Question

what is the quotient of \\(\frac{7}{18}\\) and \\(\frac{2}{3}\\)?
a. \\(\frac{27}{7}\\)
b. \\(\frac{12}{7}\\)
c. \\(\frac{7}{12}\\)
d. \\(\frac{7}{27}\\)

Explanation:

Step1: Recall division of fractions rule

To divide two fractions, we 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 $b
eq0$, $c
eq0$, $d
eq0$.
Here, $a = 7$, $b = 18$, $c = 2$, $d = 3$. So, $\frac{7}{18}\div\frac{2}{3}=\frac{7}{18}\times\frac{3}{2}$.

Step2: Multiply the numerators and denominators

Multiply the numerators: $7\times3 = 21$.
Multiply the denominators: $18\times2 = 36$.
So we have $\frac{21}{36}$.

Step3: Simplify the fraction

We can simplify $\frac{21}{36}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
$\frac{21\div3}{36\div3}=\frac{7}{12}$.

Answer:

C. $\frac{7}{12}$