Fractions · Divide · 8.3

Divide with wholes.

Dividing with a whole number: write the whole as over 1, then keep–flip–multiply. Works both for fraction ÷ whole and whole ÷ fraction.

01 / THE IDEA

See it work.

Watch the method

Divide with wholes

3/4 ÷ 3 = 3/4 × 1/3 = 1/4.

1 / 3
34÷3\frac{3}{4} \div 3
1

Flip the divisor

Dividing means multiplying by the reciprocal.

34×13\frac{3}{4} \times \frac{1}{3}
2

Multiply across

Tops times tops, bottoms times bottoms.

312\frac{3}{12}
3

Simplify

Reduce to lowest terms.

14\frac{1}{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.

Wholes in division

k = k/1. Then divide as usual with the reciprocal.

Why it works

Sharing three-quarters among 3 gives a quarter each.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Divide 1/4 ÷ 2

1

Flip the divisor

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

2

Multiply across

Tops times tops, bottoms times bottoms. 1/8

EX 2medium

Divide 4 ÷ 2/3

1

Flip the divisor

Dividing means multiplying by the reciprocal. 4 \times 3/2

2

Multiply across

Tops times tops, bottoms times bottoms. 12/2

3

Simplify

Reduce to lowest terms. 6

EX 3hard

Divide 2 ÷ 1/2

1

Flip the divisor

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

2

Multiply across

Tops times tops, bottoms times bottoms. 4/1

04 / COMMON TRAPS

Where students slip.

Trap

Flipping the whole that isn’t the divisor.

Fix

Flip only the divisor.

Trap

Forgetting to write the whole over 1.

Fix

k = k/1.

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 1/4 ÷ 2

Need a hint?
  • Write the whole over 1.
  • Keep, flip the divisor, multiply.
C2

Divide 4 ÷ 2/4

Need a hint?
  • Write the whole over 1.
  • Keep, flip the divisor, multiply.
C3

Divide 2/3 ÷ 2

Need a hint?
  • Write the whole over 1.
  • Keep, flip the divisor, multiply.
C4

Divide 3 ÷ 1/2

Need a hint?
  • Write the whole over 1.
  • Keep, flip the divisor, multiply.
Apply

Apply (4)

A1

Divide 4 ÷ 2/3

Need a hint?
  • Write the whole over 1.
  • Keep, flip the divisor, multiply.
A2

Divide 3 ÷ 1/6

Need a hint?
  • Write the whole over 1.
  • Keep, flip the divisor, multiply.
A3

Divide 1/5 ÷ 4

Need a hint?
  • Write the whole over 1.
  • Keep, flip the divisor, multiply.
A4

Divide 3/4 ÷ 4

Need a hint?
  • Write the whole over 1.
  • Keep, flip the divisor, multiply.
Extension

Extension (4)

E1

Divide 2 ÷ 1/2

Need a hint?
  • Write the whole over 1.
  • Keep, flip the divisor, multiply.
E2

Divide 3 ÷ 2/3

Need a hint?
  • Write the whole over 1.
  • Keep, flip the divisor, multiply.
E3

Divide 2/3 ÷ 3

Need a hint?
  • Write the whole over 1.
  • Keep, flip the divisor, multiply.
E4

Divide 4/5 ÷ 4

Need a hint?
  • Write the whole over 1.
  • Keep, flip the divisor, multiply.