Class Note: Comparing Fractions

Objective

To learn how to compare two fractions and determine which is greater, especially when the denominators are different.

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Steps for Comparing Fractions

1. Get a Common Denominator

   • Multiply each fraction by a form of 1 using the denominator of the other fraction.

2. Multiply Across

   • For each fraction, multiply both the numerator and denominator by the appropriate value as set in step 1.

3. Compare Numerators

   • Once denominators are the same, compare the numerators. The fraction with the larger numerator is greater.

4. (Optional) Confirm with Decimals

   • Convert each fraction to a decimal for a double check.

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Examples

Example 1: Compare 3/4 and 4/5

• Get common denominators:
  • Multiply 3/4 by 5/5 → 15/20
  • Multiply 4/5 by 4/4 → 16/20
• Compare numerators: 16 > 15
  • So, 4/5 > 3/4
• Decimal Check:
  • 3/4 = 0.75
  • 4/5 = 0.8
  • 0.8 > 0.75

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Example 2: Compare 5/6 and 6/7

• Get common denominators:
  • 5/6 × 7/7 → 35/42
  • 6/7 × 6/6 → 36/42
• Compare numerators: 36 > 35
  • So, 6/7 > 5/6

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Example 3: Compare 5/9 and 4/7

• Get common denominators:
  • 5/9 × 7/7 → 35/63
  • 4/7 × 9/9 → 36/63
• Compare numerators: 36 > 35
  • So, 4/7 > 5/9
• Decimal Check:
  • 5/9 ≈ 0.555...
  • 4/7 ≈ 0.5714
  • 0.5714 > 0.555...

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Summary

• To compare fractions with different denominators, convert them to equivalent fractions with a common denominator and compare the numerators.
• Optionally, use decimals for confirmation.
• This method works for any pair of fractions.