1Cademy - Example of Dividing $$-\frac{7}{18} \div \left(-\frac{14}{27}<br>ight)$$

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Fraction Division

Example

Example of Dividing $-\frac{7}{18} \div \left(-\frac{14}{27} ight)$

To evaluate the division of two fractions, such as $-\frac{7}{18} \div \left(-\frac{14}{27} ight)$ , first rewrite the division as multiplication by the reciprocal of the second fraction: $-\frac{7}{18} \cdot \left(-\frac{27}{14} ight)$ . Determine the sign of the product; since both fractions are negative, the result will be positive. Next, multiply the numerators and denominators directly to get $\frac{7 \cdot 27}{18 \cdot 14}$ . Before completing the multiplication, rewrite the numbers to show their common factors: $\frac{7 \cdot 9 \cdot 3}{9 \cdot 2 \cdot 7 \cdot 2}$ . Dividing out the common factors of $7$ and $9$ from the numerator and denominator leaves $\frac{3}{2 \cdot 2}$ , which simplifies to the final quotient of $\frac{3}{4}$ .