**High School Number Sense Lesson 12: Subtracting Mixed Numbers with Different Denominators**

This concept is very similar to Wednesday's lesson. (Please take a few moments to review it if you haven't seen it already). Instead of adding mixed numbers though, we will be subtracting them. This concept showed up

**16 times**this year--as early as question # 7 and as late as question # 19, but on average at

**question # 13**.

**Number Dojo Level: 70**

The main difference between this concept and adding mixed numbers is that sometimes we must regroup (borrow from) the whole numbers. We will still solve by cross-multiplying.

**Example 1: 4 5/6 - 2 3/4**

- Ignore the whole numbers for now. Subtract the "cross products" of the fractions to find the numerator. (Be sure to keep the left numerator on the left). 5 x 4 =
**20**, and 6 x 3 =**18**. 20 - 18 =**2**. - Multiply the denominators (
**6 x 4**) to get the denominator of your answer:**24**. - Reduce the resulting fraction (
**2/24**) if necessary:**1/12**. - Subtract the whole numbers in the original question: 4 - 2 =
**2**. - Combine your whole number in step 4 to your fraction from step 3 to get
**2 1/12**.

**Example 2: 5 2/7 - 3 1/9**

- Ignore the whole numbers for now. Subtract the "cross products" of the fractions to find the numerator. 2 x 9 =
**18**, and 7 x 1 =**7**. 18 - 7 =**11**. - Multiply the denominators (
**7 x 9**) to get the denominator of your answer:**63**. - Reduce the resulting fraction (
**11/63**) if necessary. This doesn't reduce. - Subtract the whole numbers in the original question: 5 - 3 =
**2**. - Combine your fraction from step 3 to get
**2 11/63**.

**Example 3: 3 1/4 - 1 5/9**

- Ignore the whole numbers for now. Subtract the "cross products" of the fractions to find the numerator. 1 x 9 =
**9**, and 4 x 5 =**20**. 9 - 20 =**-11**. - Multiply the denominators (
**4 x 9**) to get the denominator of your answer:**36**. - Your resulting fraction is
**-11/36**. Regroup by**changing the 3 to 2 + 36/36**. Then add 36/36 & -11/36 to get**25/36**. This doesn't reduce. - Subtract the whole numbers: 2 (regrouped from 3) - 1 =
**1**. - Combine your fraction from step 3 to get
**1 25/36**.

**Example 4: 4 5/12 - 2 2/3**

- Sometimes it may be easier to find the lowest common denominator. In this case it is 12, because both 3 and 12 are factors of 12. Change the problem to read:
**4 5/12 - 2 8/12**. - Notice that the first fraction is smaller than the second fraction. Regroup 1 from the 4 to get
**3 + 12/12**. Add the 5/12 to get**3 17/12**. - Subtract the fractional parts: 17/12 - 8/12 =
**9/12**. This reduces to**3/4**. - Subtract the whole numbers: 3 (regrouped from 4) - 2 =
**1**. - Combine your fraction from step 3 to get
**1 3/4**.

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

submixdiff.pdf |

**Up Next for High School: Mult%**