Ratios · Ratios · 1.4

Simplify a ratio.

A ratio is in simplest form when its parts share no common factor. Divide both parts by their greatest common factor. 12:18 → ÷6 → 2:3.

01 / THE IDEA

See it work.

Watch the method

Simplify a ratio

12:18 → ÷6 → 2:3.

1 / 2
12:1812 : 18
1

Find the common factor

6 divides both 12 and 18.

gcd⁡(12,18)=6\gcd(12,18) = 6
2

Divide both parts

Divide each part by the common factor.

12:18=2:312:18 = 2:3
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type lowest terms, e.g. 3:4.

streak 0
best 0
… →
— / WHY IT WORKS

The idea underneath.

Lowest terms

Like a fraction, divide both parts of the ratio by their greatest common factor.

Why it works

12:18 = 2:3.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Simplify the ratio 8:2 to lowest terms.

1

Find the common factor

2 divides both 8 and 2. gcd(8,2) = 2

2

Divide both parts

Divide each part by the common factor. 8:2 = 4:1

EX 2medium

Simplify the ratio 15:12 to lowest terms.

1

Find the common factor

3 divides both 15 and 12. gcd(15,12) = 3

2

Divide both parts

Divide each part by the common factor. 15:12 = 5:4

EX 3hard

Simplify the ratio 6:12 to lowest terms.

1

Find the common factor

6 divides both 6 and 12. gcd(6,12) = 6

2

Divide both parts

Divide each part by the common factor. 6:12 = 1:2

04 / COMMON TRAPS

Where students slip.

Trap

Dividing by a non-common factor.

Fix

Use a number that divides BOTH parts.

Trap

Stopping too early.

Fix

Reduce until no common factor remains.

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

Simplify the ratio 20:5 to lowest terms.

Need a hint?
  • Find the greatest common factor.
  • Divide both parts by it.
C2

Simplify the ratio 6:36 to lowest terms.

Need a hint?
  • Find the greatest common factor.
  • Divide both parts by it.
C3

Simplify the ratio 6:6 to lowest terms.

Need a hint?
  • Find the greatest common factor.
  • Divide both parts by it.
C4

Simplify the ratio 10:8 to lowest terms.

Need a hint?
  • Find the greatest common factor.
  • Divide both parts by it.
Apply

Apply (4)

A1

Simplify the ratio 12:30 to lowest terms.

Need a hint?
  • Find the greatest common factor.
  • Divide both parts by it.
A2

Simplify the ratio 30:30 to lowest terms.

Need a hint?
  • Find the greatest common factor.
  • Divide both parts by it.
A3

Simplify the ratio 24:4 to lowest terms.

Need a hint?
  • Find the greatest common factor.
  • Divide both parts by it.
A4

Simplify the ratio 24:18 to lowest terms.

Need a hint?
  • Find the greatest common factor.
  • Divide both parts by it.
Extension

Extension (4)

E1

Simplify the ratio 12:8 to lowest terms.

Need a hint?
  • Find the greatest common factor.
  • Divide both parts by it.
E2

Simplify the ratio 36:12 to lowest terms.

Need a hint?
  • Find the greatest common factor.
  • Divide both parts by it.
E3

Simplify the ratio 8:12 to lowest terms.

Need a hint?
  • Find the greatest common factor.
  • Divide both parts by it.
E4

Simplify the ratio 4:8 to lowest terms.

Need a hint?
  • Find the greatest common factor.
  • Divide both parts by it.