Fractions · Divide · 8.1

The reciprocal.

The reciprocal of a fraction swaps its top and bottom. The reciprocal of 2/3 is 3/2. A number times its reciprocal is 1.

01 / THE IDEA

See it work.

Watch the method

The reciprocal

Flip 2/3 to get 3/2.

1 / 1
23\frac{2}{3}
1

Flip it

Swap top and bottom.

23→32\frac{2}{3} \to \frac{3}{2}
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.

Flipping

The reciprocal of a/b is b/a. It is the key to dividing fractions.

Why it works

Turn the fraction upside down.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Write the reciprocal of 2/3

1

Flip it

Swap top and bottom. 2/3 \to 3/2

EX 2medium

Write the reciprocal of 3/4

1

Flip it

Swap top and bottom. 3/4 \to 4/3

EX 3hard

Write the reciprocal of 2/3

1

Flip it

Swap top and bottom. 2/3 \to 3/2

04 / COMMON TRAPS

Where students slip.

Trap

Negating instead of flipping.

Fix

Swap top and bottom, don’t change the sign.

Trap

Reciprocal of a whole.

Fix

The reciprocal of 5 is 1/5.

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

Write the reciprocal of 2/3

Need a hint?
  • Swap the numerator and denominator.
  • A whole k becomes 1/k.
C2

Write the reciprocal of 2/2

Need a hint?
  • Swap the numerator and denominator.
  • A whole k becomes 1/k.
C3

Write the reciprocal of 3/8

Need a hint?
  • Swap the numerator and denominator.
  • A whole k becomes 1/k.
C4

Write the reciprocal of 4/8

Need a hint?
  • Swap the numerator and denominator.
  • A whole k becomes 1/k.
Apply

Apply (4)

A1

Write the reciprocal of 3/4

Need a hint?
  • Swap the numerator and denominator.
  • A whole k becomes 1/k.
A2

Write the reciprocal of 4/5

Need a hint?
  • Swap the numerator and denominator.
  • A whole k becomes 1/k.
A3

Write the reciprocal of 6/8

Need a hint?
  • Swap the numerator and denominator.
  • A whole k becomes 1/k.
A4

Write the reciprocal of 2/3

Need a hint?
  • Swap the numerator and denominator.
  • A whole k becomes 1/k.
Extension

Extension (4)

E1

Write the reciprocal of 2/3

Need a hint?
  • Swap the numerator and denominator.
  • A whole k becomes 1/k.
E2

Write the reciprocal of 3/4

Need a hint?
  • Swap the numerator and denominator.
  • A whole k becomes 1/k.
E3

Write the reciprocal of 2/3

Need a hint?
  • Swap the numerator and denominator.
  • A whole k becomes 1/k.
E4

Write the reciprocal of 6/7

Need a hint?
  • Swap the numerator and denominator.
  • A whole k becomes 1/k.