Mental Math Strategies for Multiplication: Lesson for Kids

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  • 0:04 Doubling and Adding One
  • 1:24 Expanding
  • 1:57 Rewrite as a Fraction
  • 2:43 Multiplying by 9
  • 3:48 Lesson Summary
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Lesson Transcript
Instructor: Nick Rogers
This lesson has strategies for multiplying large and small numbers in your head. Learn mental math techniques so that you can convert complex multiplication into simpler multiplications and use addition and subtraction to save time.

Doubling and Adding One

Multiplication doesn't have to be a difficult or lengthy process. Let's look at strategies that will allow you to multiply numbers without pencil and paper or a calculator.

Suppose that you want to multiply 18 x 3. Traditionally, you might get out a paper and write 18 on one line and 3 on the next and start multiplying individual digits, but this seems like too much work. Let's use expansion instead.

Numbers can be expanded by making one complicated multiplication into two simpler ones. Why don't we just remember that multiplying by three is the same as doubling and adding one more of the number we're doubling? So we would write:

18 x 3

= 18 x (2 + 1)

= 18 x (2 + 18)

Double 18 is 36. We can think of this easily by making tens, or thinking of numbers in terms of 10s. 18 is 10 + 8. Doubling tens we get twenty, and doubling eights we get 16. So 20 + 16 = 36. We now need to add another 18 to get our final answer.

We can solve more easily by understanding that 36 is 4 less than 40 (40 is an easier number to work with than 36, isn't it?), and we'll take that difference of 4 and subtract it from 18 to get 14. So we can write our formula as follows:

36 + 18 = 40 + 14

The final result is 54.

Expanding

In the previous section, we were only multiplying by 3, but how can we multiply quickly if the second factor were larger? How should we approach 18 x 7? Another strategy that's effective is to expand the 18 and make one complicated multiplication into two simpler ones.

18 x 7 = (8 + 10) x 7

= (7 x 8) + (7 x 10)

= 56 + 70

= 126

By rewriting 18 as 8 + 10, we've transformed our problem into two simpler multiplications and one simpler addition.

Rewrite as a Fraction

In addition to expanded form, we can often rewrite a number as a fraction. Whenever you need to multiply a number by five, it helps if you rewrite 5 as 10/2, because multiplying by ten and dividing by two are considered simpler operations.

Try this example: 5 x 22

= 10 / 2 x 22

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