**High School Number Sense Lesson 90: Comparing Fractions**

These problems aren’t very common lately, but they show up every year on every level of tests (Elementary, Middle, and High School). So this is an important concept to master. It has shown up

**3 times**this year in middle school, with a median placement at

**question # 11**.

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These questions will look like this: "

**Which is smaller, a/b or c/d?**"

**How to Solve:**

- Cross-multiply (I think of my finger or pen
**pointing at the numerator**of each fraction when I’m cross-multiplying. In other words, I’m pointing up diagonally to the right, vs diagonally to the left). - Identify which product satisfies the question (greater or smaller). Use the fraction which contains that numerator.

**Example 1: Which is smaller, 5/7**

**or 8/11**

**? ___**

- Cross-multiply: 5 x 11 =
**55**; 8 x 7 =**56** - 55 < 56, so use the fraction with the numerator of 5:
**5/7**

**Example 2: Which is larger, 6/13**

**or 4/9**

**? ___**

- Cross-multiply: 6 x 9 =
**54**; 4 x 13 =**52** - 54 > 52, so use the fraction with the numerator of 6:
**6/13**

**Example 3: Which is smaller, - 7/9**

**or - 4/5**

**? ___**

- Cross-multiply: -7 x 5 =
**-35**; -4 x 9 =**-36** - -35 > -36, so use the fraction with the numerator of -4:
**- 4/5**

**Example 4: Which is greater, 5/7**

**or 7/10**

**? ___**

- Cross-multiply: 5 x 10 =
**50**; 7 x 7 =**49** - 50 > 49, so use the fraction with the numerator of 5:
**5/7**

**Example 5: Which is smaller, 8/13**

**or 5/8**

**? ___**

- Cross-multiply: 8 x 8 =
**64**; 5 x 13 =**65** - 64 < 65, so use the fraction with the numerator of 8:
**8/13**

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

comparefrac.pdf |

**Up Next for High School: ConvMetric**