Fractions · Divide · 8.4

Divide mixed numbers.

To divide mixed numbers, convert to improper fractions first, then keep–flip–multiply and simplify.

01 / THE IDEA

See it work.

Watch the method

Divide mixed numbers

1 1/2 ÷ 3/4 = 3/2 × 4/3 = 2.

1 / 3
112÷341\frac{1}{2} \div \frac{3}{4}
1

Flip the divisor

Dividing means multiplying by the reciprocal.

32×43\frac{3}{2} \times \frac{4}{3}
2

Multiply across

Tops times tops, bottoms times bottoms.

126\frac{12}{6}
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
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— / WHY IT WORKS

The idea underneath.

Improper, then divide

Convert any mixed numbers to improper fractions before dividing.

Why it works

Pieces only — then flip and multiply.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Divide 1 1/2 ÷ 3/4

1

Flip the divisor

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

2

Multiply across

Tops times tops, bottoms times bottoms. 12/6

3

Simplify

Reduce to lowest terms. 2

EX 2medium

Divide 1 1/2 ÷ 1/2

1

Flip the divisor

Dividing means multiplying by the reciprocal. 3/2 \times 2/1

2

Multiply across

Tops times tops, bottoms times bottoms. 6/2

3

Simplify

Reduce to lowest terms. 3

EX 3hard

Divide 2 1/2 ÷ 1/4

1

Flip the divisor

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

2

Multiply across

Tops times tops, bottoms times bottoms. 20/2

3

Simplify

Reduce to lowest terms. 10

04 / COMMON TRAPS

Where students slip.

Trap

Dividing the parts separately.

Fix

Convert to improper first.

Trap

Flipping the wrong fraction.

Fix

Flip the divisor.

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 1/2 ÷ 3/4

Need a hint?
  • Convert to improper fractions.
  • Keep, flip the divisor, multiply.
C2

Divide 2 1/2 ÷ 2/4

Need a hint?
  • Convert to improper fractions.
  • Keep, flip the divisor, multiply.
C3

Divide 2 1/2 ÷ 1/2

Need a hint?
  • Convert to improper fractions.
  • Keep, flip the divisor, multiply.
C4

Divide 2 1/2 ÷ 1/2

Need a hint?
  • Convert to improper fractions.
  • Keep, flip the divisor, multiply.
Apply

Apply (4)

A1

Divide 1 1/2 ÷ 1/2

Need a hint?
  • Convert to improper fractions.
  • Keep, flip the divisor, multiply.
A2

Divide 2 1/2 ÷ 3/4

Need a hint?
  • Convert to improper fractions.
  • Keep, flip the divisor, multiply.
A3

Divide 2 1/2 ÷ 1/3

Need a hint?
  • Convert to improper fractions.
  • Keep, flip the divisor, multiply.
A4

Divide 1 1/2 ÷ 1/2

Need a hint?
  • Convert to improper fractions.
  • Keep, flip the divisor, multiply.
Extension

Extension (4)

E1

Divide 2 1/2 ÷ 1/4

Need a hint?
  • Convert to improper fractions.
  • Keep, flip the divisor, multiply.
E2

Divide 1 1/2 ÷ 1/2

Need a hint?
  • Convert to improper fractions.
  • Keep, flip the divisor, multiply.
E3

Divide 1 1/2 ÷ 1/3

Need a hint?
  • Convert to improper fractions.
  • Keep, flip the divisor, multiply.
E4

Divide 1 1/2 ÷ 1/2

Need a hint?
  • Convert to improper fractions.
  • Keep, flip the divisor, multiply.