Fractions · Multiply · 7.3

Times a whole number.

To multiply a fraction by a whole number, write the whole as itself over 1, then multiply across.

01 / THE IDEA

See it work.

Watch the method

Times a whole number

4 × 2/5 = 4/1 × 2/5 = 8/5.

1 / 1
4×254 \times \frac{2}{5}
1

Multiply across

Multiply the tops, multiply the bottoms.

4×21×5=85\frac{4\times2}{1\times5} = \frac{8}{5}
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.

Whole over 1

k × n/d = k/1 × n/d = (k·n)/d. Multiply the numerator by the whole number.

Why it works

Four lots of two-fifths.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Multiply 5 × 2/3

1

Multiply across

Multiply the tops, multiply the bottoms. \frac{5\times2}{1\times3} = 10/3

EX 2medium

Multiply 3 × 2/3

1

Multiply across

Multiply the tops, multiply the bottoms. \frac{3\times2}{1\times3} = 6/3

2

Simplify

Reduce to lowest terms. 2

EX 3hard

Multiply 2 × 3/4

1

Multiply across

Multiply the tops, multiply the bottoms. \frac{2\times3}{1\times4} = 6/4

2

Simplify

Reduce to lowest terms. 3/2

04 / COMMON TRAPS

Where students slip.

Trap

Multiplying the denominator by the whole.

Fix

Only the numerator is multiplied.

Trap

Leaving the answer improper without checking.

Fix

Simplify or convert as required.

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

Multiply 5 × 2/3

Need a hint?
  • Write the whole over 1.
  • Multiply the numerator by it.
C2

Multiply 6 × 3/6

Need a hint?
  • Write the whole over 1.
  • Multiply the numerator by it.
C3

Multiply 2 × 1/3

Need a hint?
  • Write the whole over 1.
  • Multiply the numerator by it.
C4

Multiply 4 × 2/5

Need a hint?
  • Write the whole over 1.
  • Multiply the numerator by it.
Apply

Apply (4)

A1

Multiply 3 × 2/3

Need a hint?
  • Write the whole over 1.
  • Multiply the numerator by it.
A2

Multiply 6 × 1/2

Need a hint?
  • Write the whole over 1.
  • Multiply the numerator by it.
A3

Multiply 5 × 5/6

Need a hint?
  • Write the whole over 1.
  • Multiply the numerator by it.
A4

Multiply 3 × 2/3

Need a hint?
  • Write the whole over 1.
  • Multiply the numerator by it.
Extension

Extension (4)

E1

Multiply 2 × 3/4

Need a hint?
  • Write the whole over 1.
  • Multiply the numerator by it.
E2

Multiply 2 × 1/2

Need a hint?
  • Write the whole over 1.
  • Multiply the numerator by it.
E3

Multiply 4 × 5/6

Need a hint?
  • Write the whole over 1.
  • Multiply the numerator by it.
E4

Multiply 5 × 4/5

Need a hint?
  • Write the whole over 1.
  • Multiply the numerator by it.