Fractions · Equivalent fractions · 2.4

Equivalent by dividing.

You can also make an equivalent fraction by DIVIDING top and bottom by the same number. This is the start of simplifying.

01 / THE IDEA

See it work.

Watch the method

Equivalent by dividing

6/9: divide both by 3 → 2/3.

1 / 2
69\frac{6}{9}
1

Find a common factor

6 and 9 both divide by 3.

gcd⁡(6,9)=3\gcd(6,9)=3
2

Divide top and bottom

Divide both by 3.

69=23\frac{6}{9} = \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
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— / WHY IT WORKS

The idea underneath.

Divide both

If a common factor divides top and bottom, divide both by it for a simpler equivalent fraction.

Why it works

Group the slices: fewer, bigger pieces, same amount.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Simplify 12/21

1

Find a common factor

12 and 21 both divide by 3. \gcd(12,21)=3

2

Divide top and bottom

Divide both by 3. 12/21 = 4/7

EX 2medium

Simplify 12/21

1

Find a common factor

12 and 21 both divide by 3. \gcd(12,21)=3

2

Divide top and bottom

Divide both by 3. 12/21 = 4/7

EX 3hard

Simplify 5/25

1

Find a common factor

5 and 25 both divide by 5. \gcd(5,25)=5

2

Divide top and bottom

Divide both by 5. 5/25 = 1/5

04 / COMMON TRAPS

Where students slip.

Trap

Dividing only one part.

Fix

Divide BOTH by the common factor.

Trap

Using a number that isn’t a common factor.

Fix

It must divide top and bottom 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 12/21

Need a hint?
  • Find a number that divides both.
  • Divide top and bottom by it.
C2

Simplify 8/12

Need a hint?
  • Find a number that divides both.
  • Divide top and bottom by it.
C3

Simplify 15/30

Need a hint?
  • Find a number that divides both.
  • Divide top and bottom by it.
C4

Simplify 3/12

Need a hint?
  • Find a number that divides both.
  • Divide top and bottom by it.
Apply

Apply (4)

A1

Simplify 12/21

Need a hint?
  • Find a number that divides both.
  • Divide top and bottom by it.
A2

Simplify 4/10

Need a hint?
  • Find a number that divides both.
  • Divide top and bottom by it.
A3

Simplify 15/25

Need a hint?
  • Find a number that divides both.
  • Divide top and bottom by it.
A4

Simplify 8/28

Need a hint?
  • Find a number that divides both.
  • Divide top and bottom by it.
Extension

Extension (4)

E1

Simplify 5/25

Need a hint?
  • Find a number that divides both.
  • Divide top and bottom by it.
E2

Simplify 4/28

Need a hint?
  • Find a number that divides both.
  • Divide top and bottom by it.
E3

Simplify 24/36

Need a hint?
  • Find a number that divides both.
  • Divide top and bottom by it.
E4

Simplify 6/9

Need a hint?
  • Find a number that divides both.
  • Divide top and bottom by it.