Fractions · Compare & order · 4.5

Order a set.

To order several fractions, give them a common denominator (or use benchmarks), then line up the numerators from small to large.

01 / THE IDEA

See it work.

Watch the method

Order a set

Compare pairwise with a common denominator.

1 / 2
58  ?  23\frac{5}{8} \;?\; \frac{2}{3}
1

Cross-multiply

Compare numerator×other-denominator.

5×3=15,2×8=165\times3 = 15,\quad 2\times8 = 16
2

Compare

15 < 16.

58<23\frac{5}{8} < \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.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Ordering

Once over a common denominator, ordering is just ordering whole-number numerators.

Why it works

Same-size pieces make a fair race.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Compare: 1/3 ▢ 5/6

1

Cross-multiply

Compare numerator×other-denominator. 1\times6 = 6,\quad 5\times3 = 15

2

Compare

6 < 15. 1/3 < 5/6

EX 2medium

Compare: 1/5 ▢ 3/4

1

Cross-multiply

Compare numerator×other-denominator. 1\times4 = 4,\quad 3\times5 = 15

2

Compare

4 < 15. 1/5 < 3/4

EX 3hard

Compare: 5/6 ▢ 1/2

1

Cross-multiply

Compare numerator×other-denominator. 5\times2 = 10,\quad 1\times6 = 6

2

Compare

10 > 6. 5/6 > 1/2

04 / COMMON TRAPS

Where students slip.

Trap

Ordering by denominator size.

Fix

Convert to a common denominator first.

Trap

Mixing up ascending and descending.

Fix

Decide the direction and stick to it.

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: 1/3 ▢ 5/6

Need a hint?
  • Common denominator first.
  • Then order the tops.
C2

Compare: 2/6 ▢ 1/2

Need a hint?
  • Common denominator first.
  • Then order the tops.
C3

Compare: 4/6 ▢ 3/4

Need a hint?
  • Common denominator first.
  • Then order the tops.
C4

Compare: 2/3 ▢ 7/8

Need a hint?
  • Common denominator first.
  • Then order the tops.
Apply

Apply (4)

A1

Compare: 1/5 ▢ 3/4

Need a hint?
  • Common denominator first.
  • Then order the tops.
A2

Compare: 4/5 ▢ 1/3

Need a hint?
  • Common denominator first.
  • Then order the tops.
A3

Compare: 2/7 ▢ 1/7

Need a hint?
  • Common denominator first.
  • Then order the tops.
A4

Compare: 4/7 ▢ 3/7

Need a hint?
  • Common denominator first.
  • Then order the tops.
Extension

Extension (4)

E1

Compare: 5/6 ▢ 1/2

Need a hint?
  • Common denominator first.
  • Then order the tops.
E2

Compare: 4/7 ▢ 1/5

Need a hint?
  • Common denominator first.
  • Then order the tops.
E3

Compare: 1/3 ▢ 1/3

Need a hint?
  • Common denominator first.
  • Then order the tops.
E4

Compare: 1/3 ▢ 1/8

Need a hint?
  • Common denominator first.
  • Then order the tops.