Fractions · Decimals & percents · 9.4

Compare across forms.

To compare a fraction with a decimal (or percent), put them in the same form — usually convert both to decimals — then compare.

01 / THE IDEA

See it work.

Watch the method

Compare across forms

1/2 = 0.5, and 0.5 > 0.4, so 1/2 > 0.4.

1 / 2
12  ?  0.4\frac{1}{2} \;?\; 0.4
1

Put them in the same form

Compare as decimals.

0.50  ?  0.400.50 \;?\; 0.40
2

Compare

1/2 > 0.4.

1/2>0.41/2 > 0.4
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.

Same form to compare

Fractions, decimals, and percents are three views of the same number. Pick one form for both.

Why it works

Half is 0.5 is 50%.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Compare: 1/2 ▢ 0.4

1

Put them in the same form

Compare as decimals. 0.50 \;?\; 0.40

2

Compare

1/2 > 0.4. 1/2 > 0.4

EX 2medium

Compare: 1/5 ▢ 0.8

1

Put them in the same form

Compare as decimals. 0.20 \;?\; 0.80

2

Compare

1/5 < 0.8. 1/5 < 0.8

EX 3hard

Compare: 1/5 ▢ 0.1

1

Put them in the same form

Compare as decimals. 0.20 \;?\; 0.10

2

Compare

1/5 > 0.1. 1/5 > 0.1

04 / COMMON TRAPS

Where students slip.

Trap

Comparing a fraction and a decimal directly.

Fix

Convert to the same form first.

Trap

Reading 0.4 as bigger than 1/2.

Fix

1/2 = 0.5 > 0.4.

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 ▢ 0.4

Need a hint?
  • Convert both to decimals.
  • Then compare.
C2

Compare: 1/2 ▢ 0.6

Need a hint?
  • Convert both to decimals.
  • Then compare.
C3

Compare: 1/2 ▢ 0.2

Need a hint?
  • Convert both to decimals.
  • Then compare.
C4

Compare: 1/2 ▢ 0.5

Need a hint?
  • Convert both to decimals.
  • Then compare.
Apply

Apply (4)

A1

Compare: 1/5 ▢ 0.8

Need a hint?
  • Convert both to decimals.
  • Then compare.
A2

Compare: 3/5 ▢ 0.8

Need a hint?
  • Convert both to decimals.
  • Then compare.
A3

Compare: 6/10 ▢ 0.6

Need a hint?
  • Convert both to decimals.
  • Then compare.
A4

Compare: 9/10 ▢ 0.1

Need a hint?
  • Convert both to decimals.
  • Then compare.
Extension

Extension (4)

E1

Compare: 1/5 ▢ 0.1

Need a hint?
  • Convert both to decimals.
  • Then compare.
E2

Compare: 1/2 ▢ 0.4

Need a hint?
  • Convert both to decimals.
  • Then compare.
E3

Compare: 7/10 ▢ 0.2

Need a hint?
  • Convert both to decimals.
  • Then compare.
E4

Compare: 4/5 ▢ 0.2

Need a hint?
  • Convert both to decimals.
  • Then compare.