How To Multiply Numbers #3

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We've already seen how to multiply by single digit numbers using this simple method as well as this quicker way using regrouping. We can combine these two methods of multiplying to multiply by 2-digit numbers as shown in the example below:

Multiplying by 2-Digit Numbers

586 x 23 =
Multiply the ones (3 x 6 = 18). Write 8 in the ones' place and carry the 1 forward to the tens'
 5 8 6 x 2 3 18
Multiply the tens and add what was carried forward (3 x 8 = 24 + 1 = 25). Write 5 in the tens' place and carry the 2 forward to the hundreds'
 5 8 6 x 2 3 2518
Multiply the hundreds and add what was carried forward (3 x 5 = 15 + 2 = 17). Write 7 in the tens' place and the 1 forward in the thousands'
 5 8 6 x 2 3 1 72518
Add a zero* and multiply the ones (2 x 6 = 12). Write 2 in the tens' place and carry the 1 forward to the hundreds'
 5 8 6 x 2 3 1 72518 12 0
Multiply the tens and add what was carried forward (2 x 8 = 16 + 1 =17). Write 7 in the hundreds' place and carry the 1 forward to the thousands'
 5 8 6 x 2 3 1 72518 1712 0
Multiply the hundreds' and add what was carried forward (2 x 5 = 10 + 1 =11). Write 1 in the thousands place and 1 in the ten thousands'
 5 8 6 x 2 3 1 72518 1 11712 0
 5 8 6 x 2 3 1 72518 1 11712 0 1 3 4 7 8
586 x 23 = 13478
* We really wanted to multiply by 20, not 2. Adding a zero and multiplying by 2 is the same as multiplying by 20.

Common error when multiplying

When using the method above to multiply numbers with two or more digits, it is important that students understand where and why they must add zeros. The example below shows a fairly common error that students who do not fully understand the process can make.

As with most calculations, estimating to check whether the calculated answer is reasonable is a good way to catch errors like the made above.

Worksheets

Try the worksheets below for more practice with multiplying by 2-digit numbers.

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