Long multiplication helps you, when you do not have your calculator with you but solution must be found. Let us study the idea with an example:[br][br][math]\begin{array}{lr}[br]\text{} & 3\,5\,8\\[br]\times & 3\\[br]\hline[br]\end{array}[/math][br][br]When 8 is multiplied with 3, the result is 24. The last digit is left down and the first digit is noted down above 5. The next step would look like [br][br][math]\begin{array}{lr}[br]\text{} & 3\stackrel[]{\textcolor{blue}{2}}58\\[br]\times & 3\\[br]\hline[br]\text{} & 4[br]\end{array}[/math][br][br]Next 5 would be multiplied with 3. The result is 15, but the noted digit 2 is added to it. Thus, [math]5\cdot 3 + 2=17[/math]. The first digit 1 is noted down above 3 and 7 is left down below multiplier 3:[br][br][math]\begin{array}{lr}[br]\text{} & \stackrel[]{\textcolor{blue}{1}}3\,\stackrel[]{\textcolor{blue}{2}}58\\[br]\times & 3\\[br]\hline[br]\text{} & 74[br]\end{array}[/math][br][br]Finally, [math] 3\cdot 3 +1 = 10[/math]. The final answer is [br][br][math]\begin{array}{lr}[br]\text{} & \stackrel[]{\textcolor{blue}{1}}3\,\stackrel[]{\textcolor{blue}{2}}58\\[br]\times & 3\\[br]\hline[br]\text{} & 1074[br]\end{array}[/math]

In this case, we are multiplying with 23 instead of 3.[br][br][math]\begin{array}{lr}[br]\text{} & 3\,5\,8\\[br]\times & 2\,3\\[br]\hline[br]\end{array}[/math][br][br]At first, we multiply with 3 as explained previously:[br][br][math]\begin{array}{lr}[br]\text{} & \stackrel[]{\textcolor{blue}{1}}3\,\stackrel[]{\textcolor{blue}{2}}58\\[br]\times & 2\,3\\[br]\hline[br]\text{} & 1074[br]\end{array}[/math][br][br]When this is done, the noted numbers are not used anymore. Now, we start doing the same thing by multiplying with 2: [math] 2\cdot 8=16[/math]. The last digit is written under multiplier 2 to the next row and the first digit is noted down above 5:[br][br][math]\begin{array}{lr}[br]\text{} & 3\,\stackrel[]{\textcolor{blue}{1}}58\\[br]\times & 2\,3\\[br]\hline[br]\text{} & 1\,0\,7\,4\\[br]\text{} & 6\,\;\,[br]\end{array}[/math][br][br]At the next step: [math]2\cdot 5+1=11[/math], so[br][br][math]\begin{array}{lr}[br]\text{} & \stackrel[]{\textcolor{blue}{1}}3\,\stackrel[]{\textcolor{blue}{1}}58\\[br]\times & 2\,3\\[br]\hline[br]\text{} & 1\,0\,7\,4\\[br]\text{} & 1\,6\,\;\,[br]\end{array}[/math][br][br]Finally, we get [math]2\cdot 3+1 = 7[/math]:[br][br][math]\begin{array}{lr}[br]\text{} & \stackrel[]{\textcolor{blue}{1}}3\,\stackrel[]{\textcolor{blue}{1}}58\\[br]\times & 2\,3\\[br]\hline[br]\text{} & 1\,0\,7\,4\\[br]\text{} & 7\,1\,6\,\;\,[br]\end{array}[/math][br][br]The last step is adding up these two rows:[br][br][math]\begin{array}{lr}[br]\text{} & 3\, 5\,8\\[br]\times & 2\,3\\[br]\hline[br]\text{} & 1\,0\,7\,4\\[br]+ & 7\,1\,6\,\;\, \\[br]\hline[br][br]\text{} & 8\,2\, 3\,4[br][br]\end{array}[/math][br][br]It the multiplier has more than two digits, the procedure would be the same to all digits. You must have as many rows to add up, as you have digits in your multiplier. The row is always written from right to left and the row starts below the digit, that you are using as multiplier.

In this case, we are multiplying with decimal numbers.[br][br][math]\begin{array}{lr}[br]\text{} & 3\,5,8\\[br]\times & 2,3\\[br]\hline[br]\end{array}[/math][br][br]We do calculations like shown above. We acknowledge decimals at the final answer. Because multiplicand 35,8 has one decimal and the multiplier 2,3 has also one decimal, there are two decimals altogether.So, the decimal point is written two digits from right to left;[br][br][math]\begin{array}{lr}[br]\text{} &3\,5, 8\\[br]\times & 2,3\\[br]\hline[br]\text{} & 1\,0\,7\,4\\[br]+ & 7\,1\,6\,\;\, \\[br]\hline[br][br]\text{} & 8\,2, 3\,4[br][br]\end{array}[/math][br]

Fill in the missing numbers. First, select the box and then the correct number.

Practice long multiplication with these exercises with paper and pen. You can check your solution by marking box.

You can practice multiplication of decimal numbers with the applet below. First, select the box, where you want to write a number and then click the correct number. Before checking your answer, place the decimal delimiter correctly.