**Middle School Number Sense Lesson 52: Multiplying Mixed Numbers with the Same Fraction**

I have been waiting anxiously for today's lesson--it's one of my favorites. In the past, we have covered multiplying mixed numbers with different relationships in

**MultMixDiff**and

**MultMixF+1**. We've also covered multiplying a mixed number by a whole number in

**MultMixWhole**. Today we will multiply two whole numbers that have the fraction in common. This concept appeared

**8 times**last year, with a median placement at

**question # 51**.

**Number Dojo Level: 140**

To become proficient with this skill, it is helpful to know how to FOIL, which I first introduced in

**DiffSquares1**. But even without mastering that concept, you can still do this one.

**How to Solve:**

- Add the two whole numbers and then multiply their sum by the common fraction.
- Multiply the two whole numbers and add the result from Step 1. Write this down.
- Square the fraction and write down the result.

**Example 1: 6 1/3 x 9 1/3 = ___ (mixed number)**

- Add 6 + 9 to get
**15**. Multiply 15 x 1/3 to get**5**. - Multiply 6 x 9 to get
**54**. Add**5**to get**59**; write this down. - Square 1/3 to get
**1/9**; write this down. Your answer is**59 1/9**.

**Example 2: 12 1/7 x 2 1/7 = ___ (mixed number)**

- Add 12 + 2 to get
**14**. Multipy 14 x 1/7 to get**2**. - Multiply 12 x 2 to get
**24**. Add 2 to get**26**; write this down. - Square 1/7 to get
**1/49**; write this down. Your answer is**26 1/49**.

**Example 3: 4 1/5 x 11 1/5 = ___ (mixed number)**

- Add 4 + 11 to get
**15**. Multiply 15 x 1/5 to get**3**. - Multiply 4 x 11 to get
**44**. Add 3 to get**47**; write this down. - Square 1/5 to get
**1/25**; write this down. Your answer is**47 1/25**.

**Example 4: 17 3/10 x 3 3/10 = ___ (mixed number)**

- Add 17 + 3 to get
**20**. Multiply 20 x 3/10 to get**6**. - Multiply 17 x 3 to get
**51**. Add 6 to get**57**; write this down. - Square 3/10 to get
**9/100**; write this down. Your answer is**57 9/100**.

**Example 5: 8 3/4 x 8 3/4 = ___ (mixed number)**

- Add 8 + 8 to get
**16**. Multiply 16 x 3/4 to get**12**. - Mltiply 8 x 8 to get
**64**. Add 12 to get**76**; write this down. - Square 3/4 to get
**9/16**; write this down. Your answer is**76 9/16**.

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

multmixsamef.pdf |

**Up Next for Middle School: Triangles**