yellow jewels, what is the fewest number of jewels that could represent the value of the jewels you have?
[size=150]Here are diagrams that represent differences. Removed pieces are marked with Xs. The larger rectangle represents 1 tenth. 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Is1KHass/US/SyjxyEYvQQpP70rehtGy+ccSSxoLkydxa20LFWqxBoGs6WD+mDtFZNRU+eBJtjlz/TGF74k4XaC1C5SCYQIARYqAOkIbxuhgiiYhZDzjSXnfnHcki6tBL+ylnbNsKamuJaXHG7HcarSVAvmgNJ51aQDemNrMjtjrjbBj2LtNcb1nECFmofgebTMAE/EGCh9gN0v5/SYoEtM0Ms5KJ44jSXTbGzVXOmwXDuNOw6be4mUu9ZLoc2Zh9kQ/tC2q8b1Atnw3D2FCzpqSJ6GGycASx3iJ79loXaszy5NCYQSARYqAOpNfxgC+VyNt+/B8PJY8hc/TsUY4dBMW4YtLt3wvIw5akecXbeZ+qNUzhTShyi2bEZxsTzjh600eDeELof6h8qp2ShDpWW5Howgb8SYKH+K5MC+R/KzmWVpsNw+oQjv/OsyVBOHSeGyOl/uph9yFgyV/yPhrm1UTthupIkMntxKk7/XzIs1P5vA7aACXiLAAu1t8gGa7nk95ylgeHcKSgmjkTqjw3FivH0tj9BxBhfvQzm2zcLbtrNAG1XFuoAbRg2iwl4gAALtQcghkoRlADEKpWIoeysiK1QzZgosldR3mfF+BFQjB6MjCXzoE+IE2JN89xurRYPFXABUA8W6gBoBDaBCXiJAAu1l8AGTbHUg9ZmwZKeBuP5s8hYvkis3JYNDoN2b4QQbrvVIvyjTVeTkLF8MWR9fxNz2TT8TSvIyW+aApywaPuv1Vmo/ceez8wEvE2AhdrbhAO1fKtV+FBb5VLoDuwWKSUlv7UVK7+NF8/CbjE/33K7XUQc0x7YLQKopLf/GerFc0V6ShH1zGR0zc3r+Wfj/+aTAAt1PkHxbkwgCAmwUAdho7lrst1iEfmtyaUq7efGkPXtBm3kDlhl0vz3ioVftgWmm9egnjcDaS2aQDaghwgXalUq3TWRj3eSAAu1k8B4dyYQRARYqIOosdwylXrCMil00XshHz4A6R1/gXphOIyJFxxD1waDSz1hEn0xdJ6WKsKEykcOgKR7O9HLNl255FKZbtWzgB7MQu1aw9M1arxwViygdK0EDx1lt8MiTYc2eg8yVi2FhV6a+cMEHhFgoQ7xS8FuMAg3qowViyEb0FPMLWdFbAMly7AqZJ6bW6ZkIFkaWFJTYDhzUkQqo4Qg8hEDQEFVrAq595OBhHhb5lY9Furc6OTwnc0GXex+yEcOhGxgL2SuWwXT9augNRm++tBLLoXyVS8IFyNStGhTuz/Kke3OV0bweQKeAAt1wDeRCwbabGIRmD4+GsoZE8WKbfWSedDFHxBD1TSX7M2FX3ajAZa0VBHlTLN1PZTTxkE+digy16+C6dplR+QyF6rFh+RMgIU6ZzY5fkOjTCKBTKJIuUpTQSSUyiljQGswLCn3QZ4Qnv3YQfcHuThqdmyCcsJIKCeNQsbKJdAdioPp5nXY1CoeifIs9KAvjYU66JvwUQUe+T+TEGq2bYAqfLIQaRpG0yXEiXCh9IDw6edRyk1jUiI02zdBNX8WlNMnIGPFEuiPHBIrzTlYimdahIXaHY524dVgeXBP3Ct0z6jCp4ByplMvmwL+WGWSp6L0OXs28oqgl1f9kYPIWLFI3JsUslez8Q8YTh0XmeWE54SzBfP+BYKA34W6Q4cOuHXrFhQKBW8uMNAoFDCkPBA3u2LdStwePgA3B4XhzqwpSI2PhexuMhQymd/ZyiUSSC6cw/11q3F7zFDcGtQbKeFToY3eK3oXWrkMKhfqz9eN476ZMGECqlatChJs/rhBgBZJ6nUgV0RKCUtirZw2Hhkrl4rofLR4Mt/xA+jlWaUUU0/afVHIWDpfxNVXzZ6CrKgdYkGn6LG7k7nOjaryocFDwK9C/corr+DTTz/F2LFjMX36dN7yyWDG9OlYMmsWts+bgxOLF+DymOE41KwhVlWtgPH16mBy396YPm1awPKcOnIEJv76C2ZUKY/I2tWQ2Ps3XF40F/sWzMPq2eGYO3NGwNoeqNdpkyZNUK5cORZqDz57dTodpDeu437ULtwYMwxXOrYSL8HS9WtgvHQR5tQUZMqkkMtkkEqlYqPfNTIpzCn3xSK19JVLcaNfd1zp2gY3J4/Fg5j9kN27C6uVk9Z4sKlCvii/CXVycjLKli2L4sWL85YfBsWKodibb6JooX+jxD//gV+LvYF1NSrjaP1aWPxZVfxYrgzKvv12ULEsWbw4Pn23JIZ9VBGH69fCni8+xrAyJVH95ZdQ7MV/oejrr6NYsWJBVSd/Xs/Vq1fHypUrQ/6h5asKHj9+HDNmzMD48eMxYcwYjO3ZHWO/qo3V5d/DyYZ1cH1oPxyaNQ1/TJ+GRVOniG3t9Gk4Gj4d1waF4Vjdz7CkQmmMbVAPY3uHYcL48aKsWbNmITU1FXbuSfuqKYP+PH4TaqPRiMTERBw6dAgHDx4UP+l33p5mcDA+HgdjYhC/OwrRSxdhd9tfcPqL6kjv1RmqbZtwKT4Oh0OA2/FDhyCN3gfF5NG48v3XiGn6DfaOG4W4iJ04GH0AxOEQXyc53h90D507dw4qlSroH0qBUoG2bduiUKFC+Nvf/oYXXnjh8fbPF17Ah/9+EQNLFEHsR2URVbEUxr/zFsaXeAv7KpZCzEdl0fvtN1HmpX/hX08c9/e//x3/+7//iyJFimDNmjWw2WyBUlW2I8AJ+E2oiQtdqDQExFvODEwyKTL3RUEyKAwPWzaFInwKaHGWXa+H8GEOEX42ipRGm9kM84N7yNy0Fum9OuFhmx+hWrkExvv3YDWZ+FrJpb3pfuJemueeuLR+hkZI6tati3bt2j21dWjXDmO6dMLeru1x5ZvaOFO1LE5ULYsr9T/Dvh6dMbxzJ3R85pjWrVujVq1aYpRow4YNLNSea6qQL8mvQh3ydF2toM3m8H3+fQGkvToJP09t5HbQqlRayEJiFtIfqxU2rRZWSRoMJ46KBT2Sji1F/mv9scOwqdUhXX2uXGAQ+O2331C4cGH885//xL///W8U+ve/8fYrL6NZ8SL4vdL7iKtRCYsrlMJPb7yK0v98AWX+7x9o8carWFKxDI58VhmLKpbBD8XfQolXXhbHv/TSS6IsEv9t27axUAdGMweFFSzUAdJMFGTBKpdBFx8N+eghkA/rh4xFc2A4fgTme8mOlaa2ArYAhVbgGvTCrcV06aJwZVEQmxEDkbVlvUgIEvIvLQFyfRZEM8gbJSEhAQd27cSeeXOws30rRNWuhpO/NseDxXMhTYjHzcMJOBkfh/jYWLGdio/DrcMJkB85hPsLZ+NU6+bYXecT7Gz7C/bMDceBnTtx5MgRyOXygoiU6+wiARZqF8F56jCK5mW6koTMjWugmDRK+BlrNq6B4eQxWFIfiuAInjpXUJfzKBkIrbalrF3quTNED1u9eI5wTRO9bF6cE9RNHEjG07SS6V4yNHsixHSTbMIIKBeGI2tvhJh6okh7NrMZNGXz3Kk7i0VE/jNdTgS5ZikXzYZswkjIZ0yEJnIHzHfviKmrQKoz2xK4BFio/dg2lvRUZO3cAuXMiVDNnQ7N5nUwXroAmyaTIxPl0i52nU74oGr3RoKiSZGfKwm29sAeWB6mOMKi5nI8f8UEnkuAxFUug+HsKWRuWAPV3BlQzZyETAoadDBGTD25EpTEbjTCnPJABFPJXP07VDMnQz1nGjLXrnC8kEvS+Zp9boPwP7MJsFBnk/DDT/P9u9BsWiveuGn+Gexb6VwrUG9GqYD+xBGo5s2AYsJIkRiERin4wwTyRYCi52VmiqA7+oQ4kJAqp46FcuIoaLash+naFY8m7LDptCJMaNb2TVBMHCUCoFCkMoqHT3HGHeFDC9gUV74aqmDvxELtz/Yn9wwervVIC9htVtHLttCQol7vkTK5kBAnQBmrHqZAuzcCysljRdIaikRmOH380ZoQL7pPUdQynRbG82fEqJBscG/xokkjbDQszs+FEL/2nKweC7WTwHh3JsAEQoSAzQbN+tUOr4qonSLzm79qZpWmixCliokjxXA7x8D3V0sE5nlZqAOzXdgqJsAEfEGAppsCKfAIjbD5MM2mLxDzOdwnwELtPkMugQkwASbABJiA1wiwUHsNbe4FUxQunofKnRF/ywSYABNgAgALtZ+uAlpNql46H9r9u8WCFl7x7XpDiGAx6Wli1azd4OOc266bzUcyASbABPJFgIU6X5g8v5Ml7SGydm0TPpXCV3P9KhgvJ4rQmZ4/WwiWSKtmM9XC7zxz3UrhS63ZsAa2rKwQrCxXqcAQoDlq9gQpMM2d34qyUOeXlBf2I/9N05VL0GzdAFX4FEdwhTXLoT+aABJyV4IreMHMgCrSbjLC8vAB9IfjkfnHchHJTTV7qsPn9eZ1UHAJ/jCBfBGw24VLHyW5oUhj/lxUJq7rtIcitr0udr8j6FG+KsE7FQQCLNSB0MoWM6zpqY/cM0ZBMXYYMn5fAP3hg+JBUuAjlYnecwZMt25AfygW6iVzBSPVjIkiNrolPS0QWpFtCDYCdrsjvCeF9dzgCNsr4urTqIwverV0XatVIgCKLiEOGcsXQjF+BNQLw0WEtGDDyfZ6jwALtffYOl8yJaEwGWFKShQhMaV9f3NE29obKRJQWFXK0M+clU3tEQvq6Zhv30RWxHYoxgyFtHdXZKxYAtPVyxzYJJsV/3SZAIUM1R89BOWMiZCGdYZy6jixbsScfFv0ssUIjSdFm1KR6vWwSiUw3bgGEaFszBBI+3WDesk8GBPPw67l6RuXGzRED2ShDuCGpSAIWVE7IRsUBmn39qKXbbp+RQyLiWFxTz5AAoUDPciMBtHToIeWev4sSDr+AorcpIveC6tS6ZveTqDwYDt8QoCScFASHIoMRoIt6dIa6nkzRdxvq0LhyP/uRohfKp9i1JNA648cFC8Eaa2+h2LsUBE+1KqU83Xtk5YOzpOwUAdBu9FbvTHposjLnNq8IWT9usMxj6UJuZubejhZEdsg7dMV9CBTL5otetT+nD8MgkuETfQkAbtd9HYzls5DWpsfhWhnrlkmpqFcGRInrwTT1SRxLae3bwFJp5bQbFgNqySd4/t7st1CuCy/CbVGo8H27duxZMkSLF68mLdcGCxatAiL5s3DwhnTsWD0SMxq9DUiPquC5F+bIX3+LBxauRwrlgQvw6WLF+P8ujVInzoe15s3wpZa1TCn+fdYMHY0Fs6cgUXz52PxokV8jeRyjdA9tGXLFty+fTuEH1e+qxr1gCkWt1UuFYs7KeOVpFtbyIb0hnZfpEgGk+vLI8URT6PseFsh698dkp4dRUxv49lTsNEUFsWjD6SIaL5Dy2dygYDfhDo5ORmlS5dGkSJF8NZbb/GWXwZvvIE3X3oJJf75Auq99grCK3+A/XU+wYaaVdGuXGlUertYULB8u0gRVH/nbYRVKCvs3/vFx5hQvjRqvVoI7/zfP/BWoUJ46803gqIugXL9fvTRR1i2bJkLjwE+5HkETp06hYULFmDmxImYMWwopnX/DTO/rY+tX36KW782Q9q08Ti+ZCHWzJuL2eHhmDt7Nv6YNxdnli6EdOIoXP65CTbW+RQzmzbCtJ7dMWPEcMyYNEm8dKalpcEeilNXzwPJ/3ObgN+E+saNG3jllVfwzTffYPXq1aJ3TT1s3vLPYM+OHTgdFYmH+6LwYMl8HGv7sxDsVc2/w8apk7B1wwZs27YtoJhuWbkCG0aPwOrvGmBL7eo4060D5BvX4P6+3TgeGYGoHTsCyt5guR7bt2+PChUqIDw83O2HAhfgIDBw4EDB9P3330fFihVR8YMP8OG7JVGzWBG0LFUCc2p/gr2N6mFnvdqY/nFlTP+kCqLqf469Tepj+qdV0fy9d1CjWBF8WOo9VCxfXpRVpkwZ0AtVVFQUCzVfaPkm4FehLly4MLp37w6FQpFvg3nH5xCwWUErwo2JF6DZvgmqudOFf3HG8kXCL9Mqk4KG8vz2sVphSbkv5tXVS+eJ4CTqxXOgjdoBsThOpw25uXZfsyaBrl69Ogu1B8G3a9cO/+TLvHcAACAASURBVPnPf1C+fHl89tlnj7ean32GujVrYkjD+oht3hjnPq+GqArvYVeFd3Hx86o48NN3GPBNPdStVRO0b/axNWrUEKOIRYsWxdq1a2HjoW8PtlZoF8VCHWLtKwIn3L8L7e6dUM2a9Cgx/WLhb0wuJ3at1jc1tlpFTl9yo9Lu3iXczZRTxkC9aA50B2PEClsOm+q5pmCh9hzL7JL69+8vRJqEml6CqlepgprlyuKnCuUwqkY1bGvaAPuaNsCS2h+jZ/ky6PlBGfxe62NE/9AI279viJE1quLnCuVQ64NyqF65MqpVq4Zy5cqhUqVKiIyM5B51Nmj+mScBFuo8EQXvDhT5zHD2FFTzZoicuxT9jFycyH/TqlQANqvHK0extmk1q/HSReHqopw8BrLBYchYs0ysfLWxj6jHmVOBLNSex3r48GFMmzIFI/v1xbB2bTG00TeYVO1D7GtcDw96d8Xt2dOxdeokTB87BqNHjxbbtLFjsG3qZNybOwP3wzpjf+P6mPxxZQxpUB/D2rXByL59ED5zJmiNDs9Re77NQrVEFupQbdkn62W1wnz3jgizKRvQE7JBvZC5YTVMt64/CupgAOy2J49w7nebDSTAQqDPnELGojlipat8WD9oyfdZpeQVrs4RdXpvFmqnkeV6ALlE0upsilRGq7wVE0dB2qsTVNMniOkkG41M5bEYzJalgeHkUShnToK0dxcRvChr9y5RplWlcIS7zaOMXI3kLwsMARbqAtPUjoqSoBpOHoNi4kik/dwY1OPVnzgixFQEUcn3vBkluLeK4CQWmQTayO2QDewFSdfWyFg8B6YrSSzOPry2WKg9AJuC7ZhMwi2L3KjUc6Y5gu0M7CUi41nSU107CblqpaeKKSDZ0L5Ia/0DVDMnwnDyuJgeoukqngZyDW1BOYqFuqC0dHY96Q3+0QOJEn9krlslAjpIenRA5vrVMN+/m2dPgYqih4vx8iUow6cirUUTyIf3d0QOk8scC9fyLfjZhvFPdwiwULtDD7BbzOLaz1y7AuntfoKkUytkLFskpomEz7O7+ePpvqMXW70e5ju3QQFUKPBJevufRYxv042rnITHvSYM6aNZqEO6efOoHC34oiFrabrIRqWcNh6SXp3EAjQasvtLnGObTQRxoMVh8iF9ICVxp4fZlUuOIXQDB3HIg7jXvmahdg0tTdfoYvaKUJ6Srm1E9D/D8cOwStJAQ9ck4HkNcTt1ZophT8FUsrJA3hiGU8ehmjcT0p4dQVNFWZHbYXlw37PndMpA3jkQCbBQB2Kr+NomyuKj04rUmsaL50D5neWjB4uhbIqsZL51A4Zzp5GxZB7kQ/uI4XISa7EojXrQZg8/zHxd/xA4Hwu1C41I2bOidjhyme/YLEaIaIjaTi+cPpo7FosvKUHHtSvQ7okQ+ekzViyGnUekXGjQ0D2EhTp029almpHoWhUyIcwUZzu94y/ibT+9Y0uxejtr20aYb14HrSjnT+AQYKF2oS1o7jjlvkifalWr/LumghZkajJFljxK5+qrFwUXqPEhfiDAQu0H6AF7SnpYZKphunwJmq0bRE+DXKvUc2dAOXGUcPEi8dbF7IPl/t2Ck3IzYBvsT8NYqP9kwb8xgVAjwEIdai3qQn1oLpoWlhlOH4dmyzoop40Tq8Iz/1guVm+L+TRJukjPp144W3xHP7X7okReaFuGmletusDdk4ewUHuSJpfFBAKLAAt1YLWH76yxO4baLA/uiQUtGUvmQj60LxTjh4soZpQ393kfu14H863rYrW4rF83sb9m52aYrl0WuXZpzo0/vifAQu175nxGJuArAizUviIdCOehFadms/DdtDx8AG3UTjGcLeneHhlL54vFNHZjPoVWDJNnQBcXLVyzpGGdoZ4/C+R/SnPcJOicxs93jc5C7TvWXj0TLSJz1xXMqwZy4f4gwELtD+q+Pme2D6dOJ+afKWlH6s+NIOvfA9r9u2FVqdxbvGK3w3zjKjIWz4OkY0tI+3RFVsQ2EaZUJANxJ+qZr1kF6flYqF1rOApwIgL9+Fsc6R6xWmBTq2C+c5N9ql1rzpA9ioU6ZJv2z4qRr6g2cocjclinVlAvmQ/zzWugMIgec60SUcqMYvibFpvJRw1yRGCaMw3GpER+8PzZHF75jYXaBaw2GzJXLYWsX3doNq8ToT1dKMXtQ+geNCUlImPxXJAvN7lGWiRpbpfLBYQOARbq0GnLp2pCgRqMieehXhAueriKCSPE4i9arU1v7SKQw1NHeOgPinqm08EipcQcF5CxbKGIcywf1h/a/VGwpKfxkLiHUD9ZDAv1kzTy/7tVLoX+YAyUMyZCGtZFBD7RH4x2JK2hXra3PjYrLKkpjhfoQWGgGPzqxXNhOH3CsdaDAq3whwk8IsBCHUKXAr2ZW9JShSArRg2CYswQUE5qiuVNyQXIT9Ot5BvOsHo0H26VSUTksqyI7SLimXzkQFBAB+PlRBFkxZkied+cCbBQ58wm128eJZSxpDyA8fxZaLauFwF9KPIe3TvGC2dhU6vdmxrKNsBqFRH8DCeOQjV7GmRDekM1c5KIAU6jTjTyxYsxs2HxzycJsFA/SSNIfyf3KOo9a9avhnLqeChnToZmw2qRfIN6sGIOzs91s2VmwHT9CrR7I0XPQTl1HNTzZ4oV5qKX7c3ei5/r7ovTs1B7gDIJqVolXiwpSljG7wtELAHV3BlizQVlm7PRIkknP/SCTElqNFs2CGEm98eMlUugi90P8+2bIlQpL7x0EmoB292vQv3KK6/g66+/xooVK7B582benGCwY8tmnNq1A+mRO5AyfxaOdWyFtfVqY/mPTfHHmJHYuGoVNm/aFHBMN61di/Xhs7CqW2esrP8Fopp8jVtjhkG1fRMuR+7E/m1bsdUJDnzdOO6btm3bokKFCiIvdQF7hnmnuiTa6anQH01A5qrfRapK1eypIj2s/thhWFIfOl6AnxdqlEaTTCaR5EOXEAdK9KGaNRmq8KnIXLsShnPkGSH3jt1cakgS8JtQ37lzB6VKlcK7776LypUro2rVqrzlxaBKZXz8QTk0KFcGPatWwrpG9RDdpD5W1qqOTmVLoXaZ0qhapUpwcPzoI3xSsQIavlsCU6t8gAMNv8Sepg0wtubH+KlCOdQqVxZVP6wYHHXJq9188H3p0qUFq2XLloXkg8oflbp+/TpiYmKwZ8d2RCxagK09umBTnRqIafoNbk4YCdXeSNw/GIczMdGI3b8Psfv341xsNB4eioN69y5cGTEI+7/9Cpu//gLb+oUh8vel2BMRgbi4OMjlLNT+aNNgPaffhFqhUGDGjBkYPHgwb3kwGNS3DwZ27oT+zZth2CdVsK1ODSS3+xk3J43B+rGjMX7Y0KBmOGTwYMwfOQLHJo9HclgXHGpUF+GfVkW/BvUxoF0bDOrVK6jr56trfPr06bh48WKwPosCzu6+ffuKjkTRokXFz/fefRcflCyJb0oUx6SK7yOuzieI+vJTjP6wHL4pXgQN3i6KSZXKYW/dmoj/4mOMLF8GdUu8jXIlS4jjS5Ysibfeegvvv/8+9uzZA/vzeuMBR4ENCgQCfhPqQKh8QNtAq6eNBlhp/vniOVDITkorKRvYU/g+iwUuIZhhhxbT0AIe1eypSO/UyrEKN+6AI42mTsehSgP6og0t49q3b49ixYqhfv36aNeu3VNb5/btMbJLZ+zp0QVJDT7H+WrlcLb6B0iqXxNRYd0wqFNHdGnfHu2fOK5169aoVasWSPjXrVsHWwjev6F1BQRObVioA6ctnrKEFohRblppr05Ib9sc6gWzRCq8ApNVx26HVS5D1s4tkHZrh9SfGkH9+wKY794R+XyfgsV/MAEvEGjTpg1eeukl/Pd///dT2//+z/+g5kv/hykl3sKRymWwruw7+O2t19D1rdewoWwJnPjofUwq8RZqvPh/+Of/+5+njqWyihQpgjVr1rBQe6HNQrVIFuoAallKjmFMugjVvBlIb/+zcK/SHtgtFq5QvmgR5SuA7PW6KTSqYDAIv2/Ry54zDZJHvWzdwRjYVEqvm8AnKLgEYmNjMXLkSPTr1w99e/ZE72ZNMbRcKURWKoMrvzTFpdFDsWr4UEwcNBAjBg4Q28RBg7B6+FBcGT8Cl39qjIgqZTG8fBmEfdcYfXv1Ag2njxkzBnfv3uWh74J7aTldcxZqp5F5+ACr1eH7vH835CMGiLCeFCSEhIkyWtm0WYDNi4EXPFwdrxQnVtEaRQ/bdPM6KCc2RT6TDeyFzHUrRT5hOw8jegV9QS5Um5UFSdIlJG/4A1d7d0VSq2a4PXIQMmL3wXzvLowyKVRSKaQSCSSPNqlUIv5nksvEqm919F7cGT0ESa1/xJUeHZG8bjXSLyXCbOaAJgX52nK27izUzhLz4P6W9FRoNq2FYtxwKKdPEMO8NB8tAh+YTZ4JsuBBewOiKHKbUSnFNIA2ei9U82ZCMXYYVDMnQ38swRFfnH2yA6KpgtIIux2U1tVw/gwyli2AYvwI4Uut2bIehjMnYEm570g4k8/K2ShKX8oDGM6ehGbbRnGf0/VKed2pPE4Rm0+QBXw3Fmo/XgAURSxr51aRxcp07QpsmZl+tCb4Tm3T60XPRhd3QIQqpZcdmiqwaTTBVxm22H8ESJx1WhF8RLtnF9RzpwtBVS+eI+5N45VL4uXQraAkFAEtQ+14wdwTAfWSeVDOmABKkEMJbCgYkCNyoN1/HPjMAUuAhdqPTUNz0hTpSCTG8KMdQX/qRw9Bw5mTMF4455guCPpKcQW8ToAWLMokIr429XZVc6aJ3nPG4jnQHzn0aGTL80PUdqtFTOPoTx51vGDOmCiCodDomiOYSgqPpnm98YPrBCzUwdVebC0TYAKeImCziTCeNPVEw9HkYWBOvu3bpDGUnOP+XWj3RjhijI8eDBpmd6v37ik+XE7AEGChDpimYEOYABPwNQHzzesiDjfNS/v7Y6epnNs3YLx43t+m8PkDjAALdYA1CJvDBJgAE2ACTOBJAizUT9Lg35kAE2ACTIAJBBgBFmo/NQitTKaUeoGQgtJPCPi0TIAJMAEmkA8CLNT5gOSNXcgdQ0EZeGZOguH4EeH/643zhHyZj1Z8648fRlbEVoeLS8hXmivIBJhAQSLAQu2n1qbwl4ZTx0VkLeWUscItJGv7Jpjv3Cx4oUJdaAMKJGG6dcMRRGLSKCinjUPWvkjhD+tCcXwIE2ACTCBgCbBQ+7NpbDaRFcpw9hQ0G9dANWsKVOFTRKJ58gm2KhWAxeJPCwPr3MRLKoHh5DHxgqOaNVn4vmo2rIbx/BlY1UrOrhVYLcbWMAEm4AECLNQegOiJIij5BPlwki+nctJoKKeOReYfK6A/miD8LO2U4rEgfijON7mtJN+G/lAcMlf/LvxNacogK2K7+D8HjCmIFwbXmQkUHAIs1IHW1hTOUJMJ/YkjYjhcPrSvCDNIIkUpHm1qVYEIhkDia1UpYL51QwSlIGGW9u8O9byZMJ456eAQaG3H9jABJsAEvEDAr0JtJ1GixUC8PZeB1WyG8eZ1qNcsR3rvLpAM7InMzWthvpcs4gbbTEbYrNbnHhuUTKkuBoNYDW+8dkXUWzKgB9J+a4vMzetgenAPVqozXy85MqB7ij9MgAmEFgG/CbXVaoVcLkdaWhpv+WDw8Pp13Nm8AVe7tcOtBp9DMmkUMk8cgSrlAWTp6UjPRxmByppspzpQXdQx+5A2vD9u/dgQ13p3RfKubUh9cJ+vkTzaNzU1FTKZDEajMbSeUFwbJsAE4DehvnPnDkqXLo2XX36Zt3wwKFSoEAq9+C+88o8XUPr//oFBJYsivsaHiPq4IvqUKYEP/1M4KDm+9vLL+Og/r2NEufdwpGYV7Kj6AboXfxPv/+ufKPSPF1DoxRfxcqFCQVk3X17bdH1UrFgRq1ev5scaE2ACIUbAb0J98+ZNvPbaa+Lh0rFjR/Ts2ZO3fDLo3asXRvTpjen9+2LPsEE437UdYr+sgRkfvIeuNWugR6dOgc2yRw90a9USPWpUw/yyJXC83me41L8nNg8ZgKn9+2JY7zD06dUrsOuQz7by1XVds2ZNlC1bFrNnzw6xRxRXhwkwAb8J9Y0bN/D666+jTZs2SEpKQkpKCm9OMniYkgJ16kMYaLX4sQQ8mDMdFzu3wcUOLXF96QLcPX0SD5KTA4brg9u3kXwwDldnThE2Xu7WHg9/XwDjhbMwPrgP+cOHSHWSAV83jvtmzJgxqFKlCsLDw/mpxgSYQIgR8KtQFy5cGN27d4dCoQgxrL6vDoUitUrTQf7Xms3roJw1WbgxkYuX8eI5WDPU/slxSzl/5TLojx+Besk8KKeOEyu3tRHbYbx0weErzgug3L5gSKCrV6/OQu02SS6ACQQeARbqwGsT9ywSfsc6mK5dhmbrBuHapZoxAZlrlkGfEA/Lwwfwut8x2aDTiihr2v1RyCCBnjYe6gXh0O6LFG5mdoPevXry0U8RYKF+Cgf/wQRCigALdUg15zOVsdthSU+DLj5aRDxTjBsmRFN3MEb4J5O/ticT1AvfZ7kMxqREaPdGQDV7KhSjhwiBpp5+QfEBf6YVfPInC7VPMPNJmIBfCLBQ+wW7708qYmNfvYzMFUsgDesM5fjh0O7eKXq9FKpUZPFycQjaptfBKkmH8XKiCO0pH94fskG9kLVjMywP7nn0ZcD35ILjjCzUwdFObCUTcIUAC7Ur1IL5GAoWolSAhqRl/btB2qM9MhbPhenSRdHjtRsN+RNWCk6i04k5Zl1CvAh7KunaWoQ+1Z84Cps2K5gpBZ3tLNRB12RsMBPINwEW6nyjCs0dTVcvi3nstF+bQdqvm5hDtmVm5FpZu8UCS8oDZKz6Ham/fAdJl1+RuWENLKkP8yfyuZbOX7pCgIXaFWp8DBMIDgIs1MHRTl6zkkTXptPCkvYQ2j27IB8xAOmdfoGaetnXr8Bu/TN7l1Wtgv7IQSgmjEB6+xZQzpgIw5kTolctFodZrV6zkwvOnQALde58+FsmEMwEWKiDufU8aTsNZWdlwZKaAsO5U1AvmgNpn66Qjx4M7Z4IkbVKPjgM8pEDhPuX6fpVWGVS2ClkpYtz2540v6CXxUJd0K8Arn8oE2ChDuXWdaVu2e5dV5OgXhiO1B8bgOae01o0hrR3F2Tt3CpcvMC9Z1foeu0YFmqvoeWCmYDfCbBQ+70JAscAGgKntJJZkduFa5VyxgQRpES7LwqaLeuhnjsDyukTkLF8EfRHD4kAK9ybDoz2Y6EOjHZgK5iANwiwUHuDajCVabOKIWzDudPI2r4JqjnTHGK8bKGYf7ZRRDOrVbhvme/fg3b/bhFZTDllLDJ+XwDtgT0w377pWOVtswVTzUPKVhbqkGpOrgwTeIoAC/VTOArIH2J4Ww9Lyn0Yzp5E5tqVoGAoivEjhO+z+e5tIc7PpUE5xDMzRHxu9cLZkA3uDdWsSaBeN60gtyrk3o989lzDCvY/WagLdvtz7UObAAt1aLfvU7WzW8xCZEmg9YfjoZw+EdIeHaCaNQWGU8ches9PHZHHHzabWC2etWsLZP17QD6kDyi2uOnKJRHf267nMKF5EPTY1yzUHkPJBTGBgCPAQh1wTeJhg6j3TAJN88+3b4res7RXZ0g6tYRm0x9CaPGEC5arZ7cbDELslVPHIr1TS+HCRS8DNk2GY2U4D4u7ijZfx7FQ5wsT78QEgpIAC3VQNlv+jSaBpmQc8lGDkN7mRygnjYLh1DHYTUbH8LYnXatsNohgKA8fQLN5LSQ9OiLt1+9FQhBzyn3xXf4t5z2dIcBC7Qwt3pcJBBcBFurgaq/8WWu1wnzvDjTrVkLSvT1kQ/qIVdti0VeG2iHS+SvJtb1EeFEtrFKJeClQzZyE9M6/QjFlDPTHDsOmVrtWLh+VIwEW6hzR8BdMIOgJsFAHfRM+qoDdBqtKCYqzTTmfpX1/Eyu4dUcOirSSNP9MvV2ffmjY3WiARZLmSNixcY3o2VPSDnL3Miffhp39sT3SJCzUHsHIhTCBgCTgV6F+/fXX8fPPP+Po0aNISkry+Xbp0iUE+3b78mUozp1B5pb1uDd8AE51aIWjg/vh1JIFOL8nComnT+FSYqL/63nxIi4cjMfZDWtxYsoEHO/WAUk9OkE1fxa0x4/gftIlXElK8r+dQXpNDB48GJUqVQIJNn+YABMILQJ+FepXXnkFJUqUQP369dG4cWPenGDQqVlTTGv1M/Z0aYeDrX/CytqfoFfJYmhc8m00/LQGGjVqJLaA49qoEb798kt8W7E8WhV9A1MqlMGB5o1xuGt7LG/bCv2a/4Cfv2vC14IT1wK1cbly5VC6dGnMmTMntJ5QXBsmwATgN6FOS0tDmzZt8N1336Fp06a85cWgSRM0qV8PjSpVRNMi/8HYiu8j5odvca57B2zq1A6DWvyEFt9/H1Qcf2jaFJ1+/AFz27bCqZ5dcLztz1j6WVV0KFkMjcq8h8a1a+G7Jk2Cqk7+upbpPurUqROio6P5scYEmECIEfCbUFutVqhUKpBgp6enQyKR8PYcBukpKUi9dhUPjh5G8vo1uDa4L5K7tIFy1mToT5+A6v49SEOAnywtDdqrSSJdZsqAnrgZ1gW35s3C/dgDeJh4Aen370MSAvX01nVO95FCoYCRkqTwhwkwgZAi4DehDimKXqgMLcKyqZSgLFWZ61eLCGDSsM5iERblgkYI+yXblAroE+KgnDgSkt/ainzZhrOnxCpyu06bc9Q0L7QDF8kEmAAT8DcBFmp/t8CT5xfBSSyw63SOvM9jhyG97U9QTBwJw4kjEDmfn9w/xH+3m80wJ98RSUDSfmkKWd/fRIhTyp1tN5tC+mUlxJuWq8cEmIATBFionYDlzV2FKN2/i8w/liOtTXNIe3eFZtNaWO7fFQItXKs8GZzEm5XxZNkURMVkhC0zE7r4aMhHDUZ6x5Yg32zjudPe9wn3ZF24LCbABJiACwRYqF2A5slDhO/z0UNQTBkLSbd2UIZPgeHEUVjSUmHL0gC+9n32ZOU8WdajRCJWuQympERkrloK2cBekA3sCW3UDjEsHsrTAZ5EyWUxASYQXARYqP3YXhQpTD1/pshclblxjchIZUlNEUFCOM9zzg1jN5lE0g/T1SRo9+yCctp4yAb1QsbSeTDduFbgpghyJsXfMAEmEAoEWKj92IpWmVSE2DQmnhfpIblH6GRj2Gxi1MF08zq0B3YjY+l86PZHOUYinCyKd2cCTIAJBCoBFmp/tgzNORfEeWcvMLeLlJupsErSed7aC3y5SCbABPxHgIXaf+z5zEyACTABJsAE8iTAQp0nIt6BCTABJsAEmID/CLBQ+489n5kJMAEmwASYQJ4EWKjzRMQ7MAEmwASYABPwHwEWav+x5zMzASbABJgAE8iTAAt1noh4BybABJgAE2AC/iPAQu0/9nxmJsAEmAATYAJ5EmChzhMR78AEmAATYAJMwH8EWKj9x57PzASYABNgAkwgTwIs1Hki4h2YABNgAkyACfiPAAu1/9jzmZkAE2ACTIAJ5EmAhTpPRLwDE2ACTIAJMAH/EWCh9h97PjMTYAJMgAkwgTwJsFDniYh3YAJMgAkwASbgPwIs1P5jz2dmAkyACTABJpAnARbqPBHxDkyACTABJsAE/EeAhdp/7PnMTIAJMAEmwATyJMBCnSci3oEJMAEmwASYgP8IsFD7jz2fmQkwASbABJhAngRYqPNExDswASbABJgAE/AfARZq/7HnMzMBJsAEmAATyJMAC3WeiHgHJsAEmAATYAL+I8BC7T/2fGYmwASYABNgAnkSYKHOExHvwASYABNgAkzAfwRYqP3Hns/MBJgAE2ACTCBPAizUeSLiHZgAE2ACTIAJ+I8AC7X/2POZmQATYAJMgAnkSYCFOk9EvAMTYAJMgAkwAf8RYKH2H3s+MxNgAkyACTCBPAmwUOeJiHdgAkyACTABJuA/AizU/mPPZ2YCTIAJMAEmkCcBFuo8EfEOTIAJMAEmwAT8R4CF2n/s+cxMgAkwASbABPIkwEKdJyLegQkwAZcI2O2wZaihPxgLu14H2O0uFePKQXReqzQdNp0278PtdljSU2E4fgR2oyHv/T24h1UpF3baDfk7ryUtFcZzp2FTqzxoRR5F2e2wG/Qw372D/NpJJZKNpsuJsDy4l8cJPPu13WaD6dZ12HU6zxbsx9JYqP0In0/NBEKawCMBVE4chaztm4Row2bzepVtmRnIitgGzdb1sMpleZ/PbofpahKUk0dDd2A37Eaj918qbDZY1Spkrl2BrMjtIJvz8zFfv4qMhbORtXNLvo/JT7k57kMvW5pMcb7MNcsdbZjjzk9/YZVJoVm3ChlL58OS8uDpL730F71oGU4egyp8CiySdO+3o5fq8WyxLNTPEuG/mQAT8BgB6tHqE+Ig7dUZ2t27YFMp4TWxJlHRZkG7NxLyoX2hi90vRCY/lbGqlNDuiYCsXzfoD8XCrtV67yFvs4LOp9m8FrJBvWA8f8Yx4pAPQ21ZGmGffGgfaKN2gP722kiF3SaEWbc/CpIeHaE7GCv45sNMsYvdbIYp8QIUY4cKsbaScHrxRY1GbYwXzgimmauWwqpUeI9NfiF4aD+/CbWd3mJNJhgMBt6YAV8DHrgG6H6yefFB6Oozx242PRLrTtDtjYRJJoVRr/dsm+v1MKnV0MXsg7RnR+gPx8OWleWUyTaNBto9uyDp1AqGowkwqVQweNhOo14Hk1QiRhgknX+FMfG8U8PJVCF6iTCcOCLqqdsXCbNK6XE7qd4mhRy6WOLZAbq4A46RBqeIArCYQaMA8sFhyFgyFxapBAay3wPX++My9HoYMzNgvHQB8iF9kLF0nuNFy1lbn9if7iO9h9ueynP1HvWbUBPk06dPIzY2FnFxcYiPj+eNGfA14OI1QPfRiRMnoFAonnjcBNav08XqMQAAFblJREFUukOxQlySly3G8ZhoxHvwvj8WE40769cg9ZfvoD9y0OX5SRr21kbtBIno7U3rcTQ2xmN2HoyPx4kD+3Hv94VIa/8zTEkXQb1OVz40Z2w4dQxpLb/D/fWrcWT/Po/ZSc/i47ExuLl8CdK7t4c2Zq8rJv55jNUCy907kP7WFtK5M3AsMgLxsbEeu9cPx8UiccNaSAaFIWPxXNit1j/P7cJvVqsV6enpiI6O9qg2xcTECM1Tq9VOW+U3ob558yZee+01/P3vf8ff/vY33pgBXwNuXgMlS5bEggULnH4I+OwAuw0k1km/NEW3Yv/Byy945t5/+R8voOl/XsP5z6shJWIHrO4uIrLZoInYjvPf1kGz/7yKlzxkZ+F//gOdi72BxCZ1IUmIBy16cudjN5nEwrLrjb5EyyL/wWv/eMEj99BLf/872hUpjOPffokHG9d6ZrjaaoU1LRUPO7bEhPdLoMS//ukRW0k76r7+MrbXqIRro4cAZpM7SMWxSqUSYWFhePHFFz1mY7bGvf/++1i9erXTNvpNqG/cuIFXX30VtWvXxrRp08QDhh4yvDEDvgacvwZ++OEHlC9fHuHh4U4/BHx5gE6twqJ2rbC8XEms/qEJ5k2f7tY9P2/qFCxt2wpbK7yHn98pisvnzsHsYi/1SQ4auQwTvqyFdRXew4q2rTB/5gy37Jw7cQJWN2+KVeVKoF3VSki+eRM0/efWh+bkjUaM+74JIj4qh2Utm2PepIlu2Tlv5kysbPEDVpd/DyM//wwJ0dFumfjkwVazGasnjMWuGpWwsv4XmD9imFu2Lpg/H4u6dMS66hUxrdqHWDRt6pOnc/l3Euru3bujUKFCGDVqlHs2PqFpDRs2xIcffoiVK1c6bVueQk3j6rdv38aZM2eQmJgohgTcvsAAkFAXLlwYHTt2xJ07d6BSqXhjBnwNuHgNTJo0CVWrVg18odbp0P6nn9CqVAkcatYQ9xfMhjI11aV2Vzy4j5T1a3CuZTNMadoIRV99RTyjPCLUGg3qVP0IYRXL4thPTfBw3Sqo0tNcs/PuHdybPwunWjdHv7p1UKVcOSQnJ7sv1OQCZbPh+wbfoE2FcohrVBcpK5ZAcTfZJTuVEgkerFyKGz06Yky9OqhVpbKYmnRaVXI4gIaUJ08Yj69LlUREvVq4N208ZIkXXLJVpVQibf8eJPfrgaXf1seXH1bE9GnTcjizc//OFurXX38dZ8+edc2+59zHgwYNEvfoqlWrnDMIQK5CffnyZQwYMAA//vij2Jo1a4Y+ffpALpc7faJnD8gWanpzCeR5tWft5r+ZQCASoJ509erVg0Koqff/1cfVcSR8OhRjhkCzfhXser1TK3TFwq/IHVCMG4bktSsxZuAAvPzyyx4V6sqVK+PHenVxduZUKMcNg3b3TqcXfpE/N7lgKSaOxNV1a9CtXVvQ8Kcnhfrrr7/Gl598gqPh06GcMAJZW9c77WdNw+jk8kXtIdu1DcPDeqFixYoeF+rx48fjvbffxt7ZM6GaPkEsMDPfv+v0LWU4cRSKMUOh2bgGSydOQOVKlcTIrNMFPeeAbKGmjiTplKc+1Dune9RjQk095oyMDHTq1AnffvstJk+ejHXr1mHZsmWi267RaNy2nYXabYRcABN4TCDYhPrLL7/E8egDYnW2YuRAaDb9AXs+XY3IJYlEUzlxpHCpSrt5A2PHjvWKUNNLReLhBLEanERMtyci30FRyDdas2ENFONHiAVud5IuiSFVbwj1559/jtOHDkIfdwDKSaOQtW1D/nyeRTATg/Dllo8cAF30XmSmPMDIkSO9JtRvv/02ovfsgfHCWahmTkLGknn5D4pitcJw+gQUo4cIH21L6kMsX7YMlQqiUNPQEa0iLV26NNasWSO6/vREIAH3lPsHC/XjZyz/wgTcJhCMQn3y5EnhB6xPiIdsQE9od2519ARzWWRFftnaA3tEz49cqWxqNaRSqVeFmkYWySeX/KyFf3b03txHAGw24b+t2boB8hH9oT+aIOp59+5drwo1DdMKP+v4aAefXVtzD4pCz/MsDXQH9kA2sBe0+6KEuGu1Wu8LdXS0WPFuvHAOqiljHUFRHqbkeh/QinzjxXOgF7uMFYthlaSJUZgVK1YUTKGmeelx48ahRo0aSEpKyhWeq1+yULtKjo9jAn8lEKxCTTWhYW/ye5b26iTE0EaBKp4V60dhLHXxMZAN7Antgd2Pe4y+EGqyk4axtXsjhJ2P/bSfXRBGIp2hEj1Uae8uMJw6+jhIiC+EWtipzYLhyCHIidPunUKMn8eTevy6Q3GQhhH3XY/t9JVQi7anoCiXL0ExapDoWVulEuA57lXkjma6cgnyEQOgXjgLFHo1O9BLgRVqaiiaO27UqJFHx+ipYbI/LNTZJPgnE3CfQDALtai91Qo9iYYQa+opqx4/iOmBbKcIZ8cTIOnaRgQ1obCW2R9fCTWdz6bVighr5GdNQVFEUJVssX4k0iTm6e1/huHUcREjO9tOXwk1nY/iXNM8rqRLa+iop5yZ+efLT3ZPml6OeneGNnI7KChN9seXQi3OabHAfOs6ZP27Q714Lij06JNiTT1pEmkSc9XsqaINskWaji/QQt27d2989dVXuHr1anb7efQnC7VHcXJhBZxA0Av1o/ajcKOysM7I2rEFdoosRiKt10F//AjSfmokImU9m2jDl0JNZtotZtFTJbGmYfvshXD08kBhUtM7tIDh9HHYLZanrkpfCrWwk4aKz5xEWosmDrGml5tHc9IUaUwa1gVZu7Y+ZSP94XOhppNarbA8uC8CzVAEM9GzphcgqxXGxAuQjxwE1azJsJuMf7G3wAo1RQ2bP38+ypQpAzGP9Oww1F9QOf8PFmrnmfERTCAnAqEi1CRuNKwsH9QLmo1/gIbBDUcPIb19CyHS2aL4JAdfCzWdm+wkUaYRAFqAZVPIod21DdIeHWA4efSpHmG2rb4WamEnBUU5ewqSji0dsdZprn1fpJiTpsQlz4uM5hehJmMpKErqQ8jCuogIY5a0hyKgi2L0YKjnzcgxJGyBFWrydyPf6bJly6Jr1664cuUK6H9ZWVl4+PAhdDSsYjBgyJAhYhW4TJaPDDXZV+ujnyzUzwDhP5mAGwRCRagJQfacNfWi5EP6QtbnN+j2737cc30Wkz+EmmwQC9soAciQPpANDBMLzQzHD+e4KtwfQi160CajeHmgoWXFiAGQD+vnSOihfX4sdL8JNUG1WmG+cwuKYf2gGDUYMgoLunS+Iwta9hTDMxdAgRVq4kArv9evXw/y0aPoYfSzbt26wmUrNTUVJM7vvvuu8K+mcKDOflionSXG+zOBnAmEklBTLWnoM+P3BXjY+EvIh/UXOZtzqr2/hJrssTxMgXLSaGGnatYU0bPOyU6/CPUjY2iOWjV7Kh42+QrKaeNFbumc7PSrUJNRFguytm1E2i/fQdqnq0hb+ZfFcE8YX6CFmjhQ8PCDBw9iyZIlwpl87ty52Lt3r+hZ08pwejhs27YN5CDu7IeF2llivD8TyJlAKAk1LYTS7t8NxfjhUM2ZJtxxKK/x84a9iYi/hJpSamq2rIdi3HCR/5gCcOQWFMVvQk3D9PsiHSum584QXDWb1+UYFMXfQm24cFYEM1HNpQAuI6FeNBu5BUUp8EKd/Vig1FzUeDTcnR0+lH5S4BOj0fj4f9n75+cnC3V+KPE+TCB/BEJFqEmMKbWiYsJIESnLfC9ZBAuRD++PLBKXzIw/Vy8/QuNzoaZV0zqtsE8+eohIAWm+e0e4lpGPL6XypJXKT65MJlN9LtTZC8di9oH4Uf5qy727wl4KFpO1feNjF7cnrzJ/CTXN+1NGMXpBy1i+SAyBG8+ddgRFWTw3x6AoLNRPtp6Hf2eh9jBQLq5AEwgFobYbDSJvtXzkQLEa2apwhCqmnistMJP16QptxDbYVMqnxNqnQm23iUVNtJBMNrg3dAdjHwcVsaqU0NKc9aBe0MfuFy5lT4q1T4WaXiaI25FDkPXrjqwdmx/3oEVQlEOxYqRCG7FVBGd50k5/CLVwwbp2GYqxQ6GePwuWtFTRxrTYzZR4AcqJoxwRzNIePtX2dNOzUHvx0cdC7UW4XHSBIxDUQv2o50erpaV9fxM9PxK9Jz/0INcfPuhYZb03QqwGz5639JlQk590Zqbo8Ut+ayteKkj0nvxQj5/EWtq1DQxHDjqCjTxaBOUzoX4k0uTHLe3zGzSb1z4OZpJtq52Copw44nj5oWAn5Lr1yLvH10ItRPrWddGTVk4dB/GC9qSnkcUM87UrYhGc8LN+JigKC3V2q3rhJwu1F6BykQWWQNAKtRBpPQznTiO9U0toI3c8dzjW0bB2IY4iKErkdsd+drtv5qhJ/DSZYtg4veMv0B+KfSqYyZMXHg3fU6QvSZdfRYQwEkXqsfpKqIXf+YkjkPbrhsz1awDr0/7c2baSnYZTxyBp9xN0+yIfTyv4UqhFj/n6VTHVoZg06i/BTLJtpQVmtBqcfOwzKCjKE2LNQv2Ykud/YaH2PFMuseASCFahpgAWxvOnxQrfrIjtYu43r1YUw+C9uyBr6wYRgUsqkXg91jeJny5mr8Of+2DMc/2kn7LbZnscwUx/MEa4bPlCqIUfOgWNESK9+i/z5E/ZSK5w5Gct+DeBjkYqKOFJVpZPYn3Ty4vxapKjJz1xFGw63bPmPf03+VmnpYoXIPWiOY89AVion8bk0b9YqD2Kkwsr4ASCUahPJCQI/15Jt3bI2rVNiO6Tc6U5NSmFu6RhcEqQQSkyJXfvelWok86cFj1kchXSxVEyiT/DbeZkI/2fXkIonCiJJoXxTL5+zatJOc6cOgVd3H7Ih/WFZtPaHHv8T9lMIxpmE4xnTkDarZ0IJ6pJfegToTYmJUIxcZSIOEZJT/LT9tkRzOQDejiCojx8wHPUTzWoh/9gofYwUC6uQBMINqH+4tMaODhjCmSDeonV02KuN4eAFs9rWFp1rT9yEBS16tbMKRgzeLBX0lx+3+AbnJw8DvLh/aCL3e8Ymn2eQTn8T/RQ90VCMbw/Ls+fjW4dOnglH3XtmjWRMG0S5KMGQbNtA6wZ6hwsev6/aSEfrRGQD+4NydqVGN6rp1fTXO6ePVPk6FYvnA2KQJY9P/586575LwVFuXVDtD2lyFwyZlTBzJ71DBav/ElC/eqrr6JJkybYtWsX4uLieGMGfA24eA306NFDPFhJsAP5Q1ENf23eHG1Kl8SBRnWxv18vxGzb6lK7x+zahejJExDTpD4W1PscRV99BYkXL4pgTe4yINfTmh9VwcAPy2E/2TlyKGJ27nDNzu3bcGDEYMQ2/QajPq2GKuXK4s6dOy65tT5bL0o73ODrr9GlQllE1q2F2KEDEL15k0t2xkZFYe+EMTjZujkmflYddapUFumOnz2nq39TdMvx48fj21Ilsf2rmjjUozP2r1yOuJgY5+09cAD75s/B8fa/YFmdT9Ggwgci1oertj15HMUFoaRUpE9r16513rYc7uE2bdqIF4qVK1c+ebp8/f5f+drLCztRNLPChQvjjTfeEMZXq1YNvDEDvgZcuwaKFSsm8sdTjP5A/ujUaixp3xrh7xVDrxJFUb3Uu27d99XLlcOPbxfFkvffwZD3S+Ly6dOwmPI3NJ0bp0yZDJO/+hzzSxVHu3eKonqZ0m7Z+XGZ0uhQohgWlnkboz6rjrvXr3tEqGlOevJ332JlxdLoVPxN1CA7q1Z12daq5cqiZcniCC9dHDO/qo2TMdG5YXLqO5vVig3jx2BVtYoY8vYb+PK9kqhapbLrtlb6EA1LFMeUd4ti/ieVsXbqZKfsyWlnlUqFPn364F//+hfKly/vsn3PPsuKFCkiylu1alVOp87x/34TarlcLuZBevbsCeoN8MYM+Bpw7xoYPXq0SKKT493u5y9ozjYzPgbJA3vhQO/umNi3j0fu+2G9w7B5QB9c69QKKcsWwfK8fNb5rTvN2RoNUEdsx+2enbCzby+M7tPbI3aO6dMbEf164cZvbZG+eT3sBkP+5mVzsJ2O1x9NwLXOrZEwuD/G9emNnh54lg4NC8PWAX1ws89vSF48L5dV+DkY9px/i9XdN67hRr/uuDK0H2b27Y3eHnj29+3ZEysH9sXlPt1wZcQgWFLuP+fszv2Lom7u3r0blEHS08+kCRMm4OLFi84ZBMBvQk2RzWgoxGKx8MYM+Bpw8xqg2Px0P2VHDnT6SeDNAx4tWCK/XtnQvsjcvA6mtFSPtrmZXKcS4iHr3cWRcMIVsRb+x1ro4mMgpSAh+6JgUsg9aieVl/VogZk+PhrZrlvO4hf5ps+chKx/D2SuXQmTTCqG/D31PDVnqKFLiBML9kSQGfIXt9ucNVPsTyvLzbdvQjllDJTTxsF4/x7MRqPnuJKbGQVFGTvMscAsPc25Oe8cakX3FG0eY/roHs3hdLn+229CnatV/CUTYAKhQUD0UI0wXjwPae+u0GzZ4MiE5IXaUa/NERSlsyOl4zMRzHI9JYl0lkZE8pJ0agXtvijYNE8HM8n1eCe+FAvM9kaK3MvPBkXJTzHkKma8cE4sxMtYsdgRAS0/Bzq5j12nFQkxpD07iFXvzwvfmleRQqSTb0M5bQLkowc72v7JYCZ5FZDf78nP+uZ1sRiOYoM/6Wed3yICeT8W6kBuHbaNCQQ5ARG/+dZ1pLf/WbgM2dQqr9dInxAPaVhnR7jRZyKH5XRyio5lOH0cQqT3RDiGpXPa2QP/F65beyIg6dJa5NsWCUfyUa7dZoPxIol0GDKWLQRs1nwc5fouNLxuPH0C6S2/Ey5mFJbUmY/53l0Rq5tioAuhd2JlvzPnEftaLbDcS4a0W1uICGYUgtab53PaQNcPYKF2nR0fyQSYQB4EqFeaFbENmo1r/hLGMo9DXf/abne4bo0bJnrY+SnIKpNCs2UdsqJ2eGTYND/nJBHR7okQoTFNly/l6xDiqYvei8w/loNegnzxoZEK48WzItCI6ea1/POxWWE4cwKUBcvqgxc0wcJmFYFQJN3bQxcfna8AOr5g6O45WKjdJcjHMwEmkDMBm00E3qA5VV/2bmhBmFUpdwRRydm6P7+h+X293pFK88//ev03u0EPq1wqFrDl62TE02jwrQCJNQZmWCXpIpJZvux8tBMNfduysvIv7s4UntO+NpsQa2Lry2suJ3M88X8Wak9Q5DKYABMIPAI07BkMQ5/CRnvg8XvWomBgmW1zMNmabXMuP1moc4HDXzEBJsAEmAAT8DcBFmp/twCfnwkwASbABJhALgRYqHOBw18xASbABJgAE/A3ARZqf7cAn58JMAEmwASYQC4EWKhzgcNfMQEmwASYABPwNwEWan+3AJ+fCTABJsAEmEAuBFioc4HDXzEBJsAEmAAT8DcBFmp/twCfnwkwASbABJhALgT+P+ie+E3107f/AAAAAElFTkSuQmCC[/img][br][br]For each diagram, write a numerical subtraction expression and determine the value of the expression.
Express each subtraction in words.
[math]0.05-0.02[/math]
[math]0.024-0.003[/math]
[math]1.26-0.14[/math]
Find each difference by drawing a diagram and by calculating with numbers. Make sure the answers from both methods match. If not, check your diagram and your numerical calculation.
[math]0.05-0.02[/math]
[math]0.024-0.003[/math]
[math]1.26-0.14[/math]
IM 6.5.2 Practice: Using Diagrams to Represent Addition and Subtraction
Use the given key to answer the questions.[br][br][img]data:image/png;base64,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[/img][br][br]What number does this diagram represent?[br][img]data:image/png;base64,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[/img]
Draw a diagram that represents 0.216.
Draw a diagram that represents 0.304.
Here are diagrams that represent 0.137 and 0.284.
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PPhpyRAAiRAAiRAAiRAAiSQpxNA6PN09XBxJEACJEACJEACJEACJJBzAgf955dfjAcZwAAMwAAMwAAMwAAMwICfDBz04Q//Nh5kAAMwAAMwAAMwAAMwAAN+MnDQu9/9y3iQAQzAAAzAAAzAAAzAAAz4yQBCz4SGCR0MwAAMwAAMwAAMwIDHDCD0Hlces2g/Z9HUG/UGAzAAAzAAAzCQTgYQeoSeGTkMwAAMwAAMwAAMwIDHDCD0HldeOmd2nIuVAhiAARiAARiAARjwkwGEHqFnRg4DMAADMAADMAADMOAxAwi9x5XHLNrPWTT1Rr3BAAzAAAzAAAykkwGEHqFnRg4DMAADMAADMAADMOAxAwi9x5WXzpkd52KlAAZgAAZgAAZgAAb8ZAChR+iZkcMADMAADMAADMAADHjMAELvceUxi/ZzFk29UW8wAAMwAAMwAAPpZAChR+iZkcMADMAADMAADMAADHjMAELvceWlc2bHuVgpgAEYgAEYgAEYgAE/GUDoEXpm5DAAAzAAAzAAAzAAAx4zgNB7XHnMov2cRVNv1BsMwAAMwAAMwEA6GUDoEXpm5DAAAzAAAzAAAzAAAx4zgNB7XHnpnNlxLlYKYAAGYAAGYAAGYMBPBhB6hJ4ZOQzAAAzAAAzAAAzAgMcMIPQeVx6zaD9n0dQb9QYDMAADMAADMJBOBhB6hJ4ZOQzAAAzAAAzAAAzAgMcMIPQeV146Z3aci5UCGIABGIABGIABGPCTAYQeoWdGDgMwAAMwAAMwAAMw4DEDCL3Hlccs2s9ZNPVGvcEADMAADMAADKSTAYQeoWdGDgMwAAMwAAMwAAMw4DEDuQr9g8uetMpVq1nLNu2sdftTeJABDCSUgVZt21vVY2vYPQ8+6rTTf2TlM1bpmKrO+5wTTmxtzVq0so073nFanjE332Z16jdw3m4aNWtuA4YMd1oWrSb16N3Xmp7Q0ml5Tmp3stWoXcdunzLDeXnSuULGudK74vritp3WuPkJprbq0j9atm5rR1c5xhavWuuUt+nzFli1GjXtxLbtnZanecsTreNp3WzPlz84Lc/wv11hDRo3cVoW1Xv9ho1s5N/HOC2L2u7cRcutSrXq1sqx7x7f6iQ7qV0He/29T9JaplyFfvr9D1mhQoWCTnz43y43HmQAA8lkoPfA86xI0aJ2213T09oJZZegWQ8tsgIFCtgZZ5/jtL9p06Gjla9wlD3/+g6n5Rk0/OLgdYaNcstNrbr1rH2nLk7Lorpq3rKVHdekqdO6GTTsYitZurRd9o/rnJcnO3/8O71S/mfyXPPqG1amXDlr17GzU95OP6uX5cuXz+YuWuaUt5vunGzFihe3PoOGOC2PFiq0iLDri++dlqdbz15WtXoNp2WRb2iB56y+A5yWRZxOmjXXCh9yiPXsO8BpmTRh0MRh894P0lqmXIVegB9apIgtW7M+rS/8Zxo5f5t3OlzqIjl1ocE1o2w5mzL7Aad9wfxlK4NFBNerZeOnzbSKlavYhu27nZbn0tHXBncCXLcVTbi69ezttCwqgyZCw0Zd5vR1Xtv3cbBCf8P4iU5fx3WdcP4/1z+u27rdyh1ZwUZcOdoWPb3W2UOcSegfXP6kU97GTbvHSmWUsWlzH3RWFuV0zqDBdlzjprbbsdD3GjDIWpzUxmlZVJ4mx7ew/kOGOa0btVUtYBctVtzuuHuW0zKdf+EIq16zlm1956O0lgmh93i/FIPFnxssyC9afgh9tLxCvhD66Lkh9NEzC3k7kJ4fX7fBih92uBUoWDCY5Gu3gItHwYIFA6G/c8a9aRWs7HUxdORlwesUdFSOMBvd4dTdx52ffeu0PA0aNbH8+fM7qZOwLHrWa2hLYfY80/3vq28c+//145g31U/pjDK2ccfetJYJoUfo0wpUuhsY58s7AztCH68uEProuSH00TM7EPtKCenUufNtzsKlpjt3rh5zFy+3sZOn2Rvvf+Z0PHx1z/s2fvpMu3/J487Koozue+Qxu/+xx23ftz87Lc8zG7fYtHkLnJZF5Zk6Z75p/HHN+NZ9H9ntU2fYvMdWOC3T7EeX2L0PL7Y9X/2Y1jIh9Ah9WoFy3eA4/1830CP08bJH6KPnhtBHz4y+kcxgINkMIPQIPUIPAykxgNDHGywQ+ui5IfTRM0PmyAwGks0AQo/MpSRzdBTJ7ihU/wh9PAYQ+ui5IfTRM6OPJjMYSDYDCD1Cj9DDQEoMIPTxBguEPnpuCH30zJA5MoOBZDOA0CNzKckcHUWyOwrVP0IfjwGEPnpuCH30zOijyQwGks0AQo/QI/QwkBIDCH28wQKhj54bQh89M2SOzGAg2Qwg9MhcSjJHR5HsjkL1j9DHYwChj54bQh89M/poMoOBZDOA0CP0CD0MpMQAQh9vsEDoo+eG0EfPDJkjMxhINgMIPTKXkszRUSS7o1D9I/TxGEDoo+eG0EfPjD6azGAg2Qwg9Ag9Qg8DKTGA0McbLBD66Lkh9NEzQ+bIDAaSzQBCj8ylJHN0FMnuKFT/CH08BhD66Lkh9NEzo48mMxhINgMIPUKP0MNASgwg9PEGC4Q+em4IffTMkDkyg4FkM4DQI3MpyRwdRbI7CtU/Qh+PAYQ+em4IffTM6KPJDAaSzQBCj9Aj9DCQEgMIfbzBAqGPnhtCHz0zZI7MYCDZDCD0yFxKMkdHkeyOQvWP0MdjAKGPnhtCHz0z+mgyg4FkM4DQI/QIPQykxABCH2+wQOij54bQR88MmSMzGEg2Awg9MpeSzNFRJLujUP0j9PEYQOij54bQR8+MPprMYCDZDCD0CD1CDwMpMYDQxxssEProuSH00TND5sgMBpLNAEKPzKUkc3QUye4oVP8IfTwGEProuSH00TOjjyYzGEg2Awg9Qo/Qw0BKDCD08QYLhD56bgh99MyQOTKDgWQzkKvQz1641A459FC7f8njtuWdD3mQAQwklIElq9dZ6YwyNvneeSlNAOIOLg8secIKFipkcxYudcra9bdPsIqVKtuGN3c7Lc/Iq8ZYo2bNbctet/1n9159rOuZZzsti+q0dftTbODQC53WzXNb3rRqNWradbff6bw8cTnl79zL0zvf/GSbdu6zzXs+cMrb5r0fBP3Anq9+dMrbri++t5fe2uO8L3h1z/vBa7hmdPtHX9qmne86rRt5pxh46+OvnNaN66z2x/lzFfrb7ppu+fPnt4qVq9ixtWrzIAMYSCgDlY+pFoj2ldfd5LRjnXDPff/f51Sq7JS1suWPtJKlM+zZTa85LU+nrmfYoUWKOi2L+ubDjyhhDZs2c1oWDUo169S1EqVKOy1P1WNrWOFDDrH+g4c6L8/+GGh5jXjyr7uC1Y6tacdUP9Y5b+oL5ixa5pS3m+6YbGXKlbPqNWo5LU+VatWtyfEtTBMIl+xpEeGoSpWclkV9W4Wjj7az+w10WhaXOe2vc+cq9Bvf2ms9+w20a24dbzfeMYkHGcBAQhm47rY77JxBg+2F13c47VhffnufndV3gF0zdpxT1kbfNNYuueIq5ys/K1942QZfPNJpWdQ3j7pqjM2Y/4jTutHANH7aTLv8mhuclueGcRODuwCrX3Y72dpfAy2vE0/o127eZpp49zinn1PeBg2/2PLlyxfsRHBZV7dOnhZMvP929TVOy9P+1C5W77hGttux0J95Tj+r2+A4p2VR31azdl0759zznfdtLut+f5w7V6HfHxfBa8Tr7MiN3GAABmAABg5UBrT1SkLff8gwmzL7AWePEVeODoT+gaVPOJXG26bcbSVKlgq2krksz2k9elr9ho2dC70WXho2be6sXsKM6h3X0PqcN8Rp3RwIbQih5w2RNBIYgAEYgAEYyHMMPP3SZit/1FFWKqOMZZQt5+xRukwZK1qsmN39wENOM9B2xeKHHWYZZco6K4tyKlU6w2rVqWe7Pv/OaXnannKqHVGypNOyqDxHlChhHbp0dVoWhJ4OEMBgAAZgAAZgAAYcMLDnyx/siRc22jMvbw0+Nld76l08Vm96zRavWmtvf/aN03rUm0iXPvuCPfvK607KEWazauOW4DX2ffuz0/K8sutd05bC8HVdPT/x/MbgjdEHgnS7LAMr9A46IZcVxrm5vQ4DMAADMAADMAADMJCVAYQeoXc6g88KG1/T+cAADMAADMAADMBA+hlA6BF6hB4GYAAGYAAGYAAGYMBjBhB6jyuPGW76Z7hkSqYwAAMwAAMwAAO+MYDQI/TMyGEABmAABmAABmAABjxmAKH3uPJ8mz1yvax4wAAMwAAMwAAMwED6GUDoEXpm5DAAAzAAAzAAAzAAAx4zgNB7XHnMcNM/wyVTMoUBGIABGIABGPCNAYQeoWdGDgMwAAMwAAMwAAMw4DEDCL3Hlefb7JHrZcUDBmAABmAABmAABtLPAEKP0DMjhwEYgAEYgAEYgAEY8JgBhN7jymOGm/4ZLpmSKQzAAAzAAAzAgG8MIPQIPTNyGIABGIABGIABGIABjxlA6D2uPN9mj1wvKx4wAAMwAAMwAAMwkH4GEHqEnhk5DMAADMAADMAADMCAxwwg9B5XHjPc9M9wyZRMYQAGYAAGYAAGfGMAoUfomZHDAAzAAAzAAAzAAAx4zABC73Hl+TZ75HpZ8YABGIABGIABGICB9DOA0CP0zMhhAAZgAAZgAAZgAAY8ZgCh97jymOGmf4ZLpmQKAzAAAzAAAzDgGwMIPULPjBwGYAAGYAAGYAAGYMBjBg765Md/Gw8ygAEYgAEYgAEYgAEYgAE/GTjIOEiABEiABEiABEiABEiABLxNAKH3tuq4cBIgARIgARIgARIgARIwQ+ihgARIgARIgARIgARIgAQ8TgCh97jyuHQSIAESIAESIAESIAESQOhhgARIgARIgARIgARIgAQ8TgCh97jyuHQSIAESIAESIAESIAESQOhhgARIgARIgARIgARIgAQ8TgCh97jyuHQSIAESIAESIAESIAESQOhhgARIgARIgARIgARIgAQ8TgCh97jyuHQSIAESIAESIAESIAESQOhhgARIgARIgARIgARIgAQ8TgCh97jyuHQSIAESIAESIAESIAESQOhhgARIgARIgARIgARIgAQ8TgCh97jyuHQSIAESIAESIAESIAESQOhhgARIgARIgARIgARIgAQ8TgCh97jyuHQSIAESIAESIAESIAESQOhhgARIgARIgARIgARIgAQ8TgCh97jyuHQSIAESIAESIAESIAESQOhhgARIgARIgARIgARIgAQ8TgCh97jyuHQSIAESIAESIAESIAESQOhhgARIgARIgARIgARIgAQ8TgCh97jyuHQSIAESIAESIAESIAESQOhhgARIgARIgARIgARIgAQ8TgCh97jyuHQSIAESIAESIAESIAESQOhhgARIgARIgARIgARIgAQ8TuCgn//zi/EgAxiAARiAARiAARiAARjwk4GD3v3uX8aDDGAABmAABmAABmAABmDATwYQeiY0TOhgAAZgAAZgAAZgAAY8ZgCh97jymEX7OYum3qg3GIABGIABGICBdDKA0CP0zMhhAAZgAAZgAAZgAAY8ZgCh97jy0jmz41ysFMAADMAADMAADMCAnwwg9Ag9M3IYgAEYgAEYgAEYgAGPGUDoPa48ZtF+zqKpN+oNBmAABmAABmAgnQwg9Ag9M3IYgAEYgAEYgAEYgAGPGUDoPa68dM7sOBcrBTAAAzAAAzAAAzDgJwMIPULPjBwGYAAGYAAGYAAGYMBjBhB6jyuPWbSfs2jqjXqDARiAARiAARhIJwMIPULPjBwGYAAGYAAGYAAGYMBjBhB6jysvnTM7zsVKAQzAAAzAAAzAAAz4yQBCj9AzI4cBGIABGIABGIABGPCYAYTe48pjFu3nLJp6o95gAAZgAAZgAAbSyQBCj9AzI4cBGIABGIABGIABGPCYAYTe48pL58yOc7FSAAMwAAMwAAMwAAN+MoDQI/TMyGEABmAABmAABmAABjxmAKH3uPKYRfs5i6beqDcYgAEYgAEYgNs/qp0AABMBSURBVIF0MoDQI/TMyGEABmAABmAABmAABjxmAKH3uPLSObPjXKwUwAAMwAAMwAAMwICfDCD0CD0zchiAARiAARiAARiAAY8ZQOg9rjxm0X7Ooqk36g0GYAAGYAAGYCCdDCD0CD0zchiAARiAARiAARiAAY8ZQOg9rrx0zuw4FysFMAADMAADMAADMOAnA7kK/aKn19ixtWrbKV1Ot87devAgAxhIKAMdT+tmtevVt3mLVzhdxVn67PNWvWYtO6VLV6este/U2U5sd7K9sus9p+UZO2maNWrW3GlZ1De3bN3Who263GlZNND3PW+ItW7fwWl5Op1+htVv2NimzH7AeXkmzpxjDRo3sVNP7+60TCe1O9kGXDDceXmGXDzKWrVp57Qsp3brYQ2bNrPbp8xwWp6NO/Zai5PamNqqS//o0LmrVatR01Y8t8FpeWY/usTq1G9gHbt2c1qetqd0sm49e9uer350Wh7EP2+Jf65CP3XOfCtYqJCpAfcfMowHGcBAQhnQAHFokSJ2y8QpTgeJex581AoUKGCdup7hlDWJQrkjK9i6195yWp7+g4damXLlrf9gt/1n9Rq1rE2Hjk7LogG8yfEtrE7945zWzdn9z7UjSpa0UVeNcV6eiy670kqWLm29B57ntEy16ta35i1PdF4eTVJr1KrjtCx9z7vAMsqWtUHDL3ZanmdfeT14nZZt2jktjxYs8+XLZxJul5J6/bgJVrRYMeveq4/T8jRs0sxq1a1nu7743ml5XGbFuaNPFnIV+rmLlgWD+LI16wGD7TkwkGAG1rz6hmWULed81XT+spVWqFAhW7xqrVPexk+baRUrV7EN23c7fZ1LR19rzVq0cvoaGvwkpJp0uR4INWkYNuoyp6/z2r6PrUbtOnbD+IlOX0dZXTN2vNVtcJy9+eEXTl9r8EUj7eRTuzh9DZWnS/czrd/goU5fZ/eXP1jjZsfbldfe6PR1ntm4xUplZAR3azTBd/VQ+5TQz1zwqNPyjL7pVjvk0EPtpPYdnJVFGekOpx67Pv/OaXlc9zWcP5rUI/QJFjQaS7TGkvS8EPp4vCD00XND6KNnFvZPB5LQb9n7YbA9pdeAc23g0AudPc45d7A1aNTE1r66zakAL1n9fHCXpt/5Q52VRTmd1bd/cP69X//TaXlC5niO317TmR1Cj9DT4GEgJQYQ+nidNkIfPTeEPnpmoRgcSEIflonn+DyQXXKyQ+iRuZRkjk4hOZ3CH9U1Qh+PAYQ+em4IffTMwnaL0MfPLsyQZzL0kQGEHqFH6GEgJQYQ+niDHEIfPTeEPnpmoYAg9PGzCzPkmQx9ZAChR+ZSkjkf4eaa09spI/Tx8kToo+eG0EfPLOzvEPr42YUZ8kyGPjKA0CP0CD0MpMQAQh9vkEPoo+eG0EfPLBQQhD5+dmGGPJOhjwwg9MhcSjLnI9xcc3o7ZYQ+Xp4IffTcEPromYX9HUIfP7swQ57J0EcGEHqEHqGHgZQYQOjjDXIIffTcEPromYUCgtDHzy7MkGcy9JEBhB6ZS0nmfISba05vp4zQx8sToY+eG0IfPbOwv0Po42cXZsgzGfrIAEKP0CP0MJASAwh9vEEOoY+eG0IfPbNQQBD6+NmFGfJMhj4ygNAjcynJnI9wc83p7ZQR+nh5IvTRc0Poo2cW9ncIffzswgx5JkMfGUDoEXqEHgZSYgChjzfIIfTRc0Poo2cWCghCHz+7MEOeydBHBhB6ZC4lmfMRbq45vZ0yQh8vT4Q+em4IffTMwv4OoY+fXZghz2ToIwMIPUKP0MNASgwg9PEGOYQ+em4IffTMQgFB6ONnF2bIMxn6yABCj8ylJHM+ws01p7dTRujj5YnQR88NoY+eWdjfIfTxswsz5JkMfWQAoUfoEXoYSIkBhD7eIIfQR88NoY+eWSggCH387MIMeSZDHxlA6JG5lGTOR7i55vR2ygh9vDwR+ui5IfTRMwv7O4Q+fnZhhjyToY8MIPQIPUIPAykxgNDHG+QQ+ui5IfTRMwsFBKGPn12YIc9k6CMDCD0yl5LM+Qg315zeThmhj5cnQh89N4Q+emZhf4fQx88uzJBnMvSRAYQeoUfoYSAlBhD6eIMcQh89N4Q+emahgCD08bMLM+SZDH1kAKFH5lKSOR/h5prT2ykj9PHyROij54bQR88s7O8Q+vjZhRnyTIY+MoDQI/QIPQykxABCH2+QQ+ij54bQR88sFBCEPn52YYY8k6GPDOQq9HMWLrNDixSxRU+vsV2ff8eDDGAgoQw8veFVyyhb1u6afX9KE4C4HeL8pSutUKFC9vATq5yyduvkaVaxchXbsH230/L87eprrOkJLWynY27O7jfQTj+rl9OyqE7bnNzRhlw8ymndbNr5rh1bq7ZdP26C8/L8Y+w4q1OvgW1550OnZRo07GJr36mL8/J0PuNM6zNosNOybP/oS2vYtJldcc0NTsuz79uf7e3PvnHedtQ2d3zyte375ien5Xnnm59sx6dfO60bedrOz78NXiNuH8zf+TmhyVXox027xwoUKGA1atUJGrAaMQ8ygIHkMVC7bn0rdPDBdvWNY50OepNmzbX8+fMHQueSs6OrHGOlMsrYmlded1qe03qcZcWKH+a831RZmhzfwmlZNNDXrtfAypQr77Q89Rs2ChaSzh12kfPy9D3vAitStKg1aNTYaZkyypazesc1dF6eRk2bW+kyZZ2W5bjGTa1oseLWvXcfp+VZt3W71anfIMjNZV9Qv2FjK3dkBXtw+ZNOyzN++kw76uhKpvxclqdO/ePsxLbtbfcX3zstD+Kft8Q/V6F/cdtO69D5NPvb6Gvt79ffzIMMYCChDFw25jo7tVt3W7t5m9NB4qXte4KVTK1su+xzLrniahtwwXDTaqPLgWnpsy9Yz34DnJZFOQ0afrFNnDnHaVmU0w3jJtrQkZc6Lc8V195o3c7ubU+uf8V5eVa+8LJ179XHrrz2RqdlGnLJKLtlwhTn5blj+iw7/6IRTsty5XU32Zl9+tvytS86LY/6mrLly1uX7mc5LU/vgedbvnz5bN5jK5yWZ+ykqVb88MPtghFu28+J7U4OJkEIfd4SbpfjjM6dq9C7vgDOnyzgqG/qGwZgAAZgIBUGntvyZrByri1esx9d6uyhCbGEfv6ylU6F/vapM6xkqdJ2+5QZzsqinHqc088aNGrCCn3C3h+H0CeswlPpRPkdBlsYgAEYgIG/mgHdPSlVOsMOLVI02BalrVGuHtpOOPneeU6FfsSVo+3gwoWdlSHMRu97rHRM1WAv/V9dh7z+/utHEHqE3mkHRmPef42ZrMkaBmDgQGJg1xff24IVT9mS1etsxXMbnD20LW7WQ4vsrY+/cjoevv7eJ6YPGlm2Zr2zsiinxaueC15Dbyo+kHigLDn3bwg9Qk+DhwEYgAEYgAEYgAEY8JgBhN7jymO2mvNslXzIBwZgAAZgAAZgIAkMIPQIPTNyGIABGIABGIABGIABjxlA6D2uvCTMOCkjKyswAAMwAAMwAAMwkDMDCD1Cz4wcBmAABmAABmAABmDAYwYQeo8rj9lqzrNV8iEfGIABGIABGICBJDCA0CP0zMhhAAZgAAZgAAZgAAY8ZgCh97jykjDjpIysrMAADMAADMAADMBAzgwg9Ag9M3IYgAEYgAEYgAEYgAGPGUDoPa48Zqs5z1bJh3xgAAZgAAZgAAaSwABCj9AzI4cBGIABGIABGIABGPCYAYTe48pLwoyTMrKyAgMwAAMwAAMwAAM5M4DQI/TMyGEABmAABmAABmAABjxmAKH3uPKYreY8WyUf8oEBGIABGIABGEgCAwg9Qs+MHAZgAAZgAAZgAAZgwGMGEHqPKy8JM07KyMoKDMAADMAADMAADOTMAEKP0DMjhwEYgAEYgAEYgAEY8JgBhN7jymO2mvNslXzIBwZgAAZgAAZgIAkMIPQIPTNyGIABGIABGIABGIABjxlA6D2uvCTMOCkjKyswAAMwAAMwAAMwkDMDuQr9259+Y8vXvmhrN2+zdVu38yADGEgoA89tedMeX7fB3vr4K6erOG9/9q0tX7veeZ+z5tU3bNVLm23vVz86Lc8b739qT67f5LzdPLNxi23csddpWTSgrn9jp63e9JrT8jy3dbs98cJGe/PDz52XB0nIWRLIh3xgwA8GchX6CffcZ8UPO8zKlj/Syh1ZgQcZwEBCGVAfcNjhR9i1t453KllT58y3YvuhzylTrrxVrFwlmDi4HLB6nNPPSpQs5bzdlMooY63atHNaN8qpcbPjLaNsWeflObxECbtgxKXOy+Oy7jm3HyJEPVFPBwIDuQr9zAUL7eDChe3S0dfapFlzeZABDCSUgdE33RoI/R13z3IqWXMWLrUCBQvayL+Pccpa74HnWYWKRwcrzi4782GjLrOq1WvYpJlznJbnhBNbW6euZzitG+XUonVba9exs9Oy3DJxqpWvcJRdfeNY5+VxWfecG1GEARjYXwzkKvRzFy2zQ4sUsWVr1tOxst8eBhLMgLaoZJQtZ1NmP+CUg/nLVlqhQoVs8aq1Tl9n/LSZwQr9hu27nb6OFkOatWjl9DU0YGiC0q1nb+ev06ZDR9MkxeUg9dq+j61G7Tp2w/iJTl/HZRk4NyIHAzCwPxlA6BMsaPsTNF7L/44NoY9Xhwh99NwQ+uiZ0ceSGQwkmwGEHqFnBQwGUmIAoY83WCD00XND6KNnhsyRGQwkmwGEHplLSeboKJLdUaj+Efp4DCD00XND6KNnRh9NZjCQbAYQeoQeoYeBlBhA6OMNFgh99NwQ+uiZIXNkBgPJZgChR+ZSkjk6imR3FKp/hD4eAwh99NwQ+uiZ0UeTGQwkmwGEHqFH6GEgJQYQ+niDBUIfPTeEPnpmyByZwUCyGUDokbmUZI6OItkdheofoY/HAEIfPTeEPnpm9NFkBgPJZgChR+gRehhIiQGEPt5ggdBHzw2hj54ZMkdmMJBsBhB6ZC4lmaOjSHZHofpH6OMxgNBHzw2hj54ZfTSZwUCyGUDoEXqEHgZSYgChjzdYIPTRc0Poo2eGzJEZDCSbAYQemUtJ5ugokt1RqP4R+ngMIPTRc0Poo2dGH01mMJBsBhB6hB6hh4GUGEDo4w0WCH303BD66Jkhc2QGA8lmAKFH5lKSOTqKZHcUqn+EPh4DCH303BD66JnRR5MZDCSbAYQeoUfoYSAlBhD6eIMFQh89N4Q+embIHJnBQLIZQOiRuZRkjo4i2R2F6h+hj8cAQh89N4Q+emb00WQGA8lmAKFH6BF6GEiJAYQ+3mCB0EfPDaGPnhkyR2YwkGwGEHpkLiWZo6NIdkeh+kfo4zGA0EfPDaGPnhl9NJnBQLIZQOgReoQeBlJiAKGPN1gg9NFzQ+ijZ4bMkRkMJJsBhB6ZS0nm6CiS3VGo/hH6eAwg9NFzQ+ijZ0YfTWYwkGwGEHqEHqGHgZQYQOjjDRYIffTcEPromSFzZAYDyWYAoUfmUpI5OopkdxSqf4Q+HgMIffTcEPromdFHkxkMJJsBhB6hR+hhICUGEPp4gwVCHz03hD56ZsgcmcFAshnIVejvfXixFS58iN1851320ONP8yADGEgoA3fOuNeOKFHSJtwzO6UJQNzBZe7i5VawYEG7YdxEp6wNHXmpVTi6kr24bafT8lx46ZVWq049W7DCbf/ZruOp1vmMHk7Lojpt1aaddT3zbKd1M3PBQqtYqbKNufk25+WJyyl/l2x5ov6p/7zGQK5Cf8O4CZY/f34eZAADMBAwMOLKq51K1q2Tp+831g4vUcJWvbTZaXlatmm338pTs05dp2XRAFa5arX9Vp4e5/R1Xp68NihzPYgiDMBAHAZyFfo33vvUJs2aE6wuPbJytfEgAxhIJgMPPb7K7rrvftv6zkdOJWvbB5/ZxJmzbcGKp5z2N/OXrbT7HnnMdn3xvdPybHxrr82Y/4jTsqhNzl641J5cv8lpWTTILFn9vM17bIXT8jz8xDM2bd4Ce2XXe87LE2fg5G8QLhiAgbzGQK5Cn9cumOuhEcEADMAADMAADMAADMDArwwg9LwhkhUwGIABGIABGIABGIABjxlA6D2uPGamv85MyYIsYAAGYAAGYAAGksoAQo/QMyOHARiAARiAARiAARjwmAGE3uPKS+oslHKzAgMDMAADMAADMAADvzKA0CP0zMhhAAZgAAZgAAZgAAY8ZgCh97jymJn+OjMlC7KAARiAARiAARhIKgMIPULPjBwGYAAGYAAGYAAGYMBjBhB6jysvqbNQys0KDAzAAAzAAAzAAAz8ygBCj9AzI4cBGIABGIABGIABGPCYAYTe48pjZvrrzJQsyAIGYAAGYAAGYCCpDCD0CD0zchiAARiAARiAARiAAY8ZQOg9rrykzkIpNyswMAADMAADMAADMPArAwg9Qs+MHAZgAAZgAAZgAAZgwGMGEHqPK4+Z6a8zU7IgCxiAARiAARiAgaQygNAj9MzIYQAGYAAGYAAGYAAGPGbg/wCQxnASdm7NjwAAAABJRU5ErkJggg==[/img][br][br]Use the diagram to find the value of [math]0.137+0.284[/math]. Explain your reasoning.
Calculate the sum vertically.
How was your reasoning about [math]0.137+0.284[/math] the same with the two methods? How was it different?
Click the vertical calculation where digits of the same kind are lined up. Then, finish the calculation and find the sum.
Click the vertical calculation where digits of the same kind are lined up. Then, finish the calculation and find the sum.
Find the sum 10.6 + 1.7 using vertical calculation.
Find the sum 123 + 0.2 using vertical calculation.
Andre has been practicing his math facts. He can now complete 135 multiplication facts in 90 seconds.
If Andre is answering questions at a constant rate, how many facts can he answer per second?
Noah also works at a constant rate, and he can complete 75 facts in 1 minute. Who is working faster? Explain or show your reasoning.