Fractions · Compare & order · 4.2

Same numerator.

With the same numerator, you have the same number of pieces — but smaller pieces when the denominator is bigger. So a smaller denominator is bigger.

01 / THE IDEA

See it work.

Picture it

Shaded parts out of the whole.

1
3

Watch the method

Same numerator

1/3 vs 1/5: thirds are bigger than fifths.

1 / 2
13  ?  15\frac{1}{3} \;?\; \frac{1}{5}
1

Cross-multiply

Compare numerator×other-denominator.

1×5=5,1×3=31\times5 = 5,\quad 1\times3 = 3
2

Compare

5 > 3.

13>15\frac{1}{3} > \frac{1}{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.

Piece size

A larger denominator cuts the whole into smaller pieces. One of a big piece beats one of a small piece.

Why it works

One-third of a pizza beats one-fifth.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Compare: 1/2 ▢ 1/3

1

Cross-multiply

Compare numerator×other-denominator. 1\times3 = 3,\quad 1\times2 = 2

2

Compare

3 > 2. 1/2 > 1/3

EX 2medium

Compare: 5/6 ▢ 3/4

1

Cross-multiply

Compare numerator×other-denominator. 5\times4 = 20,\quad 3\times6 = 18

2

Compare

20 > 18. 5/6 > 3/4

EX 3hard

Compare: 4/7 ▢ 4/8

1

Cross-multiply

Compare numerator×other-denominator. 4\times8 = 32,\quad 4\times7 = 28

2

Compare

32 > 28. 4/7 > 4/8

04 / COMMON TRAPS

Where students slip.

Trap

Assuming a bigger denominator is bigger.

Fix

Bigger bottom = smaller pieces.

Trap

Ignoring that the numerators match.

Fix

Equal tops shift the focus to the bottoms.

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 ▢ 1/3

Need a hint?
  • Same top? smaller bottom wins.
  • Bigger bottom = smaller pieces.
C2

Compare: 1/6 ▢ 1/5

Need a hint?
  • Same top? smaller bottom wins.
  • Bigger bottom = smaller pieces.
C3

Compare: 2/3 ▢ 3/6

Need a hint?
  • Same top? smaller bottom wins.
  • Bigger bottom = smaller pieces.
C4

Compare: 5/6 ▢ 3/7

Need a hint?
  • Same top? smaller bottom wins.
  • Bigger bottom = smaller pieces.
Apply

Apply (4)

A1

Compare: 5/6 ▢ 3/4

Need a hint?
  • Same top? smaller bottom wins.
  • Bigger bottom = smaller pieces.
A2

Compare: 1/2 ▢ 3/8

Need a hint?
  • Same top? smaller bottom wins.
  • Bigger bottom = smaller pieces.
A3

Compare: 5/7 ▢ 2/8

Need a hint?
  • Same top? smaller bottom wins.
  • Bigger bottom = smaller pieces.
A4

Compare: 6/8 ▢ 1/2

Need a hint?
  • Same top? smaller bottom wins.
  • Bigger bottom = smaller pieces.
Extension

Extension (4)

E1

Compare: 4/7 ▢ 4/8

Need a hint?
  • Same top? smaller bottom wins.
  • Bigger bottom = smaller pieces.
E2

Compare: 2/3 ▢ 4/7

Need a hint?
  • Same top? smaller bottom wins.
  • Bigger bottom = smaller pieces.
E3

Compare: 3/6 ▢ 4/8

Need a hint?
  • Same top? smaller bottom wins.
  • Bigger bottom = smaller pieces.
E4

Compare: 2/8 ▢ 6/7

Need a hint?
  • Same top? smaller bottom wins.
  • Bigger bottom = smaller pieces.