**Middle School Number Sense Lesson 19: Multiplication using the Distributive Property (with 2 Terms)**

This concept is one of the most often-tested problems in recent years. This year it showed

**16 times**(on average more than once per test). Appearing as late as question # 69, it was

**question # 18**twelve times.

**Number Dojo Level: 97**

To recognize this type of problem, look for an opportunity to use order of operations (OrderOfOper) where the same term appears more than once. For example,

**13 x 20 + 14 x 20**. I like to think of this as "13 twenties plus 14 twenties" because it makes it easier for me to solve. I have 27 twenties, which is

**540**. To solve these problems:

- Pull out the common factor (term).
- Add or subtract the remaining factors (depending on the sign given).
- Multiply this sum or difference by the factor from step 1.

**Example 1: 16 x 22 + 34 x 22**

- Pull out the common factor (22) to get
**(16 + 34) x 22**. - Add the remaining factors. 16 + 34 =
**50**. - Multiply this by the factor in step 1 (22). 50 x 22 =
**1100**.

**Example 2: 48 x 18 - 37 x 18**

- Pull out the common factor (18) to get
**(48 - 37) x 18**. - Subtract the remaining factors. 48 - 37 =
**11**. - Multiply this 11 by 18 to get
**198**.

**Example 3: 299 x 12 + 12**

- Pull out the common factor (12) to get
**(299 + 1) x 12**. - Add inside the parentheses. 299 + 1 =
**300**. - Multiply this sum by the factor in step 1. 300 x 12 =
**3600**.

**Example 4: 52 x 17 - 17 x 35**

- Pull out the common factor (17) to get
**17 x (52 - 35)**. - Subtract inside the parentheses. 52 - 35 =
**17**. - Multiply this difference (17) by the factor in step 1 (17). 17 x 17 =
**289**.

**Example 5: 15 x 28 - 18 x 15**

- Pull out the common factor (15) to get
**15 x (28 - 18)**. - Subtract inside the parentheses. 28 - 18 =
**10**. - 10 x 15 =
**150**.

**Example 6: 12 x 12 + 24 x 19**

- This one is a bit trickier because the 2 like factors are together. You may notice that 24 is 12 x 2, so you can rethink 24 x 19 as
**12 x 38**. Then factor out a common 12 to get**12 x (12 + 38)**. - Add inside the parentheses. 12 + 38 =
**50**. - 12 x 50 =
**600**.

**Here's a free worksheet to help you practice MultDistrib2:**

multdistrib2.pdf |

**Up Next for Middle School: EstMultWhole**