Question

divide write your answer in simplest form
\frac{2}{25} \div \frac{4}{15}

select the correct choice below and, if necessary, fill in any answer boxes in your choice.
\bigcirc a. \frac{2}{25} \div \frac{4}{15} = \square (type an integer or a simplified fraction.)
\bigcirc b. the quotient is undefined.

Explanation:

Step1: Recall fraction division rule

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So, \(\frac{2}{25} \div \frac{4}{15}=\frac{2}{25}\times\frac{15}{4}\)

Step2: Simplify the fractions

First, we can simplify the numbers before multiplying. The 2 and 4 have a common factor of 2, and 15 and 25 have a common factor of 5. So, \(\frac{2\div2}{25}\times\frac{15}{4\div2}=\frac{1}{25}\times\frac{15}{2}\), and then \(\frac{1}{25\div5}\times\frac{15\div5}{2}=\frac{1}{5}\times\frac{3}{2}\)

Step3: Multiply the fractions

Multiplying the numerators and denominators, we get \(\frac{1\times3}{5\times2}=\frac{3}{10}\)

Answer:

A. \(\frac{2}{25}\div\frac{4}{15}=\frac{3}{10}\)