Fractions · Compare & order · 4.3

Common denominator.

To compare any two fractions, give them a common denominator (or cross-multiply), then compare the numerators.

01 / THE IDEA

See it work.

Watch the method

Common denominator

3/4 vs 2/3: cross-multiply 9 vs 8 → 3/4 is bigger.

1 / 2
34  ?  23\frac{3}{4} \;?\; \frac{2}{3}
1

Cross-multiply

Compare numerator×other-denominator.

3×3=9,2×4=83\times3 = 9,\quad 2\times4 = 8
2

Compare

9 > 8.

34>23\frac{3}{4} > \frac{2}{3}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a fraction like 3/4 or 1 1/2.

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— / WHY IT WORKS

The idea underneath.

Make them comparable

Cross-multiplying compares a·d with c·b — a shortcut for a common denominator.

Why it works

Put both over the same-size pieces.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Compare: 4/8 ▢ 1/2

1

Cross-multiply

Compare numerator×other-denominator. 4\times2 = 8,\quad 1\times8 = 8

2

Compare

8 = 8. 4/8 = 1/2

EX 2medium

Compare: 1/2 ▢ 1/2

1

Cross-multiply

Compare numerator×other-denominator. 1\times2 = 2,\quad 1\times2 = 2

2

Compare

2 = 2. 1/2 = 1/2

EX 3hard

Compare: 3/4 ▢ 4/6

1

Cross-multiply

Compare numerator×other-denominator. 3\times6 = 18,\quad 4\times4 = 16

2

Compare

18 > 16. 3/4 > 4/6

04 / COMMON TRAPS

Where students slip.

Trap

Comparing tops without matching bottoms.

Fix

Match the denominators first (or cross-multiply).

Trap

Cross-multiplying in the wrong direction.

Fix

Compare a·d with c·b.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Compare: 4/8 ▢ 1/2

Need a hint?
  • Cross-multiply the two fractions.
  • Bigger product = bigger fraction.
C2

Compare: 3/5 ▢ 1/2

Need a hint?
  • Cross-multiply the two fractions.
  • Bigger product = bigger fraction.
C3

Compare: 3/8 ▢ 1/2

Need a hint?
  • Cross-multiply the two fractions.
  • Bigger product = bigger fraction.
C4

Compare: 2/5 ▢ 3/4

Need a hint?
  • Cross-multiply the two fractions.
  • Bigger product = bigger fraction.
Apply

Apply (4)

A1

Compare: 1/2 ▢ 1/2

Need a hint?
  • Cross-multiply the two fractions.
  • Bigger product = bigger fraction.
A2

Compare: 3/4 ▢ 1/7

Need a hint?
  • Cross-multiply the two fractions.
  • Bigger product = bigger fraction.
A3

Compare: 2/3 ▢ 4/6

Need a hint?
  • Cross-multiply the two fractions.
  • Bigger product = bigger fraction.
A4

Compare: 3/4 ▢ 1/2

Need a hint?
  • Cross-multiply the two fractions.
  • Bigger product = bigger fraction.
Extension

Extension (4)

E1

Compare: 3/4 ▢ 4/6

Need a hint?
  • Cross-multiply the two fractions.
  • Bigger product = bigger fraction.
E2

Compare: 1/2 ▢ 1/6

Need a hint?
  • Cross-multiply the two fractions.
  • Bigger product = bigger fraction.
E3

Compare: 2/5 ▢ 4/7

Need a hint?
  • Cross-multiply the two fractions.
  • Bigger product = bigger fraction.
E4

Compare: 7/8 ▢ 7/8

Need a hint?
  • Cross-multiply the two fractions.
  • Bigger product = bigger fraction.