Algebra II - Multiplying and Dividing Fractions

Divide the fractions: $\frac{\frac{2}{3}}{5}\div \frac{\frac{1}{2}}{3}$

$\frac{4}{5}$

$\frac{5}{4}$

$\frac{1}{45}$

$\textup{The answer is not given.}$

Explanation

We will need to solve each complex fraction first.

Rewrite the complex fractions using a division sign, change the sign to a multiplication sign, and then take the reciprocal of the second term.

$\frac{\frac{2}{3}}{5} = \frac{2}{3}\div 5 =\frac{2}{3}\times \frac{1}{5} = \frac{2}{15}$

$\frac{\frac{1}{2}}{3} = \frac{1}{2}\div 3 = \frac{1}{2}\times \frac{1}{3} = \frac{1}{6}$

Divide the two fractions.

$\frac{2}{15}\div \frac{1}{6} = \frac{2}{15}\times \frac{6}{1} = \frac{12}{15}$

Reduce this fraction.

The answer is: $\frac{4}{5}$

Divide these fractions:

$\frac{25}{60}\div \frac{1}{5}$

$2\frac{1}{12}$

$1\frac{1}{12}$

$2\frac{3}{12}$

Explanation

When dividing fractions, first we need to flip the second fraction. Then multiply the numerators together and multiply the denominators together:

$\frac{25}{60}\div \frac{1}{5}=\frac{25}{60}*\frac{5}{1}=\frac{25*5}{60}=\frac{125}{60}$

Simplify the fraction to get the final answer:

$\frac{125}{60}\div \frac{5}{5}=\frac{25}{12}=2\frac{1}{12}$

Multiply the fractions:

$\frac{2}{5}\cdot\frac{2}{3}$

$\frac{4}{15}$

$\frac{6}{15}$

$\frac{1}{5}$

$\frac{8}{15}$

Explanation

When multiplying fractions, multiply the numbers on the top together and the numbers on the bottom together. Then simplify accordingly.

$\frac{2}{5}\cdot \frac{2}{3}=\frac{4}{15}$

Divide the fractions: $\frac{10}{3}\div\frac{7}{9}$

$\frac{30}{7}$

$\frac{70}{27}$

$\frac{27}{70}$

$\frac{7}{30}$

$\frac{17}{3}$

Explanation

Change the division sign in the expression and take the reciprocal of the second term.

$\frac{10}{3}\div\frac{7}{9} = \frac{10}{3}\times\frac{9}{7}$

Reduce the three and nine in the numerator and denominator.

The fractions become:

$\frac{10}{1} \times \frac{3}{7} = \frac{30}{7}$

The answer is: $\frac{30}{7}$

Divide the following fractions: $\frac{\frac{4}{9}}{\frac{8}{7}} \div \frac{3}{\frac{2}{3}}$

$\frac{7}{81}$

$\frac{64}{567}$

$\frac{4}{7}$

$\frac{9}{7}$

$\frac{19}{81}$

Explanation

In order to solve this, we will need to evaluate term by term. First rewrite the complex fractions by using a division sign.

$\frac{\frac{4}{9}}{\frac{8}{7}} =\frac{4}{9} \div\frac{8}{7}$

Change the sign from a division to multiplication and take the reciprocal of the second term.

$\frac{4}{9} \div\frac{8}{7} = \frac{4}{9} \times\frac{7}{8} = \frac{28}{72} =\frac{7\times 4}{18\times 4}=\frac{7}{18}$

Evaluate the second complex fraction.

$\frac{3}{\frac{2}{3}} = 3\div \frac{2}{3} = 3\times \frac{3}{2} = \frac{9}{2}$

This means that:

$\frac{\frac{4}{9}}{\frac{8}{7}} \div \frac{3}{\frac{2}{3}} = \frac{7}{18}\div \frac{9}{2}=\frac{7}{18}\times \frac{2}{9} = \frac{7}{9}\times\frac{1}{9}$

The answer is: $\frac{7}{81}$

Simplify the following:

$\frac{5}{6}\left(\frac{12}{5}\div \frac{6}{7}\right)$

$\frac{7}{3}$

$\frac{3}{5}$

$\frac{144}{17}$

$\frac{13}{14}$

Explanation

Simplify the following:

$\frac{5}{6}\left(\frac{12}{5}\div \frac{6}{7}\right)$

Let's begin by recalling that when dividing fractions, we need to multiply by the reciprocal, then just simplify:

$\frac{5}{6}\left(\frac{12}{5}\ast \frac{7}{6}\right)=\frac{5}{6}\left(\frac{14}{5}\right)=\frac{14}{6}=\frac{7}{3}$

So our answer is:

$\frac{7}{3}$

Divide the fractions: $\frac{3}{8}\div \frac{16}{9}$

$\frac{27}{128}$

$\frac{2}{3}$

$\frac{3}{2}$

$\frac{13}{72}$

$\textup{The answer is not given.}$

Explanation

In order to divide these fractions, we will need to rewrite the expression using a multiplication sign, and take the reciprocal of the second term.

$\frac{3}{8}\div \frac{16}{9} = \frac{3}{8}\times\frac{9}{16} = \frac{27}{128}$

The answer is: $\frac{27}{128}$

Divide the two fractions: $\frac{x}{x-2}\div \frac{x+2}{x}$

$\frac{x^2}{x^2-4}$

$\frac{x-2}{x+2}$

$\frac{x^2-4}{x^2}$

$\frac{x+2}{x-2}$

$-\frac{1}{4}$

Explanation

Change the division sign to a multiplication sign and take the reciprocal of the second term.

$\frac{x}{x-2}\div \frac{x+2}{x} = \frac{x}{x-2} \times \frac{x}{x+2}$

Multiply the numerators together.

$x\times x =x^2$

Multiply the denominators together.

Divide the numerator with denominator. Do not cancel the on the numerator and denominator.

The answer is: $\frac{x^2}{x^2-4}$

Divide the fractions: $\frac{5}{9}\div \frac{1}{6}$

$\frac{10}{3}$

$\frac{54}{5}$

$\frac{15}{2}$

$\frac{3}{10}$

$\frac{2}{15}$

Explanation

In order to divide the fraction, we will need to change the division sign to a multiplication sign and take the reciprocal of the second term.

$\frac{5}{9}\div \frac{1}{6} = \frac{5}{9}\times \frac{6}{1} = \frac{5}{3}\times \frac{2}{1}$

Simplify the fraction by multiplying the numerator with the numerator and denominator with the denominator.

The answer is: $\frac{10}{3}$

Simplify the following fraction operation:

$\frac{6}{7}*\frac{14}{3}\div\frac{4}{7}$

$\frac{3}{7}$

$\frac{14}{3}$

Explanation

Simplify the following fraction operation:

$\frac{6}{7}*\frac{14}{3}\div\frac{4}{7}$

We can take this problem one step at a time.

Let's start with the first two fractions. When multiplying fractions, we simply need to multiply stright across. However, we can make this easier by first simplifying diagonally.

$\frac{6}{7}*\frac{14}{3}=\frac{2}{1}*\frac{2}{1}=\frac{4}{1}$

Note that we can simplify the 14 and the 7 because 14 is divisible by 7. Same with the 6 and the 3.

Next, let's do the division step. To divide fractions, we multiply by the reciprocal.

$\frac{4}{1}\div\frac{4}{7}=\frac{4}{1}*\frac{7}{4}=\frac{7}{1}=7$

So our answer is 7.

Multiplying and Dividing Fractions

Help Questions

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation