**High School Number Sense Lesson 29: Multiplying Mixed Numbers with Different Denominators**

This concept showed up

**11 times**this year on high school tests--with a median spot of

**question # 28**.

**Number Dojo Level: 298**

I'm not sure how I was taught to multiply mixed numbers in school, but I'm guessing that it had something to do with converting them to improper fractions. That may be one way to solve these problems, but it's probably not the quickest way. The way I will teach you involves the

**FOIL**method, which I introduced in my DiffSquares1 blog entry. You may want to review that explanation (under "Why it Works") before you proceed.

*Using the FOIL method is best when each whole number is a multiple of the opposite fraction's denominator*.

**Mixed Numbers**

Mixed numbers are essentially made up of a whole number plus a fraction. When you multiply two mixed numbers together, you can multiply each of the parts and then add all the products together. Let's represent our mixed number problem like this:

**(W1 + F1) x (W2 + F2)**

- W1 is the 1st whole number,
- F1 is the 1st fraction,
- W2 is the 2nd whole number, and
- F2 is the 2nd fraction.

**FOIL**ing. (As a reminder, FOIL stands for

**F**irst,

**O**utside,

**I**nside,

**L**ast. In this case:

**F**: W1 x W2**O**: W1 x F2**I**: F1 x W2**L**: F1 x F2

**Example 1: 3 3/4 x 4 2/3 = ___**

**F**= W1 x W2 = 3 x 4 =**12**.**O**= W1 x F2 = 3 x 2/3 =**2**.**I**= F1 x W2 = 3/4 x 4 =**3**.**L**= F1 x F2 = 3/4 x 2/3 = 6/12 =**1/2**.- Add these up.
**12 + 2 + 3 + 1/2 = 17 1/2**.

**Example 2: 7 2/3 x 6 3/7 = ___**

**F**= W1 x W2 = 7 x 6 =**42**.**O**= W1 x F2 = 7 x 3/7 =**3**.**I**= F1 x W2 = 2/3 x 6 =**4**.**L**= F1 x F2 = 2/3 x 3/7 =**2/7**.- Add these up.
**42 + 3 + 4 + 2/7 = 49 2/7**.

**Example 3: 10 1/3 x 6 1/5 = ___**

**F**= W1 x W2 = 10 x 6 =**60**.**O**= W1 x F2 = 10 x 1/5 =**2**.**I**= F1 x W2 = 1/3 x 6 =**2**.**L**= F1 x F2 = 1/3 x 1/5 =**1/15**.- Add these up.
**60 + 2 + 2 + 1/15 = 64 1/15**.

**Example 4: 8 2/3 x 9 1/2 = ___**

**F**= W1 x W2 = 8 x 9 =**72**.**O**= W1 x F2 = 8 x 1/2 =**4**.**I**= F1 x W2 = 2/3 x 9 =**6**.**L**= 2/3 x 1/2 =**1/3**.- Add these up. 72 + 4 + 6 + 1/3 =
**82 1/3**.

**Example 5: 1 2/5 x 1 1/14 = ___**

- Notice that the FOIL method will not produce easy products, because the whole numbers are NOT multiples of the opposite denominators. (1 is not a multiple of 5 or 14).
**Convert each mixed number to an improper fraction instead**. - 1 2/5 =
**7/5**. 1 1/14 =**15/14**. **7/5 x 15/14**has common factors that can be canceled. 7 becomes 1, and 14 becomes 2. Also, 5 becomes 1, and 15 becomes 3. We are left with**1/1 x 3/2**.- The answer is
**3/2**.

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

multmixdiff.pdf |

**Up Next for High School: EstMultFrac**