Fractions · Simplify · 3.3

Reduce in one step.

The fastest way: divide by the GREATEST common factor of the top and bottom — then you are done in one move.

01 / THE IDEA

See it work.

Watch the method

Reduce in one step (GCD)

18/24: the GCD is 6 → 3/4.

1 / 2
1824\frac{18}{24}
1

Find a common factor

18 and 24 both divide by 6.

gcd⁡(18,24)=6\gcd(18,24)=6
2

Divide top and bottom

Divide both by 6.

1824=34\frac{18}{24} = \frac{3}{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.

Greatest common factor

The GCD is the largest number dividing both. Divide by it once to reach lowest terms.

Why it works

Make the biggest groups you can in one go.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Simplify 4/14

1

Find a common factor

4 and 14 both divide by 2. \gcd(4,14)=2

2

Divide top and bottom

Divide both by 2. 4/14 = 2/7

EX 2medium

Simplify 6/10

1

Find a common factor

6 and 10 both divide by 2. \gcd(6,10)=2

2

Divide top and bottom

Divide both by 2. 6/10 = 3/5

EX 3hard

Simplify 24/42

1

Find a common factor

24 and 42 both divide by 6. \gcd(24,42)=6

2

Divide top and bottom

Divide both by 6. 24/42 = 4/7

04 / COMMON TRAPS

Where students slip.

Trap

Using a small common factor and stopping.

Fix

Use the greatest one for a one-step reduce.

Trap

Picking a number that isn’t common.

Fix

It must divide both exactly.

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 4/14

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

Simplify 4/12

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

Simplify 20/30

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

Simplify 5/35

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

Apply (4)

A1

Simplify 6/10

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

Simplify 3/9

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

Simplify 8/24

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

Simplify 6/10

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

Extension (4)

E1

Simplify 24/42

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

Simplify 5/20

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

Simplify 12/21

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

Simplify 15/30

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