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DD.2 Compare fractions with like numerators

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What is comparing fractions?

Comparing fractions means deciding which fraction represents a larger or smaller part of a whole. When fractions have the same numerators, we compare the denominators to find the answer.

Examples:
  • Which is greater: 34 or 38?
  • Which is smaller: 25 or 23?
Note

The numerator (top number) tells how many parts you have. The denominator (bottom number) tells how many equal parts make one whole.

How to compare fractions with like numerators

When two fractions have the same numerator, look at the denominators. The fraction with the smaller denominator is the larger fraction.

Steps:
  • Check that the numerators are the same.
  • Look at the denominators: 58 vs. 56.
  • Since 6 is less than 8, the parts are larger. So, 56 > 58.
Note

Think of a pizza cut into 6 slices versus one cut into 8 slices. The slices from the pizza cut into 6 pieces are larger. Five of the larger slices is more pizza than five of the smaller slices.

Understanding the rule with models

A visual model can show why a smaller denominator means a larger fraction when numerators are the same.

Example:
  • 23 of a bar is larger than 24 of an identical bar.
  • Both have 2 parts, but thirds are larger pieces than fourths.
  • So, 23 > 24.
Note

If you share something among fewer people, each person gets more. That's the idea behind this rule.

Using symbols to compare

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

Examples:
  • 12 1512 > 15
  • 49 4749 < 47
  • 38 3838 = 38
Note

Remember, the "greater than" symbol (>) always opens toward the larger fraction. The "less than" symbol (<) points toward the smaller fraction.

Applying the skill in problems

Use the rule to solve comparison problems and check your reasoning with a simple drawing if needed.

Word Problem:
  • Maria ate 34 of her sandwich. Leo ate 36 of his identical sandwich. Who ate more?
  • Numerators are the same (3). Compare denominators: 4 and 6.
  • Since 4 < 6, the fraction with denominator 4 is larger. Maria ate more.
Note

Always ask yourself: "Are the numerators the same?" If yes, then the smaller denominator means the bigger fraction.