Multiplying and Dividing Fractions - Algebra 2

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Question

Multiply these fractions:

$\frac{4}{9}*\frac{2}{3}$

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Answer

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{4}{9}\frac{2}{3}=\frac{42}{3*9}=\frac{8}{27}$

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Question

Multiply the fractions:

$\frac{3}{7}\cdot \frac{14}{23}$

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Answer

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

$\frac{3}{7}\cdot \frac{14}{23}=\frac{42}{161}\div \frac{7}{7}=\frac{6}{23}$

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Question

Multiply the fractions:

$\frac{3}{4}\cdot \frac{2}{7}$

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Answer

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

$\frac{3}{4}\cdot \frac{2}{7}=\frac{6}{28}\div \frac{2}{2}=\frac{3}{14}$

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Question

Multiply the fractions:

$\frac{7}{8}\cdot\frac{1}{2}$

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Answer

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

$\frac{7}{8}\cdot \frac{1}{2}=\frac{7}{16}$

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Question

Multiply the fractions:

$\frac{1}{6}\cdot \frac{1}{6}$

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Answer

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

$\frac{1}{6}\cdot \frac{1}{6}=\frac{1}{36}$

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Question

Multiply the fractions:

$\frac{3}{5}\cdot \frac{5}{7}$

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Answer

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

$\frac{3}{5}\cdot \frac{5}{7}=\frac{15}{35}\div \frac{5}{5}=\frac{3}{7}$

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Question

Divide the fractions:

$\frac{1}{2}\div \frac{1}{3}$

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Answer

When dividing fractions, first we flip the second fraction in the problem. Then we multiply the numbers on the top together and the numbers on the bottom together. Finally simplify accordingly.

$\frac{1}{2}\div \frac{1}{3}=\frac{1}{2}\cdot \frac{3}{1}=\frac{3}{2}=1\frac{1}{2}$

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Question

Divide the fractions:

$\frac{7}{9}\div \frac{5}{6}$

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Answer

When dividing fractions, first we flip the second fraction in the problem. Then we multiply the numbers on the top together and the numbers on the bottom together. Finally simplify accordingly.

$\frac{7}{9}\div \frac{5}{6}=\frac{7}{9}\cdot \frac{6}{5}=\frac{42}{45}\div \frac{3}{3}=\frac{14}{15}$

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Question

Divide the fractions:

$\frac{2}{5}\div \frac{3}{4}$

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Answer

When dividing fractions, first we flip the second fraction in the problem. Then we multiply the numbers on the top together and the numbers on the bottom together. Finally simplify accordingly.

$\frac{2}{5}\div \frac{3}{4}=\frac{2}{5}\cdot \frac{4}{3}=\frac{8}{15}$

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Question

Divide the fractions:

$\frac{3}{5}\div \frac{4}{7}$

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Answer

When dividing fractions, first we flip the second fraction in the problem. Then we multiply the numbers on the top together and the numbers on the bottom together. Finally simplify accordingly.

$\frac{3}{5}\div \frac{4}{7}=\frac{3}{5}\cdot \frac{7}{4}=\frac{21}{20}=1\frac{1}{20}$

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Question

Multiply:

$\left(\frac{ab^2c}{a^{\frac{1}{2}}b^4c^3}\right)\cdot \left(\frac{abc^2}{c}\right)$

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Answer

To multiply fractions, multiply the numerators and denominators together, then simplify.

$(\frac{ab^2c}{a^{\frac{1}{2}}b^4c^3})(\frac{abc^2}{c})=\frac{a^2b^3c^3}{a^{\frac{1}{2}}b^4c^4}=\frac{a^{\frac{3}{2}}}{bc}$

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Question

Multiply:

$\left(\frac{4}{5}x\right)\cdot \left(\frac{6}{13}y\right)$

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Answer

Multiply the numerators and denominators. Then, simplify.

$(\frac{4}{5}x)(\frac{6}{13}y)=(\frac{4x}{5})(\frac{6y}{13})=\frac{24xy}{65}$

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Question

Multiply:

$\left(\frac{15}{7x}\right)\cdot \left(\frac{12x^2}{5}\right)$

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Answer

Multiply the numerators and denominators, then simplify.

$(\frac{15}{7x})(\frac{12x^2}{5})=\frac{180x^2}{35x}=\frac{36}{7}x$

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Question

Multiply these fractions:

$\frac{1}{2}*\frac{2}{3}$

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Answer

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{1}{2}\frac{2}{3}=\frac{12}{2*3}=\frac{2}{6}$

Simply the fraction to get the final answer:

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

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Question

Multiply these fractions:

$\frac{5}{7}*\frac{1}{3}$

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Answer

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{5}{7}\frac{1}{3}=\frac{51}{7*3}=\frac{5}{21}$

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Question

Divide the fractions:

$\frac{2}{7}\div \frac{3}{21}$

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Answer

When dividing fractions, first we flip the second fraction in the problem. Then we multiply the numbers on the top together and the numbers on the bottom together. Finally simplify accordingly.

$\frac{2}{7}\div \frac{3}{21}=\frac{2}{7}\cdot \frac{21}{3}=\frac{42}{21}=2$

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Question

Divide the fractions:

$\frac{7}{8}\div \frac{3}{4}$

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Answer

When dividing fractions, first we flip the second fraction in the problem. Then we multiply the numbers on the top together and the numbers on the bottom together. Finally simplify accordingly.

$\frac{7}{8}\div \frac{3}{4}=\frac{7}{8}\cdot \frac{4}{3}=\frac{28}{24}\div \frac{4}{4}=\frac{7}{6}=1\frac{1}{6}$

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Question

Multiply:

$\frac{5}{6}\cdot \frac{2}{50}$

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Answer

Remember, when multiplying fractions, multiply straight across.

But first, try to see if you can reduce diagonally. You can in this case.

Then, multiply across to get your answer of $\frac{1}{30}$ .

Make sure it's in simplest form.

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Question

Divide the fractions: $\frac{\frac{1}{3}\div\frac{1}{9}}{\frac{7}{2}}$

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Answer

Evaluate the top term first. We can change the sign to multiplication and take the reciprocal of the second term.

$\frac{1}{3}\div\frac{1}{9} = \frac{1}{3}\times \frac{9}{1} = 3$

Rewrite the fraction.

$\frac{\frac{1}{3}\div\frac{1}{9}}{\frac{7}{2}}=\frac{3}{\frac{7}{2}}$

Write the complex fraction using the division sign and repeat the process.

$\frac{3}{\frac{7}{2}}= 3\div \frac{7}{2}= 3\times \frac{2}{7} =\frac{6}{7}$

The answer is: $\frac{6}{7}$

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Question

Multiply:

$\left(\frac{x^2}{z}\right)\cdot \left(\frac{x^2z^2}{y}\right)$

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Answer

To multiply fractions, just multiply the numerators, then the denominators, and then simplify.

$(\frac{x^2}{z})(\frac{x^2z^2}{y})=\frac{x^4z^2}{zy}=\frac{x^4z}{y}$

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