Equivalent Fractions

In the pizza on the left, what fraction is one slice of pizza? The answer is 1 part out of the 8 parts, one-eighth or ¹⁄₈.

In the pizza on the right, what fraction is two slices of pizza? The answer is 2 parts out of the 16 parts, two-sixteenths or ²⁄₁₆.

These pizza servings are the same so ¹⁄₈ and ²⁄₁₆ are equivalent fractions.

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Examples

Multiplying both numerator and denominator by the same number:

1⁄2 = 2⁄4 = 4⁄8

To change 1⁄2 to 2⁄4, multiply both the numerator and the denominator by 2.

To change 2⁄4 to 4⁄8, multiply both the numerator and the denominator by 2.

2⁄3 = 4⁄6 = 8⁄12

To change 2⁄3 to 4⁄6, multiply both the numerator and the denominator by 2.

To change 4⁄6 to 8⁄12, multiply both the numerator and the denominator by 2.

Dividing both numerator and denominator by the same number:

4⁄8 = 2⁄4 = 1⁄2

To change 4⁄8 to 2⁄4, divide both the numerator and the denominator by 2.

To change 2⁄4 to 1⁄2, divide both the numerator and the denominator by 2.

8⁄12 = 4⁄6 = 2⁄3

To change 8⁄12 to 4⁄6, divide both the numerator and the denominator by 2.

To change 4⁄6 to 2⁄3, divide both the numerator and the denominator by 2.

More examples of equivalent fractions:

³ ⁄₄ = ⁹ ⁄₁₂ (Multiplied by 3)

⁵ ⁄₆ = ²⁰ ⁄₂₄ (Multiplied by 4)

³⁰ ⁄₃₆ = ⁵ ⁄₆ (Divided by 6)

²⁰ ⁄₃₀ = ² ⁄₃ (Divided by 10)

Changing a Mixed Number to an Improper Fraction

A mixed number is a mixture of a whole number and a fraction. An example of a mixed number is 2¹⁄₂ When a mixed number is converted to a fraction only, it is called an improper fraction. An example of an improper fraction is ⁵ ⁄₂

13⁄4 = 7⁄4

To change the mixed number of 13⁄4 to the improper fraction of 7⁄4, multiply the whole number 1 by the denominator 4, and then add on the numerator 3.

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Changing an Improper Fraction Back to a Mixed Number

12⁄3 = 5⁄3

To change the mixed number of 12⁄3 to the improper fraction of 5⁄3, multiply the whole number 1 by the denominator 3, and then add on the numerator 2.