Skip to content
seshvi.
Fractions course overview
Section 02 · Comparison and Equivalence · F04

Comparing fractions with the same numerator or denominator

I can compare fractions that share a numerator or a denominator by reasoning about parts.

Builds on: F02 Non-unit fractions and fractions greater than one

Learn

Would you rather have 3/8 or 5/8 of a cake? What about 2/3 or 2/5?

Same denominator: the parts are the same size. Whoever has more parts has more. 5/8 > 3/8.

Same numerator: you have the same number of parts, so compare part size. Fewer equal parts in the whole means bigger parts. 2/3 > 2/5.

Comparisons only make sense when both fractions refer to the same-sized whole.

Use < for “less than”, > for “greater than”, and = for “equal to”.

Worked examples

Same denominator

1/81/81/81/81/81/81/81/8
1/81/81/81/81/81/81/81/8
  1. Both are eighths, so the parts match.
  2. 3 parts compared with 5 parts.
  3. 3/8 < 5/8.

Same numerator

1/31/31/3
1/51/51/51/51/5
  1. Both have 2 parts.
  2. Thirds are larger than fifths.
  3. 2/3 > 2/5.

Explore

Keep the numerator at 2 and change the denominator. Then fix the denominator and change the numerator. Which change makes the shaded amount grow?

Fraction circles showing 2 fifths: 1 circle, each cut into 5 equal slices, with 2 shaded.
Numerator2
Denominator5

Guided practice

Use the hints as much as you like. You can try each question as many times as you need.

0 of 2 solved

1

Choose the symbol: 3/8 ? 5/8

2

Choose the symbol: 2/3 ? 2/5

Independent practice

Answers are checked exactly — equivalent fractions count unless a question asks for a particular form.

0 of 4 solved

1

Choose the symbol: 4/7 ? 4/9

2

Choose the symbol: 7/10 ? 9/10

3

Choose the symbol: 3/4 ? 3/4

4

Maya says 1/6 > 1/4 because 6 > 4. Is she right?

Common mistakes

Deciding 2/5 > 2/3 because 5 > 3.

Why it happens: The denominator is how many parts the whole is split into; bigger denominator, smaller parts.

What to do: When numerators match, the smaller denominator wins.

Comparing fractions of different-sized wholes.

Why it happens: 1/2 of a small pizza can be less than 1/4 of a giant pizza.

What to do: Always picture the same whole for both fractions.

Lesson check

Three practice questions to check your understanding. Hints and retries are allowed, so this counts as practice — not mastery.

0 of 3 solved

1

Choose the symbol: 5/12 ? 7/12

2

Choose the symbol: 3/5 ? 3/8

3

Choose the symbol: 6/7 ? 6/6

Show mastery on your own

Ready? Answer 4 new questions with no hints and one try each. This is the only way a lesson is marked as mastered.

Start mastery check
Previous: F03Next: F05