Fractions · Divide · 8.2

Keep, flip, multiply.

To divide by a fraction, keep the first, flip the second (its reciprocal), and multiply. Dividing by 1/4 is the same as multiplying by 4.

01 / THE IDEA

See it work.

Watch the method

Keep–flip–multiply

1/2 ÷ 1/4 = 1/2 × 4/1 = 2.

1 / 3
12÷14\frac{1}{2} \div \frac{1}{4}
1

Flip the divisor

Dividing means multiplying by the reciprocal.

12×41\frac{1}{2} \times \frac{4}{1}
2

Multiply across

Tops times tops, bottoms times bottoms.

42\frac{4}{2}
3

Simplify

Reduce to lowest terms.

22
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.

Why flip

Dividing asks “how many of these fit?”. 1/2 ÷ 1/4 asks how many quarters in a half — two.

Why it works

How many 1/4s in 1/2? Two.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Divide 1/2 ÷ 4/5

1

Flip the divisor

Dividing means multiplying by the reciprocal. 1/2 \times 5/4

2

Multiply across

Tops times tops, bottoms times bottoms. 5/8

EX 2medium

Divide 1/6 ÷ 4/6

1

Flip the divisor

Dividing means multiplying by the reciprocal. 1/6 \times 6/4

2

Multiply across

Tops times tops, bottoms times bottoms. 6/24

3

Simplify

Reduce to lowest terms. 1/4

EX 3hard

Divide 1/2 ÷ 1/6

1

Flip the divisor

Dividing means multiplying by the reciprocal. 1/2 \times 6/1

2

Multiply across

Tops times tops, bottoms times bottoms. 6/2

3

Simplify

Reduce to lowest terms. 3

04 / COMMON TRAPS

Where students slip.

Trap

Flipping the first fraction.

Fix

Flip the divisor (the second one).

Trap

Dividing the numerators and denominators.

Fix

Use keep–flip–multiply instead.

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

Divide 1/2 ÷ 4/5

Need a hint?
  • Keep the first fraction.
  • Flip the second and multiply.
C2

Divide 1/4 ÷ 1/2

Need a hint?
  • Keep the first fraction.
  • Flip the second and multiply.
C3

Divide 1/2 ÷ 4/6

Need a hint?
  • Keep the first fraction.
  • Flip the second and multiply.
C4

Divide 1/2 ÷ 1/2

Need a hint?
  • Keep the first fraction.
  • Flip the second and multiply.
Apply

Apply (4)

A1

Divide 1/6 ÷ 4/6

Need a hint?
  • Keep the first fraction.
  • Flip the second and multiply.
A2

Divide 3/5 ÷ 1/2

Need a hint?
  • Keep the first fraction.
  • Flip the second and multiply.
A3

Divide 5/6 ÷ 2/3

Need a hint?
  • Keep the first fraction.
  • Flip the second and multiply.
A4

Divide 2/4 ÷ 1/5

Need a hint?
  • Keep the first fraction.
  • Flip the second and multiply.
Extension

Extension (4)

E1

Divide 1/2 ÷ 1/6

Need a hint?
  • Keep the first fraction.
  • Flip the second and multiply.
E2

Divide 4/6 ÷ 1/5

Need a hint?
  • Keep the first fraction.
  • Flip the second and multiply.
E3

Divide 1/5 ÷ 1/6

Need a hint?
  • Keep the first fraction.
  • Flip the second and multiply.
E4

Divide 2/6 ÷ 1/3

Need a hint?
  • Keep the first fraction.
  • Flip the second and multiply.