Multiplying & dividing fractions

Japanese school year: Elementary 6

What you learn

You will learn how to multiply fractions directly and divide fractions using reciprocals. You will also learn how to calculate efficiently by simplifying during calculations. These operations are commonly used when finding quantities from proportions, so mastering simplification steps is essential.

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Key points

This formula is used to multiply fractions. Simply multiply the denominators together ( $b \times d$ ) and the numerators together ( $a \times c$ ).

\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

This formula is used to divide by a fraction. You turn the operation into multiplication by flipping the divisor $\frac{c}{d}$ upside down into its reciprocal $\frac{d}{c}$ .

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

This formula shows the reciprocal relationship, where two numbers multiply to $1$ . Swapping the numerator and denominator of $\frac{a}{b}$ produces its reciprocal $\frac{b}{a}$ .

\frac{a}{b} \times \frac{b}{a} = 1

This is a helpful technique for multiplying fractions. Canceling common factors between numerators and denominators before multiplying keeps numbers small and prevents mistakes.

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Practice 1Coming soon