Question

what is the quotient of \\(\frac{3}{5}\\) and \\(\frac{1}{10}\\)?

0 \\(\frac{1}{5}\\) \\(\frac{2}{5}\\) \\(\frac{3}{5}\\) \\(\frac{4}{5}\\) 1

\\(\circ\\) \\(\frac{1}{6}\\)
\\(\circ\\) \\(\frac{1}{3}\\)
\\(\circ\\) 3
\\(\circ\\) 6

Explanation:

Step1: Recall division of fractions

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So, for $\frac{3}{5} \div \frac{1}{10}$, we use the rule $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$.

Step2: Apply the rule

Substitute $a = 3$, $b = 5$, $c = 1$, $d = 10$ into the formula: $\frac{3}{5} \times \frac{10}{1}$.

Step3: Multiply the numerators and denominators

Multiply the numerators: $3 \times 10 = 30$. Multiply the denominators: $5 \times 1 = 5$. So we get $\frac{30}{5}$.

Step4: Simplify the fraction

$\frac{30}{5} = 6$.

Answer:

6