Multiplying Fractions

Study Sheet

Multiplying Fractions

Straight across, and why

Why Straight Across Works

Concept
The Big Idea
a part of a part

Multiplying fractions means taking a part of a part. Cutting a rectangle both ways shows why you multiply tops and bottoms separately.

Example
Finding 23×34\dfrac{2}{3} \times \dfrac{3}{4}

Straight across: 2×33×4=612=12\dfrac{2 \times 3}{3 \times 4} = \dfrac{6}{12} = \dfrac{1}{2}.

Tip
It gets smaller

Multiplying by a fraction less than 11 makes the result smaller — surprising at first, but taking part of something gives less than you started with.

In Plain Terms & More Examples

Concept
In plain terms

Multiply the top numbers together and the bottom numbers together, then simplify. Taking a part of a part gives a smaller result.

Example
Finding 35×56\dfrac{3}{5} \times \dfrac{5}{6}

Straight across: 3×55×6=1530=12\dfrac{3 \times 5}{5 \times 6} = \dfrac{15}{30} = \dfrac{1}{2}.

Example
Finding 12×23\dfrac{1}{2} \times \dfrac{2}{3}

Straight across: 1×22×3=26=13\dfrac{1 \times 2}{2 \times 3} = \dfrac{2}{6} = \dfrac{1}{3}.