Fractions · What is a fraction? · 1.4

A fraction is division.

The fraction bar means divide: 12/4 is 12 ÷ 4 = 3. When the top is a multiple of the bottom, the fraction is a whole number.

01 / THE IDEA

See it work.

Watch the method

A fraction is division

12/4 = 12 ÷ 4 = 3.

1 / 2
124\frac{12}{4}
1

Find a common factor

12 and 4 both divide by 4.

gcd⁡(12,4)=4\gcd(12,4)=4
2

Divide top and bottom

Divide both by 4.

124=3\frac{12}{4} = 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
best 0
… =
— / WHY IT WORKS

The idea underneath.

Top ÷ bottom

a/b = a ÷ b. If b divides a, the result is a whole number. Sharing 12 among 4 gives 3 each.

Why it works

12 cookies shared by 4 friends = 3 each.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Simplify 20/5

1

Find a common factor

20 and 5 both divide by 5. \gcd(20,5)=5

2

Divide top and bottom

Divide both by 5. 20/5 = 4

EX 2medium

Simplify 10/5

1

Find a common factor

10 and 5 both divide by 5. \gcd(10,5)=5

2

Divide top and bottom

Divide both by 5. 10/5 = 2

EX 3hard

Simplify 8/2

1

Find a common factor

8 and 2 both divide by 2. \gcd(8,2)=2

2

Divide top and bottom

Divide both by 2. 8/2 = 4

04 / COMMON TRAPS

Where students slip.

Trap

Thinking 12/4 cannot be a whole number.

Fix

It equals 3.

Trap

Dividing the wrong way (4 ÷ 12).

Fix

Top divided by bottom.

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 20/5

Need a hint?
  • Divide the top by the bottom.
  • A multiple of the bottom gives a whole number.
C2

Simplify 12/6

Need a hint?
  • Divide the top by the bottom.
  • A multiple of the bottom gives a whole number.
C3

Simplify 12/6

Need a hint?
  • Divide the top by the bottom.
  • A multiple of the bottom gives a whole number.
C4

Simplify 6/2

Need a hint?
  • Divide the top by the bottom.
  • A multiple of the bottom gives a whole number.
Apply

Apply (4)

A1

Simplify 10/5

Need a hint?
  • Divide the top by the bottom.
  • A multiple of the bottom gives a whole number.
A2

Simplify 8/2

Need a hint?
  • Divide the top by the bottom.
  • A multiple of the bottom gives a whole number.
A3

Simplify 12/4

Need a hint?
  • Divide the top by the bottom.
  • A multiple of the bottom gives a whole number.
A4

Simplify 4/2

Need a hint?
  • Divide the top by the bottom.
  • A multiple of the bottom gives a whole number.
Extension

Extension (4)

E1

Simplify 8/2

Need a hint?
  • Divide the top by the bottom.
  • A multiple of the bottom gives a whole number.
E2

Simplify 15/5

Need a hint?
  • Divide the top by the bottom.
  • A multiple of the bottom gives a whole number.
E3

Simplify 18/6

Need a hint?
  • Divide the top by the bottom.
  • A multiple of the bottom gives a whole number.
E4

Simplify 24/6

Need a hint?
  • Divide the top by the bottom.
  • A multiple of the bottom gives a whole number.