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DD.3 Compare fractions with like denominators

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What are like denominators?

Like denominators are denominators that are the same number. When fractions have like denominators, it means they are divided into the same number of equal parts.

Examples:
  • 25 and 35 have like denominators (both are 5).
  • 18 and 78 have like denominators (both are 8).
Note

The denominator is the bottom number in a fraction. It tells you how many total parts make one whole.

How to compare fractions with like denominators

When denominators are the same, you compare only the numerators. The fraction with the greater numerator is the greater fraction because it has more parts of the same size.

Steps:
  • Check that the denominators are the same.
  • Look at the numerators (the top numbers).
  • The fraction with the larger numerator is larger.
  • Example: Compare 37 and 57.
    Denominators are the same (7). Compare 3 and 5. Since 5 > 3, then 57 > 37.
Note

If the numerators are equal, then the fractions are equal. For example, 49 = 49.

Using symbols to compare

We use the symbols > (greater than), < (less than), and = (equal to) to show the relationship between two fractions.

Examples:
  • 23 < 33
  • 710 > 410
  • 512 = 512
Note

Remember, the "open" side of the > or < symbol always points to the larger number or fraction.

Solving comparison problems

Apply the rules for comparing fractions to solve word problems and number sentences.

Practice Problems:
  • John ate 38 of a pizza, and Lisa ate 58 of the same pizza. Who ate more?
    Solution: Compare 38 and 58. Since 5 > 3, Lisa ate more.
  • Fill in the blank with >, <, or =: 46 ____ 26
    Solution: 4 > 2, so 46 > 26.
Note

Drawing two equal-sized models (like rectangles or circles) divided into the same number of parts can help you visualize which fraction is greater.

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