**High School Number Sense Lesson 11: Adding Mixed Numbers with Different Denominators**

This concept is a continuation from yesterday's Middle School lesson. (Please take a few moments to review it if you haven't seen it already). But instead of adding regular fractions, we will add mixed numbers. This concept showed up

**16 times**on high school tests this year--as early as question # 1 and as late as question # 26, but usually around

**question # 11**.

**Number Dojo Level: 69**

The long way to add mixed numbers with different denominators is to convert each one to an improper fraction, then find the lowest common denominator, then "un-reduce" each fraction so it has the same denominator, then add them, and then convert the result back to a mixed number.... Confused? Good. Let's solve these by cross-multiplying instead:

**Example 1: 1 2/3 + 3 4/5**

- Ignore the whole numbers until the last step. Add the "cross products" of the fractions to find the numerator. 2 x 5 =
**10**, and 3 x 4 =**12**. 10 + 12 =**22**. - Multiply the denominators (
**3 x 5**) to get the denominator of your answer:**15**. - Convert your answer to a mixed number. 22/15 =
**1 7/15**. This doesn't reduce. - Add the whole numbers from the original question to this result. 1 + 3 + 1 7/15 =
**5 7/15**.

**Example 2: 5 3/4 + 1 2/7**

- Ignore the whole numbers for now. Add the "cross products" of the fractions to get your numerator. 3 x 7 =
**21**, and 4 x 2 =**8**. 21 + 8 =**29**. - Multiply the denominators (
**4 x 7**) to get the denominator of your answer:**28**. - Convert your answer to a mixed number. 29/28 =
**1 1/28**. This doesn't reduce. - Add the whole numbers to this result. 5 + 1 + 1 1/28 =
**7 1/28**.

**Example 3: 14 3/10 + 9 4/5**

- In this case, it is easy to find the lowest common denominator:
**10**. So you are going to convert 4/5 to**8/10**. - Add 3/10 + 8/10 to get
**11/10**. - Convert this answer to a mixed number:
**1 1/10**. This doesn't reduce. - Add the whole numbers to this result. 14 + 9 + 1 1/10 =
**24 1/10**.

Example 4: 4 5/6 + 7 8/9

Example 4: 4 5/6 + 7 8/9

- Ignore the whole numbers for now. Add the "cross products" of the fractions to get your numerator. 5 x 9 =
**45**, and 6 x 8 =**48**. 45 + 48 =**93**. - Multiply the denominators (
**6 x 9**) to get the denominator of your answer:**54**. - Convert the resulting fraction (
**93/54**) to a mixed number:**1 39/54**. Reduce this fraction to get**1 13/18**. - Add the whole numbers to this result. 4 + 7 + 1 13/18 =
**12 13/18**.

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

addmixdiff.pdf |

**Up Next for High School: SubMixDiff**