Fractions · Compare & order · 4.1

Same denominator.

With the same denominator, the pieces are the same size, so just compare the numerators — more pieces means bigger.

01 / THE IDEA

See it work.

Picture it

Shaded parts out of the whole.

3
5

Watch the method

Same denominator

3/5 vs 2/5: 3 pieces beats 2 pieces.

1 / 2
35  ?  25\frac{3}{5} \;?\; \frac{2}{5}
1

Cross-multiply

Compare numerator×other-denominator.

3×5=15,2×5=103\times5 = 15,\quad 2\times5 = 10
2

Compare

15 > 10.

35>25\frac{3}{5} > \frac{2}{5}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

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

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Equal-size pieces

When denominators match, the fraction with the bigger numerator is bigger.

Why it works

Three fifths is more than two fifths.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Compare: 1/2 ▢ 6/7

1

Cross-multiply

Compare numerator×other-denominator. 1\times7 = 7,\quad 6\times2 = 12

2

Compare

7 < 12. 1/2 < 6/7

EX 2medium

Compare: 3/5 ▢ 5/8

1

Cross-multiply

Compare numerator×other-denominator. 3\times8 = 24,\quad 5\times5 = 25

2

Compare

24 < 25. 3/5 < 5/8

EX 3hard

Compare: 3/7 ▢ 4/7

1

Cross-multiply

Compare numerator×other-denominator. 3\times7 = 21,\quad 4\times7 = 28

2

Compare

21 < 28. 3/7 < 4/7

04 / COMMON TRAPS

Where students slip.

Trap

Thinking a bigger denominator means bigger.

Fix

Here the denominators are equal; compare tops.

Trap

Reversing the inequality.

Fix

More pieces = larger fraction.

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: 1/2 ▢ 6/7

Need a hint?
  • Same bottom? compare tops.
  • More on top is bigger.
C2

Compare: 1/2 ▢ 3/8

Need a hint?
  • Same bottom? compare tops.
  • More on top is bigger.
C3

Compare: 1/4 ▢ 4/7

Need a hint?
  • Same bottom? compare tops.
  • More on top is bigger.
C4

Compare: 3/5 ▢ 1/3

Need a hint?
  • Same bottom? compare tops.
  • More on top is bigger.
Apply

Apply (4)

A1

Compare: 3/5 ▢ 5/8

Need a hint?
  • Same bottom? compare tops.
  • More on top is bigger.
A2

Compare: 1/2 ▢ 2/3

Need a hint?
  • Same bottom? compare tops.
  • More on top is bigger.
A3

Compare: 3/6 ▢ 3/6

Need a hint?
  • Same bottom? compare tops.
  • More on top is bigger.
A4

Compare: 2/4 ▢ 2/5

Need a hint?
  • Same bottom? compare tops.
  • More on top is bigger.
Extension

Extension (4)

E1

Compare: 3/7 ▢ 4/7

Need a hint?
  • Same bottom? compare tops.
  • More on top is bigger.
E2

Compare: 4/8 ▢ 1/6

Need a hint?
  • Same bottom? compare tops.
  • More on top is bigger.
E3

Compare: 3/5 ▢ 6/7

Need a hint?
  • Same bottom? compare tops.
  • More on top is bigger.
E4

Compare: 1/3 ▢ 2/4

Need a hint?
  • Same bottom? compare tops.
  • More on top is bigger.