Scholars & Parents
ExplainerMathGrades 3–5

Comparing and Ordering Fractions

What Does It Mean to Compare Fractions?

When we compare fractions, we figure out which fraction is greater, which is smaller, or whether they are equal.

We use three symbols:

  • > means "greater than" → 3/4 > 1/4
  • < means "less than" → 1/3 < 2/3
  • = means "equal to" → 2/4 = 1/2

Method 1 — Same Denominator (Easiest!)

When two fractions have the same denominator, just compare the numerators. The bigger numerator wins.

Example: Compare 5/8 and 3/8

Both fractions have denominator 8. Compare the tops:

  • 5 > 3, so 5/8 > 3/8 ✓

Think of it like slices of the same-sized pizza — 5 slices is more than 3 slices.

Method 2 — Same Numerator

When two fractions have the same numerator, the one with the smaller denominator is larger.

Example: Compare 2/5 and 2/9

Both have numerator 2. Compare the bottoms:

  • 5 < 9, and smaller denominator = bigger piece, so 2/5 > 2/9 ✓

Why? If you split something into 5 equal pieces, each piece is bigger than if you split it into 9 pieces.

Method 3 — Common Denominator

When denominators are different, rewrite both fractions so they share a common denominator, then compare numerators.

Example: Compare 3/4 and 5/6

Step 1: Find the Least Common Denominator (LCD) of 4 and 6.

  • Multiples of 4: 4, 8, 12, 16 …
  • Multiples of 6: 6, 12, 18 …
  • LCD = 12

Step 2: Convert each fraction.

  • 3/4 = 9/12 (multiply top and bottom by 3)
  • 5/6 = 10/12 (multiply top and bottom by 2)

Step 3: Compare.

  • 9/12 < 10/12, so 3/4 < 5/6 ✓

Method 4 — Benchmark Fractions

Benchmark fractions are friendly fractions you already know: 0, 1/2, and 1.

Use them as reference points to compare quickly.

Example: Compare 3/8 and 5/7

  • Is 3/8 greater or less than 1/2? → 3/8 < 4/8, so 3/8 < 1/2
  • Is 5/7 greater or less than 1/2? → 5/7 > 3.5/7, so 5/7 > 1/2
  • Since 3/8 < 1/2 and 5/7 > 1/2, we know 3/8 < 5/7 ✓

Quick benchmark check: A fraction equals 1/2 when the numerator is exactly half the denominator.

Method 5 — Cross Multiplication

A fast method for comparing any two fractions.

Example: Compare 4/7 and 5/9

Cross-multiply:

  • 4 × 9 = 36
  • 5 × 7 = 35

Compare the products (match them to the fraction on the same side):

  • 36 > 35, and 36 came from the left fraction, so 4/7 > 5/9 ✓

⚠️ Important: Cross multiplication only works when both fractions are positive.

Ordering Fractions

Ordering fractions means arranging three or more fractions from least to greatest (or greatest to least). Use the same methods above — find a common denominator for all fractions, then sort.

Example: Order 1/2, 3/8, and 5/6 from least to greatest.

Step 1: LCD of 2, 8, and 6.

  • Multiples of 8: 8, 16, 24 …
  • Multiples of 6: 6, 12, 18, 24 …
  • LCD = 24

Step 2: Convert all fractions.

  • 1/2 = 12/24
  • 3/8 = 9/24
  • 5/6 = 20/24

Step 3: Order the numerators: 9 < 12 < 20

Answer: 3/8 < 1/2 < 5/6 ✓

Fractions on a Number Line

A number line is a great visual tool. Fractions closer to 0 are smaller; fractions closer to 1 (or beyond) are larger.

0 -------- 1/4 -------- 1/2 -------- 3/4 -------- 1
           smaller              larger

To place a fraction on a number line, divide the space between 0 and 1 into equal parts matching the denominator, then count up to the numerator.

Key Vocabulary

Word Meaning
Numerator The top number — how many parts you have
Denominator The bottom number — how many equal parts in the whole
Common denominator A shared denominator for two or more fractions
LCD Least Common Denominator — the smallest common denominator
Benchmark fraction A simple reference fraction (0, 1/2, 1) used for estimating
Equivalent fractions Different fractions that represent the same value

Common Mistakes to Avoid

❌ "Bigger denominator = bigger fraction" — WRONG! 1/8 is much smaller than 1/2, even though 8 > 2.

❌ Forgetting to find a common denominator before comparing You cannot simply compare 3/5 and 4/7 by looking at 3 vs. 4 — the denominators are different.

❌ Mixing up < and > Remember: the open side of the symbol faces the larger number. 1/4 < 3/4 (the mouth "eats" the bigger number).

Quick Summary

Situation Strategy
Same denominator Compare numerators directly
Same numerator Smaller denominator = larger fraction
Different numerator & denominator Find common denominator OR cross-multiply
Quick estimate Use benchmark fractions (0, 1/2, 1)
Three or more fractions Convert all to common denominator, then sort

Scholars & Parents — Free K–8 Learning | scholarsandparents.com

Was this helpful?