**Middle School Number Sense Lesson 23: Multiplying Mixed Numbers by Whole Numbers**

This concept was tested

**9 times**this year--as early as question 12 but most often as

**question 23 or 24**. Usually the whole number will be a multiple of the fraction's denominator.

**Number Dojo Level: 64**

When this type of problem appears on the test, it will usually have the whole number in front, followed by the mixed number. Check to see if the fraction's denominator is the same as the whole number (it most likely is). Either way, you will go through the 2 steps of converting a mixed number to an improper fraction. I will illustrate the variations in the examples below.

**How to Solve:**

- For now, ignore the whole number in front. Convert the mixed number to an improper fraction by multiplying its denominator by its whole number and adding the numerator. Put this over the denominator.
- Multiply the whole number (in front) by the new improper fraction.

**Example 1: 5 x 4 2/5**

- Convert the mixed number to an improper fraction. Multiply its denominator (5) by its whole number (4). 5 x 4 =
**20**. Add the numerator. 20 + 2 =**22**. You have**22/5**. - Now check the whole number in front. Your problem has become
**5 x 22/5**. The 5's cancel out, so your answer is**22**.

**Example 2: 7 x 3 2/7**

- Convert the mixed number to an improper fraction. Multiply its denominator (7) by its whole number (3). 7 x 3 =
**21**. Add the numerator. 21 + 2 =**23**. You have**23/7**. - Now check the whole number in front. Your problem has become
**7 x 23/7**. The 7's cancel, so your answer is**23**.

**Example 3: 6 x 7 5/6**

- Convert the mixed number to an improper fraction. 6 x 7 =
**42**. 42 + 5 =**47**. You have**47/6**. - Check the whole number in front. Your problem is now 6 x 47/6. The 6's cancel, so the answer is
**47**.

**Example 4: 16 x 5 3/8**

- Convert the mixed number to an improper fraction. 8 x 5 =
**40**. 40 + 3 =**43**. You have**43/8**. - Check the whole number in front. Your problem is now 16 x 43/8, or (2 x 8) x 43/8. The 8's cancel, so you have 2 x 43 =
**86**.

**Example 5: 12 x 9 1/6**

- Convert the mixed number to an improper fraction. 6 x 9 = 54. 54 + 1 =
**55**. You have**55/6**. - Your problem is now 12 x 55/6, which is (2 x 6) x 55/6. The 6's cancel, so you have 2 x 55 =
**110**.

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

multmixwhole.pdf |

**Up Next for Middle School: Mult101-109**