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How to Multiply by 12

Instructor: Dina Albert
Multiplication is a quicker way to add equal amounts. The better you are at multiplying quickly and accurately, the easier math problems and more complex math concepts will be to solve. In this lesson, we will focus on multiplying by 12 quickly and accurately.

Multiplication is an important skill that you will use when shopping and cooking, among many other everyday situations. The secret to multiplying two digit numbers quickly is breaking down a number into smaller parts. Let's apply this method to multiplying by 12.

Breaking Down 12

We can multiply by 12 by breaking the number down into two smaller numbers. Let's review the ways we can break down 12.

1 + 11

2 + 10

3 + 9

4 + 8

5 + 7

6 + 6

For this lesson we will focus on the breakdown 2 + 10 because multiplying by 2 and 10 is simple.

Let's very quickly go over multiplying by 2 and 10.

Multiplying by 2 is the same as adding that number twice: 5 x 2 = 5 + 5 = 10.

The trick to multiplying by 10 is to add a 0 to the end. For 5 x 10 we will add a 0 after the 5 to make 50. So 5 x 10 = 50. But adding groups of numbers is harder when we have a very large number, so the trick of adding 0 to the end is valuable. For example, 125 x 10 = 1,250.

Multiplying by 12 by Breaking it Down

Let's start with the following expression: 1 x 12. You may know the identity property of multiplication. This property says that any number multiplied by one is itself. But we will also prove this by breaking down the 12 into 10 and 2. We can rewrite 1 x 12 into 1 x (10 + 12), and then apply the distributive property.

The distributive property says we will multiply the number on the outside of the parentheses by both numbers on the inside. Then we will add them together since there is an addition sign between the 10 and 2. We show the property this way:

distrib

Notice that we got to the same answer. We get 1 x 12 = 12, whether we use the identity property or break down the number and use the distributive property.

Another Example

Let's apply the breakdown of 10 and 2 and use the distributive property to solve the following problem: 25 x 12.

Step 1: Rewrite the problem so that the 12 is broken down into 10 and 2.

Step 2: Apply the distributive property to make two separate multiplication problems. Use the math tricks for multiplying by 10 (add a 0 at the end) and multiplying by 2 (double the number).

Step 3: Add the solutions of the problems to make one total.

distrib2

So 25 x 12 = 300.

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