What Are Equivalent Fractions?

Equivalent fractions encompass different types of fractions that represent equal values, or portions, as a whole. Although they have different forms, both will yield the same results when compared. To create an equivalent fraction, multiply/divide both the numerator (top number) and denominator (bottom number) by the same non-zero number.

Key Points:
✔ Different looks with the same message.
✔ Created from scaling (multiplying or dividing).
✔ Allow for easier calculation and/or simplification of fractions.

Examples of Equivalent Fractions

Example 1: ½, 2⁄4, and 3⁄6 are all the same fraction.
For the pizza example:
½ means 1 slice out of 2: 2 slices out of 4, and that is the same as ½; 3 slices out of 6, or ½.
Example 2: ⅓, 2⁄6, and 3⁄9 are all the same fraction.
For the cake example:
⅓ means 1 piece out of 3; 2 pieces out of 6 is the same as ⅓; 3 pieces out of 9 is still the same as ⅓.
Example 3: ⅖ and 4⁄10 are equal fractions.
Chocolate bar example:
⅖ means 2 squares out of 5; 4 squares out of 10, which are the same as ⅖.

How to Find Equivalent Fractions

Method 1: Multiply Numerator & Denominator
To find an equivalent fraction, multiply both the numerator and denominator by the same number.

Example: Find a fraction equivalent to ¾.

Multiply numerator & denominator by 2:3×24×2=684×23×2​=86​→ ¾ = 6⁄8
Method 2: Divide Numerator & Denominator
You can also divide both numbers by the same number (simplifying).

Example: Simplify 8⁄12.

Divide numerator & denominator by 4:8÷412÷4=2312÷48÷4​=32​→ 8⁄12 = ⅔

Exercises

Exercise 1: Identifying Equivalent Fractions
Circle the fractions that are equivalent to 1/2:

2/4
3/6
4/8
2/5
5/10

Exercise 2: Fill in the Missing Number
Fill in the blank to make the fractions equivalent:

1/3 = /6
2/5 = /10
3/4 = /8
5/6 = 10/
2/3 = __/9

Exercise 3: Creating Equivalent Fractions
Multiply the numerator and denominator by the same number to create equivalent fractions:

2/3 (Multiply by 2) = /
3/5 (Multiply by 3) = /
4/6 (Multiply by 4) = /
1/4 (Multiply by 5) = /

Exercise 4: True or False
Determine if the following pairs of fractions are equivalent (True or False):

3/6 and 1/2
4/8 and 2/4
2/3 and 3/5
6/9 and 2/3
8/10 and 4/5