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Fractions course overview
Section 02 · Comparison and Equivalence · F07

Comparing fractions with different numerators and denominators

I can compare any two fractions using benchmarks, common denominators or common numerators.

Builds on: F04 Comparing fractions with the same numerator or denominator, F06 Generating equivalent fractions

Learn

Which is a bigger share of the class: 5 of 8 students, or 7 of 12?

Benchmarks help: compare each fraction with 1/2 or 1. 5/8 is more than 1/2, while 3/7 is less than 1/2, so 5/8 > 3/7.

Common denominators make the parts the same size. To compare 2/3 and 3/4, rewrite them as 8/12 and 9/12. Now 8/12 < 9/12.

Cross-multiplying is a shortcut for the same idea: compare 2 × 4 with 3 × 3.

Always check: if the rewritten fractions are equal, the originals are equal.

Worked examples

Using a common denominator

1/31/31/3
1/41/41/41/4
  1. A common denominator for 3 and 4 is 12.
  2. 2/3 = 8/12 and 3/4 = 9/12.
  3. 8/12 < 9/12, so 2/3 < 3/4.

Using the benchmark 1/2

  1. Half of 8 is 4, and 5 > 4, so 5/8 > 1/2.
  2. Half of 9 is 4.5, and 4 < 4.5, so 4/9 < 1/2.
  3. So 5/8 > 4/9.

Explore

Place 5/8 on the line, then try 7/12 and 2/3. Which lands furthest to the right?

01/82/83/84/85/86/87/81
Number line from 0 to 1, each whole split into 8 equal parts. A point marks 5 eighths, 5 jumps of one 8th from zero.
Numerator5
Denominator8

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: 3/5 ? 2/3

2

Choose the symbol: 5/8 ? 1/2

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: 7/12 ? 5/9

2

Choose the symbol: 3/5 ? 6/10

3

Choose the symbol: 3/7 ? 5/8

4

What is the smallest common denominator of 4/6 and 3/4?

Type a whole number.

Common mistakes

Saying 3/4 < 4/7 because 4 < 7 and 3 < 4.

Why it happens: The numbers alone do not tell you the size; part sizes differ.

What to do: Rewrite with a common denominator or compare to 1/2.

Making a common denominator but forgetting to scale the numerator.

Why it happens: 2/3 is not 2/12 — the numerator must be multiplied by the same factor.

What to do: Write the multiplier beside both numbers: 2/3 × 4/4 = 8/12.

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: 4/5 ? 5/6

2

Choose the symbol: 2/9 ? 1/3

3

Choose the symbol: 9/12 ? 3/4

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
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