Question

an expression is shown.
\\(\frac{5}{12} \div \frac{1}{3}\\)
what is the value of the expression?
\\(\bigcirc\\) a. \\(\frac{4}{5}\\)
\\(\bigcirc\\) b. \\(\frac{36}{5}\\)
\\(\bigcirc\\) c. \\(\frac{5}{4}\\)
\\(\bigcirc\\) d. \\(\frac{5}{36}\\)

Explanation:

Step1: Recall division of fractions rule

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of $\frac{1}{3}$ is $\frac{3}{1}$. So, $\frac{5}{12}\div\frac{1}{3}=\frac{5}{12}\times\frac{3}{1}$.

Step2: Multiply the numerators and denominators

Multiply the numerators: $5\times3 = 15$. Multiply the denominators: $12\times1 = 12$. So the expression becomes $\frac{15}{12}$.

Step3: Simplify the fraction

We can simplify $\frac{15}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 3. $\frac{15\div3}{12\div3}=\frac{5}{4}$.

Answer:

C. $\frac{5}{4}$