Fractions · Simplify · 3.1

Common factors.

To simplify, look for a number that divides BOTH the top and the bottom — a common factor. Divide by it to shrink the fraction.

01 / THE IDEA

See it work.

Watch the method

Common factors

4/10: 2 divides both → 2/5.

1 / 2
410\frac{4}{10}
1

Find a common factor

4 and 10 both divide by 2.

gcd⁡(4,10)=2\gcd(4,10)=2
2

Divide top and bottom

Divide both by 2.

410=25\frac{4}{10} = \frac{2}{5}
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
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— / WHY IT WORKS

The idea underneath.

Shared factors

A common factor of numerator and denominator can be divided out without changing the value.

Why it works

Both 4 and 10 are even, so halve both.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Simplify 6/12

1

Find a common factor

6 and 12 both divide by 6. \gcd(6,12)=6

2

Divide top and bottom

Divide both by 6. 6/12 = 1/2

EX 2medium

Simplify 6/18

1

Find a common factor

6 and 18 both divide by 6. \gcd(6,18)=6

2

Divide top and bottom

Divide both by 6. 6/18 = 1/3

EX 3hard

Simplify 3/15

1

Find a common factor

3 and 15 both divide by 3. \gcd(3,15)=3

2

Divide top and bottom

Divide both by 3. 3/15 = 1/5

04 / COMMON TRAPS

Where students slip.

Trap

Using a factor of only one part.

Fix

It must divide both.

Trap

Stopping too early.

Fix

Keep going 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 6/12

Need a hint?
  • Look for a number dividing both.
  • Even/even? divide by 2.
C2

Simplify 8/24

Need a hint?
  • Look for a number dividing both.
  • Even/even? divide by 2.
C3

Simplify 20/25

Need a hint?
  • Look for a number dividing both.
  • Even/even? divide by 2.
C4

Simplify 24/30

Need a hint?
  • Look for a number dividing both.
  • Even/even? divide by 2.
Apply

Apply (4)

A1

Simplify 6/18

Need a hint?
  • Look for a number dividing both.
  • Even/even? divide by 2.
A2

Simplify 15/30

Need a hint?
  • Look for a number dividing both.
  • Even/even? divide by 2.
A3

Simplify 8/12

Need a hint?
  • Look for a number dividing both.
  • Even/even? divide by 2.
A4

Simplify 4/24

Need a hint?
  • Look for a number dividing both.
  • Even/even? divide by 2.
Extension

Extension (4)

E1

Simplify 3/15

Need a hint?
  • Look for a number dividing both.
  • Even/even? divide by 2.
E2

Simplify 15/25

Need a hint?
  • Look for a number dividing both.
  • Even/even? divide by 2.
E3

Simplify 2/6

Need a hint?
  • Look for a number dividing both.
  • Even/even? divide by 2.
E4

Simplify 6/9

Need a hint?
  • Look for a number dividing both.
  • Even/even? divide by 2.