Multiply Fractions Concept

The concept of multiplying fractions is explained using examples then the rule is given.

Examples with Solutions

Example 1

Let us explain how do the following multiplication $ \dfrac{1}{2} \times \dfrac{1}{3 } $
We start with a rectangle. We use a picture to represent $ \dfrac{1}{3 } $ (in red).

$multiply fractions concept 1$ .

We now take $ \dfrac{1}{2} $ of the red part (blue). The blue part which is $ \dfrac{1}{2} $ of $ \dfrac{1}{3} $ is also $ \dfrac{1}{6} $ of the unit we started with. We can write
\[ \dfrac{1}{2} \times \dfrac{1}{3 } = \dfrac{1}{6} \]

$multiply fractions concept 2$ .

Example 2

Let us explain how do the following multiplication $ \dfrac{1}{3} \times \dfrac{3}{4} $
We start with a rectangle. We use a picture to represent $ \dfrac{3}{4} $ (in red).

$multiply fractions concept 3$ .

We now take $ \dfrac{1}{3} $ of the red part (blue). The blue part which is $ \dfrac{1}{3} $ of $ \dfrac{3}{4} $ is also $ \dfrac{3}{12} $ of the unit we started with. We can write

\[ \dfrac{1}{3} \times \dfrac{3}{4} = \dfrac{3}{12} \]

$multiply fractions concept 4$ .

General Rule of Multiplication of Fractions

\[ \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d} = \dfrac{a \times c}{b \times d} \] multiply numerators and denominators.

Example 3

Evaluate
a) $ \dfrac{2}{3} \times \dfrac{5}{3} $
b) $ \dfrac{3}{10} \times \dfrac{5}{21} $

Solution to Example 3

a) $ \dfrac{2}{3} \times \dfrac{5}{3} = \dfrac{2 \times 5}{3 \times 3} = \dfrac{10}{9} $
b) $ \dfrac{3}{10} \times \dfrac{5}{21} = \dfrac{3 \times 5}{10 \times 21} = \dfrac{15}{210} $