← Back to Math Adventures

Equivalent Fractions

Overview

Same amount, different name.

What is it?

1/2 is the same as 2/4, 3/6, and 50/100.

History

Crucial for adding fractions with different denominators.

Key Idea

Whatever you multiply the top by, multiply the bottom by.

Practice This Topic

Concept Guide

Plain English: If you cut a cake into 2 pieces and eat 1, it's the same amount of cake as cutting it into 100 pieces and eating 50. The numbers change, but the hunger satisfied is the same.

Real-world example: Cooking. If a recipe calls for 1/2 cup of sugar but you only have a 1/4 cup scoop, you use 2 scoops (2/4).

Common Pitfall

Adding to the top and bottom instead of multiplying. 1/2 is NOT the same as (1+1)/(2+1) = 2/3.

Word Problem
"You need a 3/4 inch wrench, but your set is in 16ths. Which wrench do you grab?"
Reasoning: Multiply top and bottom of 3/4 by 4. 3x4=12. 4x4=16. Grab the 12/16 wrench.

Practice Examples

Scaling Up
1 x2 2 - = = - 3 x2 6
Multiplied both by 2.