**High School Number Sense Lesson 38: Multiplying a Fraction by a Whole Number (2nd type)**

A few months ago we learned

**MultFracWhole**. In those cases (multiplying fractions by whole numbers), the whole number was a multiple of the fraction's denominator. This resulted in an integer answer.

Today we will look at problems where the whole number is NOT a multiple of the denominator, which will result in mixed number answers. This concept appeared

**13 times**on high school tests this year--with a median placement at

**question # 37**.

**Number Dojo Level: TBD**

**(Special thanks to my student Riki for figuring out and teaching me how to solve these problems.)**These questions almost always appear in the form of

**A x B/C**, where:

**A**= the whole number,**B**= the numerator, and**C**= the denominator.

**Multa*a/b**, where the whole number is equal to the fraction's numerator).

The solution to these problems will be in the form of

**W N/D**, where:

**W**= the whole number:**A + (B - C)****N**= the numerator:**(C - A)(C - B)****D**= the denominator:**C**

**How to Solve:**

- For the
**numerator**: Subtract the whole number from the denominator. Then subtract the numerator from the denominator. Multiply these differences together. (*Don't write this down yet!)* - For the
**denominator**: use the denominator.**Reduce this fraction if possible**, and write the fraction down. - For the
**whole number**: Look at the original fraction. Subtract the denominator from the numerator, and then add this difference to the original whole number. Write this down.

**This takes practice, so let's look at a few examples. In each case, we will use the A x B/C notation.****Example 1: 9 x 11/13**

- Multiply (C - A) by (C - B). (13 - 9)(13 - 11) = (4)(2) =
**8**. This is your numerator. - C (
**13**) is the denominator. Write down**8/13**as the fraction (since it doesn't reduce). - Take (B - C) and add it to A. 11 - 13 =
**-2**; -2 + 9 =**7**. Write this down as the whole number. - The answer is
**7 8/13**.

**Example 2: 15 x 16/17**

- Multiply (C - A) by (C - B). (17 - 15)(17 - 16) = (2)(1) =
**2**. This is your numerator. - C (
**17**) is the denominator. Write down**2/17**as the fraction (since it doesn't reduce). - Take (B - C) and add it to A. 16 - 17 =
**-1**; -1 + 15 =**14**. Write this down as the whole number. - The answer is
**14 2/17**.

**Example 3: 17 x 18/19**

- Multiply (C - A) by (C - B). (19 - 17)(19 - 18) = (2)(1) =
**2**. This is your numerator. - C (
**19**) is the denominator. Write down**2/19**as the fraction (since it doesn't reduce). - Take (B - C) and add it to A. 18 - 19 =
**-1**; -1 + 17 =**16**. Write this down as the whole number. - The answer is
**16 2/19**.

**Example 4: 11 x 14/17**

- Multiply (C - A) by (C - B). (17 - 11)(17 - 14) = (6)(3) =
**18**. This is your numerator. - C (
**17**) is the denominator, which is less than the numerator. So 18/17 becomes**1 1/17**; write down the**1/17**and regroup the 1. - Take (B - C) and add it to A. 14 - 17 =
**-3**; -3 + 11 =**8**, plus the regrouped 1 =**9**. Write this down as the whole number. - The answer is
**9 1/17**.

**Example 5: 44 x 47/50**

- Multiply (C - A) by (C - B). (50 - 44)(50 - 47) = (6)(3) =
**18**. This is your numerator. - C (
**50**) is the denominator.**18/50**reduces to**9/25**; write this down as the fraction. - Take (B - C) and add it to A. 47 - 50 =
**-3**; -3 + 44 =**41**. Write this down as the whole number. - The answer is
**41 9/25**.

**Here's a free worksheet to help you practice MultFracWhol2:**

multfracwhol2.pdf |

**Up Next for High School: Squares**