Fractions · Multiply · 7.5

Multiply mixed numbers.

To multiply mixed numbers, first turn them into improper fractions, then multiply across and simplify.

01 / THE IDEA

See it work.

Watch the method

Multiply mixed numbers

1 1/2 × 2 1/3 = 3/2 × 7/3 = 21/6 = 7/2 = 3 1/2.

1 / 2
112×2131\frac{1}{2} \times 2\frac{1}{3}
1

Multiply across

Multiply the tops, multiply the bottoms.

3×72×3=216\frac{3\times7}{2\times3} = \frac{21}{6}
2

Simplify

Reduce to lowest terms.

72\frac{7}{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
… =
— / WHY IT WORKS

The idea underneath.

Improper, then multiply

You cannot multiply the whole and fraction parts separately — convert to improper fractions first.

Why it works

Turn everything into pieces, then multiply.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Multiply 2 1/2 × 1 1/2

1

Multiply across

Multiply the tops, multiply the bottoms. \frac{5\times3}{2\times2} = 15/4

EX 2medium

Multiply 1 2/3 × 2 1/3

1

Multiply across

Multiply the tops, multiply the bottoms. \frac{5\times7}{3\times3} = 35/9

EX 3hard

Multiply 1 1/3 × 2 1/3

1

Multiply across

Multiply the tops, multiply the bottoms. \frac{4\times7}{3\times3} = 28/9

04 / COMMON TRAPS

Where students slip.

Trap

Multiplying wholes and fractions separately.

Fix

Convert to improper fractions first.

Trap

Forgetting to convert back if needed.

Fix

Give a mixed number when asked.

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 2 1/2 × 1 1/2

Need a hint?
  • Convert to improper fractions.
  • Multiply across, then simplify.
C2

Multiply 2 1/2 × 1 1/2

Need a hint?
  • Convert to improper fractions.
  • Multiply across, then simplify.
C3

Multiply 2 2/3 × 2 2/3

Need a hint?
  • Convert to improper fractions.
  • Multiply across, then simplify.
C4

Multiply 2 1/2 × 2 1/2

Need a hint?
  • Convert to improper fractions.
  • Multiply across, then simplify.
Apply

Apply (4)

A1

Multiply 1 2/3 × 2 1/3

Need a hint?
  • Convert to improper fractions.
  • Multiply across, then simplify.
A2

Multiply 1 1/2 × 2 1/2

Need a hint?
  • Convert to improper fractions.
  • Multiply across, then simplify.
A3

Multiply 1 1/2 × 1 1/2

Need a hint?
  • Convert to improper fractions.
  • Multiply across, then simplify.
A4

Multiply 1 1/2 × 1 1/2

Need a hint?
  • Convert to improper fractions.
  • Multiply across, then simplify.
Extension

Extension (4)

E1

Multiply 1 1/3 × 2 1/3

Need a hint?
  • Convert to improper fractions.
  • Multiply across, then simplify.
E2

Multiply 1 1/3 × 1 1/3

Need a hint?
  • Convert to improper fractions.
  • Multiply across, then simplify.
E3

Multiply 2 1/3 × 1 2/3

Need a hint?
  • Convert to improper fractions.
  • Multiply across, then simplify.
E4

Multiply 2 1/3 × 1 1/3

Need a hint?
  • Convert to improper fractions.
  • Multiply across, then simplify.