**Middle School Number Sense Lesson 89: Subtracting Fractions with Different Denominators**

This concept is very similar to

**AddFracDiff**, but with two important differences. It has appeared 10 times so far this year in middle school, with a median placement at question # 7.

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**How to Solve:**

Similar to

**AddFracDiff**, we will cross-multiply these fractions. But with these, we will:

**Always**start at the top left, and- Subtract instead of adding (obviously).

**Example 1:**

**4/3 –**

**2/7 = ___**

- Cross-multiply, starting at the top left. 4 x 7 =
**28**; 3 x 2 =**6**. - Subtract these results to find the numerator: 28 – 6 =
**22**. - Multiply straight across the bottom to find the denominator: 3 x 7 =
**21**. - The answer is
**22/21**

**Example 2: 5/9**

**– 2/5**

**= ___**

- Cross-multiply, starting at the top left. 5 x 5 =
**25**. 9 x 2 =**18**. - Subtract to find the numerator: 25 – 18 =
**7**. - Multiply straight across to find the denominator: 9 x 5 =
**45**. - The answer is
**7/45**

**Example 3: 7/11**

**– 4/7**

**= ___**

- Cross-multiply, starting at the top left. 7 x 7 =
**49**. 11 x 4 =**44**. - Subtract to find the numerator: 49 – 44 =
**5**. - Multiply straight across to find the denominator: 11 x 7 =
**77**. - The answer is
**5/77**

**Example 4: 5/8**

**+ 3/4**

**– 1/2**

**= ___**

- Since all of these denominators are factors of 8, it may be easier to use that as the lowest common denominator. This becomes
**5/8 + 6/8****– 4/8** - Now add and subtract straight across to find the numerator: 5 + 6 – 4 =
**7**. - Use
**8**as the denominator. - The answer is
**7/8**

**Example 5: 6/13**

**– 2/5**

**= ___**

- Cross-multiply, starting at the top left. 6 x 5 =
**30**. 13 x 2 =**26**. - Subtract to find the numerator: 30 – 26 =
**4**. - Multiply straight across to find the denominator: 13 x 5 =
**65**. - The answer is
**4/65**

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

subfracdiff.pdf |

**Up Next for Middle School: MultFrac100**