The Distributive Property, Part 1: IM 6.6.9
[url=https://im.kendallhunt.com/MS/teachers/1/6/9/preparation.html]“The Distributive Property, Part 1”[/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 6.6.9
- IM 6.6.9 Lesson: The Distributive Property, Part 1
- Practice 6.6.9
- IM 6.6.9 Practice: The Distributive Property, Part 1
IM 6.6.9 Lesson: The Distributive Property, Part 1
Find each product mentally.
[math]5\cdot102[/math]
[math]5\cdot98[/math]
[math]5\cdot999[/math]
Select [b]all[/b] the expressions that represent the area of the large, outer rectangle in figure A.[br][br][img]data:image/png;base64,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[/img]
Explain your reasoning.
Select [b]all[/b] the expressions that represent the area of the shaded rectangle on the left side of figure B. [br][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAT0AAAEPCAYAAAAwKRM7AAAgAElEQVR4Ae2dC5AVxb2HFwMYeQoY0CggQcUgBE2CIF5REQMCRiUqWBiDeAETjS8sBNTSRMXySRI0JBFSSywSQdFgfAAawGCpGAjIQ4OiqAgoRHkbef5v/cZ7KFoWdk4zfWbPmW+qpnZnd7rPzNfz/05Pd09PmbFAAAIQyBCBsgydK6cKAQhAwJAeFwEEIJApAkgvU8XNyUIAAkiPawACEMgUAaSXqeLmZCEAAaTHNQABCGSKQKXS+/TTT+3FF1+0qVOnVri+9NJLtnDhQluzZo3t2LEjU/A4WQhAoPgIVCq9OXPm2EknnWStWrWqcG3durW1a9fOOnXqZD/+8Y9twoQJtmrVquIjwRFDAAKZIFCp9GbOnGl16tSxsrIya9q0aSS+448/3nJrs2bNrHbt2latWrXo53HHHWdXX321LV26NBMAOUkIQKC4COQlvfvuu8+mTZtmM2bM2L3qtnfixIl28803RzXCGjVq2OGHH2633HKLbdu2rbhocLQQgEDJE8hLei+88IJt3bp1Lyg7d+601atX2/jx4619+/Z20EEHWefOnant7UWKP0AAAmkTSER6uZNYuXKlDRkyJLoVbtOmTVQrzP2PnxCAAASqAoFEpbd582a79957I+mpg+O5556rCufIMUAAAhDYTSBR6a1duzZqy1Onh25zFyxYsPuD+AUCEIBAVSCQmPS++OKLqHPj7LPPtrp161r//v1t/fr1VeEcOQYIQAACuwnkJb2xY8fa/PnzbcmSJbtXDUx+5ZVX7LHHHrO+fftGw1rOPffcaEDz7k/hFwhAAAJVhEBe0jv11FPtvPPOs969e+9ee/XqZR06dLAjjzzSWrRoYQMGDLDZs2ebenRZIAABCFQ1AnlJr3HjxqbByM2bN9+9asCy/t6kSRPr1q2bPfLII7Z48WLbtGlTVTtXjgcCEIBA5ZOI7vlExtChQ023uOXl5btXSe6Xv/yl/ehHPzI9jSEBnnnmmTZlyhTbsmULiCEAAQhUKQJ51fT2NThZZ6RBy7NmzTLd7tasWTN6OkPbLBCAAASqEoHEpKeT2rVrlz311FNR2556cC+//HLa9qpSaXMsEIBAfre3+6vp5VjOnTvXunfvHg1Q7tixo61bty73L35CAAIQSJ1AojU9nY2GtOgWVwOUTz755OiZ3NTPkgOAAAQg8P8EEpfeq6++GnVkSHqnnHIKvbhcahCAQJUikKj01Jkxbtw4a9iwYTS33mWXXRa181WpM+ZgIACBTBNITHqfffaZ/fGPfzTNrqKppU444QR79tlnMw2Xk4cABKoegbyk169fPxs+fHg0qYAmCdV600032U9+8pPoqQyN0dMkohrAfM8995hmXWGBAAQgUJUI5CW9evXqRbeujRo1styqW1lNJ1+9enVr0KCB9ejRI3oOVzOuVJVl3rx59vDDD9tdd93FCgOugSK8BkaPHp3YBCaVSm/ZsmU2bNgwu+GGG/a5qsY3ZswYmz59ejRb8saNG6uK76Lj0JMkqn3qUTlWGHANFN810LJlS3v66acT8Uql0tOUUZoRecWKFftcNVX8hg0bbPv27YkcVNKZqENFvckNmx9jx57e3Y4/qxcrDKrkNdDkuDbRtar3zOiuac/JPbL4u57n191krVq1okdfk3BDpdJL4kPSzkOvppT0Tjz/Urv80RftyidfZYVBlbwG/ud/v3zdgmY00mxFe07jlsXf9c7ttm3bIr18JZqT3in9r7EbX/7AblmwjhUGVfIa6Dbsy9ctqIazZs2afC/1ktv/gw8+iB5yoKaXZ9EiPSRfLF90SM8NbqTn8oi9hfSQHtKLHS5Vakek51kcSA/pIT3P4Ek5GdLzLACkh/SQnmfwpJwM6XkWANJDekjPM3hSTob0PAsA6SE9pOcZPCknQ3qeBYD0kB7S8wyelJMhPc8CQHpID+l5Bk/KyZCeZwEgPaSH9DyDJ+VkSM+zAJAe0kN6nsGTcjKk51kASA/pIT3P4Ek5GdLzLACkh/SQnmfwpJwM6XkWANJDekjPM3hSTob0PAsA6SE9pOcZPCknQ3qeBYD0kB7S8wyelJMhPc8CQHpID+l5Bk/KyZCeZwEgPaSH9DyDJ+VkSM+zAJAe0kN6nsGTcjKk51kASA/pIT3P4Ek5GdLzLACkh/SQnmfwpJwM6XkWANJDekjPM3hSTob0PAsA6SE9pOcZPCknQ3qeBYD0kB7S8wyelJMhPc8CQHpID+l5Bk/KyZCeZwEgPaSH9DyDJ+VkSM+zAJAe0kN6nsGTcjKk51kASA/pIT3P4Ek5GdLzLACkh/SQnmfwpJwM6XkWANJDekjPM3hSTob0PAsA6SE9pOcZPCknQ3qeBYD0kB7S8wyelJMhPc8CQHpID+l5Bk/KyZCeZwEgPaSH9DyDJ+VkSM+zAJAe0kN6nsGTcjKk51kASA/pIT3P4Ek5GdLzLACkh/SQnmfwpJwM6XkWANJDekjPM3hSTob0PAsA6SE9pOcZPCknQ3qeBYD0kB7S8wyelJMhPc8CQHpID+l5Bk/KyZCeZwEgPaSH9DyDJ+VkSM+zAJAe0kN6nsGTcjKk51kASA/pIT3P4Ek5GdLzLACkh/SQnmfwpJwM6XkWANJDekjPM3hSTob0PAsA6SE9pOcZPCknQ3qeBYD0kB7S8wyelJMhPc8CQHpID+l5Bk/KyZCeZwEgPaSH9DyDJ+VkSM+zAJAe0kN6nsGTcjKk51kASA/pIT3P4Ek5GdLzLACkh/SQnmfwpJwM6XkWANJDekjPM3hSTpYJ6e3atctya1K8kR7SQ3pJRVNh88mE9JYtW2Yvv/yyLVmyxDZv3pwIYaSH9JBeIqFU8ExKXnoLFy60c845x+rWrWv9+vWzxYsXJwIZ6SE9pJdIKBU8k5KW3qZNm2zgwIFWv359q1atmvXu3dveeOONRCAjPaSH9BIJpYJnUtLSGz16tLVs2dI6dOhgTZs2RXoLEFWxiCrJ4+w27F4rKyuzbt262Zo1awoumar2gSUrvdmzZ0eyO+200+zGG2+073znO0gP6VmSMimWvJCeq92SlN7atWvt4osvtqOPPtrGjh1r48ePt3bt2iE9pIf0qOlZyUlv586dNnLkSDvyyCPtuuuus/fffz+SXqtWrZAe0kN6SK/0pPfCCy9YmzZtrGvXrjZnzhzbtm2bjRs3zo499likh/SQHtIrLel99NFH1rNnTzvmmGNs4sSJtnHjxuhmHunRgVEs7W8hjpM2vRJt09u6davdcsstdthhh9mIESPs448/3n2mSA/phZBJseSJ9HarIPqlJNr09IjZ3/72N2vWrFlU03vrrbdsx44du88U6SG9YhFUiONEertVUBrSU8eFHjPr3Llz1G73/PPP2+eff+6cJdJDeiFkUix5Ij1HB8Xdpqca3rp16+z666+3mjVr2rXXXmtvv/22rV692llHjRplLVq0sB49etiMGTOi/61fv94lkecWT2QgUqSXZ9BUkd2L+vZ2+/btNm/ePKtXr14kvUGDBtmwYcNs+PDhzqrOjYYNG5qGrVxxxRXR/yZPnnxARYD0kB7SO6AQSi1xUUtPnRfTp0+PxuRpXN6+1kMPPdSqV69uhxxyiDVu3Djab8iQIQcEHekhPaR3QCGUWuKilp46K95991174IEH9rv26dMn6tVt27Zt9Eia9p82bdoBQUd6SA/pHVAIpZa4qKUXlxodGQiqWAQV4jjpyHBNgfRcHrG3qOkh0hCCCpEn0nPDOhPSKy8vt9atW5tucxctWuQS8NxCekgvhKBC5In03CDPhPT0PO7gwYPt7rvvtuXLl7sEPLeQHtILIagQeSI9N8gzIT33lJPZQnpIL4SgQuSJ9NyYR3ouj9hbSA/phRBUiDyRnhvWSM/lEXsL6SG9EIIKkSfSc8Ma6bk8Ym8hPaQXQlAh8kR6blgjPZdH7C2kh/RCCCpEnkjPDWuk5/KIvYX0kF4IQYXIE+m5YY30XB6xt5Ae0gshqBB5Ij03rJGeyyP2FtJDeiEEFSJPpOeGNdJzecTeQnpIL4SgQuSJ9NywRnouj9hbSA/phRBUiDyRnhvWSM/lEXsL6SG9EIIKkSfSc8Ma6bk8Ym8hPaQXQlAh8kR6blgjPZdH7C2kh/RCCCpEnkjPDWuk5/KIvYX0kF4IQYXIE+m5YY30XB6xt5Ae0gshqBB5Ij03rJGeyyP2FtJDeiEEFSJPpOeGNdJzecTeQnpIL4SgQuSJ9NywRnouj9hbSA/phRBUiDyRnhvWSM/lEXsL6SG9EIIKkSfSc8Ma6bk8Ym8hPaQXQlAh8kR6blgjPZdH7C2kh/RCCCpEnkjPDWuk5/KIvYX0kF4IQYXIE+m5YY30XB6xt5Ae0gshqBB5Ij03rJGeyyP2FtJDeiEEFSJPpOeGNdJzecTeQnpIL4SgQuSJ9NywRnouj9hbSA/phRBUiDyRnhvWSM/lEXsL6SG9EIIKkSfSc8Ma6bk8Ym8hPaQXQlAh8kR6blgjPZdH7C2kh/RCCCpEnkjPDWuk5/KIvYX0kF4IQYXIE+m5YY30XB6xt5Ae0gshqBB5Ij03rJGeyyP2FtJDeiEEFSJPpOeGNdJzecTeQnpIL4SgQuSJ9NywRnouj9hbSA/phRBUiDyRnhvWSM/lEXsL6SG9EIIKkSfSc8Ma6bk8Ym8hPaQXQlAh8kR6blgjPZdH7C2kh/RCCCpEnkjPDWuk5/KIvYX0kF4IQYXIE+m5YY30XB6xt5Ae0gshqBB5Ij03rJGeyyP2FtJDeiEEFSJPpOeGNdJzecTeQnpIL4SgQuSJ9NywRnouj9hbSA/phRBUiDyRnhvWSM/lEXsL6SG9EIIKkSfSc8Ma6bk8Ym8hPaQXQlAh8kR6blgjPZdH7C2kh/RCCCpEnkjPDWuk5/KIvYX0kF4IQYXIE+m5YY30XB6xt5Ae0gshqBB5Ij03rJGeyyP2FtJDeiEEFSJPpOeGNdJzecTeQnpIL4SgQuSJ9NywRnouj9hbSA/phRBUiDyRnhvWSM/lEXsL6SG9EIIKkSfSc8Ma6bk8Ym8hPaQXQlAh8kR6blgjPZdH7C2kh/RCCCpEnkjPDWuk5/KIvYX0kF4IQYXIE+m5YY30XB6xt5Ae0gshqBB5Ij03rJGeyyP2FtJDeiEEFSJPpOeGNdJzecTeQnpIL4SgQuSJ9NywRnouj9hbOem1v2SQXf3sGzbkpfdYYVAlr4Eu195uZWVl1qVLF1u6dKl9+umnmV7feOMN++53v2u1atWy8vLy2DG/vx3L9vfPUvlfTnrN259mZ1x1s3W94Q5WGFTJa6BVl56R9Fq1amW333673X///Zleb775ZmvWrBnSy1fGV155pdWuXdtq1qzJCgOugSK7Bg4++GBr1KiRTZo0Kd/Qr3D/TNT0BKtPnz7WtWtXVhhwDRTZNXD22WfbRRddZMuWLatQYvn+MRPSyxcK+0MAAqVLIBPS27Vrl+3cudP0kwUCECguAordJOM3E9L7+OOP7e2337a1a9dG8IqryDlaCGSXwPbt2+3DDz+0d955xzZs2JAIiExIr3///lajRg0bNmyYrV+/PhFwZAIBCIQnIOF16tTJ6tevb+PHj0/kAzMhvdyQlaFDhyK9RC4bMoFAYQgwONmTM9LzBEcyCKRMAOl5FgDS8wRHMgikTADpeRbAvHnzbMqUKbZkyRLbtm2bZy4kgwAECk3g888/t5deesmeeeaZqEMjic/PRJueRPff//7X1BPEsJUkLhvygEBhCChet27dal988YXt2LEjkQ/NhPQSIUUmEIBASRBAeiVRjJwEBCAQl0AmpPf444+bZmuYOnVqdJsbFw77QQAC6RJYt26djRkzJppxRm3zSSyZkN6gQYOsbt26duuttyY2qjsJ+OQBAQjsn8CKFSvsjDPOsCZNmtiECRP2v3PM/2ZCegxZiXk1sBsEzKK7IT22OWvWrKjX9Pnnn7e5c+em8hgnQ1Y8L0mk5wmOZJkioFEOc+bMsQcffNAUM6eddlo0a/HJJ59sPXv2tBEjRtjMmTMLereE9DwvQbXnnXjiiTZq1CjbtGmTZy4kg0BpE3juueesV69edsQRR1i7du0i0WkeyvPPPz/abty4cTSNvcbMaRhJIZbVq1dbv379rGPHjvb0008n8pGZuL2dP39+BOzNN99kcHIilw2ZlCKBkSNHRnIbMGCATZ48OXpHxyeffGLLly+3p556yrp37x61jV9yySWJTehZGcctW7bY7NmzTULW5ANJLJmQXhKgyAMCpU5Ataq//OUv0YuIKhrEr/+1bt3a2rZtaxoRUawL0ivWkuO4IVBgAnoz2XnnnWdHHXWU/eY3vynwpyf3cZmQnsb6rFy5MmqA1QysLBCAQP4EFi1aFLXv6e1kDz30UP4ZeKTQo2ea/Fe1UN3qJrFkQnrjxo2zgQMH2hNPPGF6gJkFAhDIn8D06dOjDgV1cjz55JP5Z+CRQu/9VVvjVVddZa+88opHDnsnyYT0GLKyd8HzFwjkQ0C9tXfccYd94xvfiN4sqHF8hVgYsuJJGel5giMZBMyi98poeqfTTz89as/TY2GFWpCeJ+nLLrvMqlWrZkwX7wmQZJkm8NFHH1nfvn2tdu3adu2115petFWoRdLr0KGD1alTx8rLyxP52Ezc3t55553R6HJ9QzE4OZHrhkwyQkBtapdffnkkvAsvvNAWLFhQ0DkpJdjBgwebXvitx+GSWDIhPU0gunHjxmgiworGHyUBkjwgUGoENOrhZz/7mTVs2NB++MMf2muvvZbYRJ5xWWm0hXptVVlJatbzTEgvLmD2gwAEviQg4f30pz+1ww47LBqm8uqrryYmnbQZI720S4DPh0AVI5Cr4amn9oILLjAJT9O1l8qSCenpBd8a3KhbXAYnl8qly3mEIJCr4e0pPDUPpbVocPJ//vOfqPMkqTG2mZDebbfdFvUAjR49mo6MtK5ePrfKE/hqDU9teGkKT8DUkaGOFA2X0ewuSSyZkB7j9JK4VMijlAlIbnrqQW14xxxzjN133302bdq06PWLGqP31fVf//pX9HhYaCaM0/MkjPQ8wZEsEwQ0omHVqlXRPHoaz9qgQYNoiilNHrqv9dJLL7WXX345OB+k54kY6XmCI1kmCEh6uo3UDCo/+MEPYq3q2X399deD80F6nognTZpkw4cPjwY3pt1G4XkKJINAUALqndV7MDRdfJx18eLF9tlnnwU9JmWudsbf/va3pnZ53oaWB271+qgHV8JjcHIe4NgVAikT0GgLDUzesGFDYlPUZ6IjI+Vy4+MhAIEqRADpVaHC4FAgAIHwBDIhPV4MFP5C4hMgEIKAmqZ4MZAHWT00rRHmv/jFLwr6zk6PQyUJBCCwBwFNa6UeZU1RrxcTJbFkoqbHkJUkLhXygEDhCTBkxZM50vMERzIIpEwA6XkWgG5v9XjN7bffzu2tJ0OSQSANArq91QSiTZs25fY2nwLQW5x+/etfR4/NlNIUOfkwYF8IFCMBzYw0ceLEaIDym2++mcgpZKJNLxFSZAIBCJQEAaRXEsXISUAAAnEJIL24pNgPAhAoCQKZkN6zzz5r9957r82aNaukpr0uiSuQk4DAfgjomdtHH33URo0aZYsWLdrPnvH/lQnpDRo0yOrVq2e33norvbfxrw32hEDqBFasWGFnnnmmHX744TZhwoREjicT0gsxTm/79u22dOlS+/DDDxMpCDKpnIDel7B27VpbuXJl7FU1Bd6LUjnbJPbYunWrLVu2LNGYYJyeZ8kkKT1Ntvj444+b8rzuuutM84qxFIaA2F9yySXWtm3b2Ktui3jBe2HKR19Kb731VvQ+i6uvvtr+/ve/H3BzEtLzLLthw4bZCSecYA888ED0RrR8s9FLhjWB4d13321nnXWWfetb34pWTW5IQOVL039/Sa9v375RWao897Uef/zxUXPGQQcdFDVpbN682f9DSRmbgOaq1MSiN954ox166KGmctBLwseMGWPvvfee13tz9RZDlfn3v/99++tf/xr7WPa3YyZub1Xl1rs79a2h29K4i26lJk+ebGoT7NixY/QOgRo1alhZWZn169fPkhosGfd4sr6fBparMVtlub/1kUceiWqCRx99dNQIrhoIS2EIiLXiomXLlqb3bdSsWdOaN28e1f5uuummqPYnMcadzDdX5prNec2aNYmcRCaklw8pQdabnlQr1DsDVJuoU6dOVICSnVa9LUq3uEw9nw/Zwu2rN3kdddRRfDEVDrnzSYoLNSuopp2LGQlQj4J+73vfM71UaNy4cVGbuNoBC70gPTPTt5Oq0ao+X3/99da1a9coaFRQuULL/VRNb8iQIYk21ha60Ev585YvX249evSwb37zm/b73//eknpBdCkzS/rc1HGkZ2Y7depkX/va1/aKoYMPPtiOPfZYO/fcc6Pn4dX2pxd6F2rJhPS2bNkSvWBEAbBntVrtcWqre/jhh61///520kknWe3atfcqpJzw9FPfVDNnzszrNrlQhcnnmP3hD3+wFi1a2DnnnGP//Oc/QZISAYlPd0MNGzZ07pL2jKVc7e/UU081dXxoPN6///1v510YykfP3+oFQUnVCjMhPcG85pprbMqUKVHHg8b+aMCyJhXt2bNnNEFhRbW6PQtIv+s29/777y/IS45TulaL+mM/+eSTqElCt1EPPvhgFChFfUJFfvDqQLr44ovt61//+n4rEoot7XPcccdFnRaKMb1cXLU/tf+pqUmdI2rXS2LJhPRyQ1YuuuiiqFanbxXV2OrWrVtpYewpPg1w1vs+1WakgmFNhoFq2+ohP9DliSeeiNpb27dvb//4xz+cWn1leatGoU4StUVRrsmUqzhecMEFsaSXizNVPlQ7PP30023EiBH20EMP2be//W2rVauWlZeXV1aMsf6fKempR0ltCRW1M+Sg8/PLzppCckhiLJ1qFRraoKESekeq2mjzWSRdNa6rt7GQ585n7ft6O+SQQ6LaX+PGjZFePhez9s3V9M444wwbOHBg9C2i3r3c8JO4F54aYE855RTr1atX1AirhljWA2egZocD7QnX7ZC+0NSzPmPGjLyfwtBQJs27qJoJZXrgZZpj2KZNG6tevXpeXySSnSoo3bt3j+JVbbTU9PK03siRI61Lly5Rb57G3i1YsCC6hZG8VHWuX79+rELR7a0GJKuHUGOGWJNh8NUOpjyLN2rgHjx4cFTLU9OFxmP6LBKvrg/KNZly1eOCV1xxhUlilVUsdPfVqFEjO/HEE6OnblTrfuedd0zttGpSUsfU1KlTfYp1rzSZuL3V85eCp97aXO+tfuri1jAV1f4E+4gjjqj0W0nwNY5PbUAsVYPAwoULo1qe3ng3bdq0RNoHq8aZFe9RKD5ef/11a9KkyT57byVC1eD0pjMNb1FnhWZCUm9tbtFwMnVmKFYP9G4gl2cmpJc72X39zI36vueee6xz587RCPJ9DV1RL5N6BlUQLOkTUFAMHTo0quWpTe/dd99N/6AyfgSqUKiiceGFF1bYhKRandpedQt7/vnnR8OM9NRUoSoSSG+PC1SFpW+ZJ598Mqpi6xlb9SR9tU1CzwG++OKL0aDmPZLzawoENMuN2vL0JaXeW43JZEmXgDqFnnnmmb06hdQmrtq4JozQZB1qh92zVleoo86E9NavXx/15glwPt8mGih55513RoOWNfZLhaYudT1eo9qF2ixY0iWgYRFqk9UQB7UBsaRLQBUHTQyhYUOKFa26hZXs1K7+u9/9zjRONm4cqiav8XrKM6mnazIhPX2r6BVyd911l9ckooKtiQd69+4dtfvpFle1wMcee4zaXooxplqdBrSqF17BpC83lnQJqN38V7/6VTQsTLLT44DqiNAEET5tcnqcTT3BKmc94ZHEkgnp5YasqHZ2oIGhiUP1/tzWrVvbgAEDosdmkigI8siPgGoUGqyq29pWrVrRlpcfviB7q0zUpqq2Og3+1xdRPjOqVHRQzKdXEZUYf0tSeipYVbn1LODs2bOjSRNjHAK7JExAZaDpvtTeescdd9CxlDBfn+xUk5s7d6699tprUQ963FvY/X0W0tsfnf38L0np5T5G8tOAVgUfS2EJiLnGWurdCVoL2fNX2DMtrk/LVQiSjAmk53kN/OlPf7Kf//zn0Zi8pBpDPQ+FZAkRUA+hBhJrTTLIEjo8skmIgG6P1Vml6dyYcCAPqGpcVXDo+Ux9G7FAAALFQUBfaGpKUg+uT0dIRWeZiY6Mik6cv0EAAtkkgPSyWe6cNQQySyAT0lOPksbZab60JOZty+zVwolDoMAENBZTM5XrGfn3338/kU/PhPT0CkiNq1ODaBqPvSRSUmQCgQwSWLVqlfXp0yca98crIPO4AEIMWcnj49kVAhDwJMCQFU9wSM8THMkgkDIBpOdZAHs+e8vtrSdEkkEgBQKa1INnbz3Aa/pwPQeox2OSeo2cx2GQBAIQyJOAxthqqrexY8dGLwfPM3mFu2eiI6PCM+ePEIBAJgkgvUwWOycNgewSyIT0dEurZ241Ro/H0LJ7sXPmxUdA8arXOSh+k3rGOhPS0wSGf/7zn23+/PkMTi6+654jzjABPS+vlz1NmjTJ3nvvvURIZEJ6DFlJ5FohEwgUnABDVjyRIz1PcCSDQMoEkJ5nASA9T3Akg0DKBJCeZwFceeWV1qBBA7vtttu8Xgzk+bEkgwAEDpCA3px21llnRS8YUrt8Eksm2vSSAEUeEIBAaRBAeqVRjpwFBCAQkwDSiwmK3SAAgdIggPRKoxw5CwhAICYBpBcTFLtBAAKlQQDplUY5chYQgEBMAkgvJih2gwAESoMA0iuNcuQsIACBmASQXkxQ7AYBCJQGAaRXGuXIWUAAAjEJIL2YoNgNAhAoDQJIrzTKkbOAAARiEkB6MUGxGwQgUBoEkF5plCNnAQEIxCSA9GKCYjcIQKA0CJdwba0AAAAcSURBVCC90ihHzgICEIhJAOnFBMVuEIBAaRD4P4SY+lozKhuUAAAAAElFTkSuQmCC[/img]
Explain your reasoning.
Complete the table. If you get stuck, skip an entry and come back to it, or consider drawing a diagram of two rectangles that share a side.
Use the distributive property to write two expressions that equal 360. (There are many correct ways to do this.)
Is it possible to write an expression like [math]a(b+c)[/math] that equals 360 where [math]a[/math] is a fraction? Either write such an expression, or explain why it is impossible.
Is it possible to write an expression like [math]a(b-c)[/math] that equals 360? Either write such an expression, or explain why it is impossible.
How many ways do you think there are to make 360 using the distributive property?
IM 6.6.9 Practice: The Distributive Property, Part 1
Select [b]all[/b] the expressions that represent the area of the large, outer rectangle.[br][img]data:image/png;base64,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[/img]
Draw and label diagrams that shows these two methods for calculating 19 ᐧ 50: (1) First find 10 ᐧ 50 and then add 9 ᐧ 50.
Draw and label diagrams that shows these two methods for calculating 19 ᐧ 50: (2) First find 20 ᐧ 50 and then take away 50.
Complete each calculation using the distributive property.
[math]98\cdot24[/math][br][math]\left(100-2\right)\cdot24[/math][br]...
[math]21\cdot15[/math][br][math]\left(20+1\right)\cdot15[/math][br]...
[math]0.51\cdot40[/math][br][math]\left(0.5+0.01\right)\cdot40[/math][br]...
A group of 8 friends go to the movies. A bag of popcorn costs $2.99. How much will it cost to get one bag of popcorn for each friend? Explain how you can calculate this amount mentally.
Draw diagrams of a+a+a+a and 4a when a is 1, 2, and 3. What do you notice?
Do [math]a+a+a+a[/math] and [math]4a[/math] have the same value for any value of [math]a[/math]? Explain how you know.
120% of x is equal to 78.
Write an equation that shows the relationship of 120%, [math]x[/math] , and 78.
Use your equation to find [math]x[/math]. Show your reasoning.
Kiran’s aunt is 17 years older than Kiran.
How old will Kiran’s aunt be when Kiran is: 15 years old?
How old will Kiran’s aunt be when Kiran is: 30 years old?
How old will Kiran’s aunt be when Kiran is: [math]x[/math] years old?
How old will Kiran be when his aunt is 60 years old?