How To Multiply Numbers #3
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 2digit numbers as shown in the example below:
Multiplying by 2Digit 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'


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' 

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
7^{2}5^{1}8


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
7^{2}5^{1}8
^{1}2 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
7^{2}5^{1}8
^{1}7^{1}2 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
7^{2}5^{1}8
1 1^{1}7^{1}2 0 

Add the two products to get the answer. 
5 8 6
x 2 3 
1
7^{2}5^{1}8
1 1^{1}7^{1}2 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 2digit
numbers.
You'll find more printable multiplication
worksheets here.
More
Math Help
Look at the fractions section for help with how
to multiply fractions or the decimals
section for guidance on multiplying decimals.