Fractions · Multiply · 7.2

Cancel first.

You can cancel a common factor between any top and any bottom BEFORE multiplying — it keeps the numbers small.

01 / THE IDEA

See it work.

Watch the method

Cancel first

2/3 × 3/4: cancel the 3s → 2/4 → 1/2.

1 / 3
23×34\frac{2}{3} \times \frac{3}{4}
1

Cancel common factors

Simplify across the fractions first.

11×12\frac{1}{1} \times \frac{1}{2}
2

Multiply across

Multiply the tops, multiply the bottoms.

2×33×4=612\frac{2\times3}{3\times4} = \frac{6}{12}
3

Simplify

Reduce to lowest terms.

12\frac{1}{2}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a fraction like 3/4 or 1 1/2.

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— / WHY IT WORKS

The idea underneath.

Cancel diagonally

A factor shared by a numerator and a denominator (even from the other fraction) can be divided out first.

Why it works

Cross out the matching factor early.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Multiply 3/4 × 4/16

1

Cancel common factors

Simplify across the fractions first. 3/1 \times 1/16

2

Multiply across

Multiply the tops, multiply the bottoms. \frac{3\times4}{4\times16} = 12/64

3

Simplify

Reduce to lowest terms. 3/16

EX 2medium

Multiply 2/3 × 3/12

1

Cancel common factors

Simplify across the fractions first. 1/1 \times 1/6

2

Multiply across

Multiply the tops, multiply the bottoms. \frac{2\times3}{3\times12} = 6/36

3

Simplify

Reduce to lowest terms. 1/6

EX 3hard

Multiply 3/4 × 4/12

1

Cancel common factors

Simplify across the fractions first. 1/1 \times 1/4

2

Multiply across

Multiply the tops, multiply the bottoms. \frac{3\times4}{4\times12} = 12/48

3

Simplify

Reduce to lowest terms. 1/4

04 / COMMON TRAPS

Where students slip.

Trap

Cancelling two numerators or two denominators.

Fix

Cancel a top with a bottom only.

Trap

Forgetting to simplify after.

Fix

Reduce if anything remains.

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 3/4 × 4/16

Need a hint?
  • Cancel a top with a bottom.
  • Then multiply across.
C2

Multiply 1/5 × 5/15

Need a hint?
  • Cancel a top with a bottom.
  • Then multiply across.
C3

Multiply 1/3 × 3/12

Need a hint?
  • Cancel a top with a bottom.
  • Then multiply across.
C4

Multiply 4/5 × 5/15

Need a hint?
  • Cancel a top with a bottom.
  • Then multiply across.
Apply

Apply (4)

A1

Multiply 2/3 × 3/12

Need a hint?
  • Cancel a top with a bottom.
  • Then multiply across.
A2

Multiply 4/5 × 5/20

Need a hint?
  • Cancel a top with a bottom.
  • Then multiply across.
A3

Multiply 2/4 × 4/12

Need a hint?
  • Cancel a top with a bottom.
  • Then multiply across.
A4

Multiply 2/6 × 6/12

Need a hint?
  • Cancel a top with a bottom.
  • Then multiply across.
Extension

Extension (4)

E1

Multiply 3/4 × 4/12

Need a hint?
  • Cancel a top with a bottom.
  • Then multiply across.
E2

Multiply 1/3 × 3/12

Need a hint?
  • Cancel a top with a bottom.
  • Then multiply across.
E3

Multiply 1/4 × 4/16

Need a hint?
  • Cancel a top with a bottom.
  • Then multiply across.
E4

Multiply 1/6 × 6/24

Need a hint?
  • Cancel a top with a bottom.
  • Then multiply across.