Multiplying Fractions - Only Models

A fraction represents a part of a whole and is expressed as $$\frac{a}{b}$$ , where 'a' is the numerator and 'b' is the denominator.

To multiply fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ .

Finding the product of two fractions means calculating the result of multiplying the two fractions together.

$$\frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4} = \frac{3}{8}$$ .

$$\frac{2}{3} \times \frac{1}{5} = \frac{2 \times 1}{3 \times 5} = \frac{2}{15}$$ .

A model visually represents the multiplication of fractions, often using area models or number lines to show how parts of wholes combine.

Draw a rectangle, divide it into 3 equal parts (for $$\frac{2}{3}$$ ) and then shade 2 parts. Next, divide the same rectangle into 4 equal parts (for $$\frac{3}{4}$$ ) and shade 3 parts. The overlapping shaded area represents the product.

$$\frac{4}{5} \times \frac{3}{6} = \frac{4 \times 3}{5 \times 6} = \frac{12}{30} = \frac{2}{5}$$ after simplification.

Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator have no common factors other than 1.

$$\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6}$$ .