**Middle School Number Sense Lesson 34: Multiplying Mixed Numbers with the Same Whole Number and the Fractions Add up to 1**

Once again, we have a concept whose name sounds more complicated than it is to solve. This is one of my favorite number sense concepts. It appeared

**11 times**this year--always between questions 33 & 35 inclusive, with the median spot at

**question # 34**.

**Number Dojo Level: 117**

This idea is very closely related to

**SquareEnd5**and

**Mult10s,U+10**. (You may wish to review them now by clicking on their hyperlinked nicknames). You will be asked something like this:

**2 1/6 x 2 5/6 = ___ (mixed number)**

**Notice that:**

- The whole numbers are the same (2), and
- The fractional parts add up to 1 (1/6 + 5/6 = 1).

**When these 2 conditions are met, simply:**

- Write down the product of the fractional parts. From the example above, 1/6 x 5/6 =
**5/36**. - Multiply the whole number by its upper neighbor (in other words, itself + 1), and write this product in front of the fraction from Step 1. 2 x (2 + 1) = 2 x 3 =
**6**. The answer is**6 5/36**.

**Example 1: 8 3/4 x 8 1/4 = ___ (mixed number)**

- Multiply the fractional parts: 3/4 x 1/4 =
**3/16**; write this down. - Multiply the whole number by its upper neighbor. 8 x 9 =
**72**; write this in front. The answer is**72 3/16**.

**Example 2: 5 1/3 x 5 2/3 = ___ (mixed number)**

- Multiply the fractions: 1/3 x 2/3 =
**2/9**; write this down. - Multiply the whole number by its upper neighbor. 5 x 6 =
**30**; write this in front. The answer is**30 2/9**.

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

- Multiply the fractions: 5/8 x 3/8 =
**15/64**; write this down. - Multiply 4 by its neighbor (5) to get
**20**; write this in front. The answer is**20 15/64**.

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

- Multiply the fractions: 1/5 x 4/5 =
**4/25**; write this down. - Multiply 11 by 12 to get
**132**; write this in front. The answer is**132 4/25**.

**Example 5: 6 2/9 x 6 7/9 = ___**

- Multiply the fractions: 2/9 x 7/9 =
**14/81**; write this down. - Multiply 6 by 7 to get
**42**; write this in front. The answer is**42 14/81**.

**Example 6: 90 6/25 = 9 3/5 x ___ (mixed number)**

* The test writer is mixing it up a bit. Now that you know the pattern to solving these problems, you will be able to determine that the answer has to be

**9 2/5**. Here's why:

- 2/5 x 3/5 =
**6/25**. - 9 x 10 =
**90**.

**Here's a free worksheet to help you practice MultMixF+1:**

multmixf_1.pdf |

**Up Next for Middle School: AddFracRecip**