Question

divide. write your answer in simplest form.\\(\frac{7}{12} div \frac{2}{9}\\)

Explanation:

Step1: Recall fraction division rule

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, $\frac{7}{12} \div \frac{2}{9} = \frac{7}{12} \times \frac{9}{2}$.

Step2: Multiply numerators and denominators

Multiply the numerators: $7 \times 9 = 63$. Multiply the denominators: $12 \times 2 = 24$. So we get $\frac{63}{24}$.

Step3: Simplify the fraction

Find the greatest common divisor (GCD) of 63 and 24. The GCD of 63 and 24 is 3. Divide both numerator and denominator by 3: $\frac{63 \div 3}{24 \div 3} = \frac{21}{8}$.

Answer:

$\frac{21}{8}$