Fractions · Compare & order · 4.4

Benchmark to one half.

A quick check: is the fraction more or less than ½? If the top is more than half the bottom, it beats ½. Benchmarks make comparisons fast.

01 / THE IDEA

See it work.

Watch the method

Benchmark to ½

3/5: half of 5 is 2.5, and 3 > 2.5, so 3/5 > 1/2.

1 / 2
35  ?  12\frac{3}{5} \;?\; \frac{1}{2}
1

Cross-multiply

Compare numerator×other-denominator.

3×2=6,1×5=53\times2 = 6,\quad 1\times5 = 5
2

Compare

6 > 5.

35>12\frac{3}{5} > \frac{1}{2}
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.

Benchmarks

Compare each fraction to ½ (or 1). One above and one below ½ are easy to order.

Why it works

Past the halfway mark?

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Compare: 2/3 ▢ 4/8

1

Cross-multiply

Compare numerator×other-denominator. 2\times8 = 16,\quad 4\times3 = 12

2

Compare

16 > 12. 2/3 > 4/8

EX 2medium

Compare: 5/6 ▢ 7/8

1

Cross-multiply

Compare numerator×other-denominator. 5\times8 = 40,\quad 7\times6 = 42

2

Compare

40 < 42. 5/6 < 7/8

EX 3hard

Compare: 1/2 ▢ 2/3

1

Cross-multiply

Compare numerator×other-denominator. 1\times3 = 3,\quad 2\times2 = 4

2

Compare

3 < 4. 1/2 < 2/3

04 / COMMON TRAPS

Where students slip.

Trap

Comparing tops directly across different bottoms.

Fix

Use a benchmark like ½ instead.

Trap

Mis-judging half of the denominator.

Fix

Half of 5 is 2.5.

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: 2/3 ▢ 4/8

Need a hint?
  • Half the bottom — is the top above it?
  • Above half beats ½.
C2

Compare: 1/5 ▢ 6/8

Need a hint?
  • Half the bottom — is the top above it?
  • Above half beats ½.
C3

Compare: 4/5 ▢ 1/4

Need a hint?
  • Half the bottom — is the top above it?
  • Above half beats ½.
C4

Compare: 1/3 ▢ 5/6

Need a hint?
  • Half the bottom — is the top above it?
  • Above half beats ½.
Apply

Apply (4)

A1

Compare: 5/6 ▢ 7/8

Need a hint?
  • Half the bottom — is the top above it?
  • Above half beats ½.
A2

Compare: 4/5 ▢ 1/3

Need a hint?
  • Half the bottom — is the top above it?
  • Above half beats ½.
A3

Compare: 3/4 ▢ 1/4

Need a hint?
  • Half the bottom — is the top above it?
  • Above half beats ½.
A4

Compare: 2/4 ▢ 5/7

Need a hint?
  • Half the bottom — is the top above it?
  • Above half beats ½.
Extension

Extension (4)

E1

Compare: 1/2 ▢ 2/3

Need a hint?
  • Half the bottom — is the top above it?
  • Above half beats ½.
E2

Compare: 1/3 ▢ 1/4

Need a hint?
  • Half the bottom — is the top above it?
  • Above half beats ½.
E3

Compare: 2/3 ▢ 2/3

Need a hint?
  • Half the bottom — is the top above it?
  • Above half beats ½.
E4

Compare: 4/5 ▢ 1/2

Need a hint?
  • Half the bottom — is the top above it?
  • Above half beats ½.