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K.2 Simplify fractions

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What does it mean to simplify fractions?

To simplify a fraction means to make the fraction as small as possible without changing its value. You do this by dividing both the numerator and the denominator by the same number, called a common factor.

Example:
  • 48 → divide both by 4 → 12
Note

A simplified fraction means the numerator and denominator have no common factor other than 1.

How to simplify fractions

Follow these steps to simplify any fraction to its lowest terms.

Steps:
  • Step 1: Find the greatest common factor (GCF) of the numerator and denominator.
  • Step 2: Divide both the numerator and denominator by the GCF.
  • Step 3: Write the new fraction using the results.
Note

You can check your work by confirming that no number (other than 1) divides evenly into both parts of the new fraction.

Examples of simplifying fractions

Let’s look at how to simplify different fractions step by step.

Examples:
  • 69 → GCF is 3 → 63 = 2 and 93 = 3 → 23
  • 1216 → GCF is 4 → 124 = 3 and 164 = 4 → 34
  • 1025 → GCF is 5 → 105 = 2 and 255 = 5 → 25
Note

Simplifying fractions does not change their value. For example, 23 and 69 represent the same amount.

Improper fractions and mixed numbers

When the numerator is greater than the denominator, the fraction is called an improper fraction. You can simplify it and write it as a mixed number if needed.

Example:
  • 84 → divide both by 4 → 21 or just 2
  • 96 → divide both by 3 → 32 → as a mixed number: 1 12
Note

Improper fractions and mixed numbers show the same value. You can use either form depending on the problem.