**Middle School Number Sense Lesson 81: Multiplication using the Distributive Property**

Last summer we looked at

**MultDistrib2**, which is an extension of today's concept. Today we will use the

**distributive property**to make multiplication a little easier. It is best to use this skill when multiplying by 9 or 99 (or something close to 100) or by some large number just above a multiple of 100 or 1000. This concept has appeared

**8 times**this year in middle school, with a median placement at

**question # 2**.

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The most common variation of this problem used to be

**multiplying by 9**. For example:

**78 x 9 = ___**

**78 x (10 - 1)**, which can then be distributed as

**(78 x 10) - (78 x 1)**. Now the multiplication is much easier. Simplify it to

**780 - 78**, and we can see that the answer is

**702**.

This year, half of these problems were

**multiplying by 2017**. (Test writers love to play with the dates). For example:

**2017 x 3 = ___**

**(2000 + 17) x 3**, which can be distributed as

**(2000 x 3) + (17 x 3)**. Now the multiplication is easier. Simplify it to

**6000 + 51**, and we can see that the answer is

**6051**.

Let's look at some more examples.

**Example 1: 1998 x 6 = ___**

- Think of this as
**(2000 - 2) x 6**. - Distribute to
**(****2000 x 6) - (2 x 6)**. This becomes**12000 - 12**. - The answer is
**11988**.

**Example 2: 12 x 997 = ___**

- Think of this as
**12 x (1000 - 3)**. - Distribute to
**(12 x 1000) - (12 x 3)**. This becomes**12000 - 36**. - The answer is
**11964**.

**Example 3: 2016 x 6 = ___**

- Think of this as
**(2000 + 16) x 6**. - Distribute to
**(2000 x 6) + (16 x 6)**. This becomes**12000 + 96**. - The answer is
**12096**.

**Example 4: 99 x 18 = ___**

- Think of this as
**(100 - 1) x 18**. - Distribute to
**(100 x 18) - (1 x 18)**. This becomes**1800 - 18**. - The answer is
**1782**.

**Example 5: 2017 x 17 = ___**

- Think of this as
**(2000 + 17) x 17**. - Distribute to
**(2000 x 17) + (17 x 17)**. This becomes**34000 + 289**. - The answer is
**34289**.

**Here's a free worksheet to help you practice MultDistribPr:**

multdistribpr.pdf |

**Up Next for Middle School: Conv%FtoFrac**