Question

problem #2 - dividing rational numbers (medium) find the quotients. a. \\(\frac{2}{3} \div \frac{1}{4}\\) b. \\(\frac{2}{4} \div \frac{3}{4}\\) c. \\(\frac{3}{7} \div \frac{1}{3}\\) d. \\(\frac{2}{3} \div \frac{1}{6}\\)

Explanation:

Step1: Recall division of fractions rule

To divide two fractions, multiply the first fraction by the reciprocal of the second fraction. The formula is $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$ (where $b
eq0$, $c
eq0$, $d
eq0$).

Part a: $\frac{2}{3} \div \frac{1}{4}$

Step2: Apply the division rule

Multiply $\frac{2}{3}$ by the reciprocal of $\frac{1}{4}$, which is $\frac{4}{1}$. So, $\frac{2}{3} \times \frac{4}{1} = \frac{2\times4}{3\times1} = \frac{8}{3}$.

Part b: $\frac{2}{4} \div \frac{3}{4}$

Step3: Apply the division rule

Reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$. Multiply: $\frac{2}{4} \times \frac{4}{3} = \frac{2\times4}{4\times3}$. The 4s cancel out, giving $\frac{2}{3}$.

Part c: $\frac{3}{7} \div \frac{1}{3}$

Step4: Apply the division rule

Reciprocal of $\frac{1}{3}$ is $\frac{3}{1}$. Multiply: $\frac{3}{7} \times \frac{3}{1} = \frac{3\times3}{7\times1} = \frac{9}{7}$.

Part d: $\frac{2}{3} \div \frac{1}{6}$

Step5: Apply the division rule

Reciprocal of $\frac{1}{6}$ is $\frac{6}{1}$. Multiply: $\frac{2}{3} \times \frac{6}{1} = \frac{2\times6}{3\times1} = \frac{12}{3} = 4$.

Answer:

a. $\boldsymbol{\frac{8}{3}}$
b. $\boldsymbol{\frac{2}{3}}$
c. $\boldsymbol{\frac{9}{7}}$
d. $\boldsymbol{4}$