What Are Equivalent Fractions?

Equivalent fractions are different fractions that represent the same value or same portion of a whole, even though they look different. They are created by multiplying or dividing both the numerator (top number) and denominator (bottom number) by the same non-zero number.

Key Idea:

✔ They look different but mean the same thing.
✔ You can make them by scaling up or down (multiplying or dividing).
✔ They help simplify fractions for easier calculations.

Examples of Equivalent Fractions

Example 1: ½ = 2⁄4 = 3⁄6

• Pizza Example:
  • ½ → 1 slice out of 2.
  • 2⁄4 → 2 slices out of 4 (same amount as ½).
  • 3⁄6 → 3 slices out of 6 (still the same as ½).

Example 2: ⅓ = 2⁄6 = 3⁄9

• Cake Example:
  • ⅓ → 1 piece out of 3.
  • 2⁄6 → 2 pieces out of 6 (same as ⅓).
  • 3⁄9 → 3 pieces out of 9 (still equal to ⅓).

Example 3: ⅖ = 4⁄10

• Chocolate Bar Example:
  • ⅖ → 2 squares out of 5.
  • 4⁄10 → 4 squares out of 10 (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. 1/3 = __/6
2. 2/5 = __/10
3. 3/4 = __/8
4. 5/6 = 10/__
5. 2/3 = __/9

Exercise 3: Creating Equivalent Fractions

Multiply the numerator and denominator by the same number to create equivalent fractions:

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

Exercise 4: True or False

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

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