Multiplying and Dividing Fractions - Algebra II

Card 0 of 428

Question

Multiply these fractions:

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

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

Multiply the fractions:

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

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:

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

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:

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

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:

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

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:

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

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

Divide the fractions:

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

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:

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

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:

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

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

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:

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

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:

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

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:

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

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

Simplify $\frac{3}{6}\cdot\frac{12}{4}$ .

Answer

The problem can be made easier by first simplifying each fraction: $\frac{3}{6}=\frac{1}{2}$ and $\frac{12}{4}=\frac{3}{1}$ .

This brings our new problem to $\frac{1}{2}\cdot\frac{3}{1}$ .

Now, the numerators are multiplied by each other then the denomenators are multiplied by each other: $\frac{1\cdot3}{2\cdot1}=\frac{3}{2}$ .

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Question

Simplify $\frac{5}{3}\div\frac{7}{6}$ .

Answer

To solve, we must turn the division problem into a multiplication problem by "flipping" the second fraction (dividing by a fraction is the same as multiplying by its reciprocal):

$\frac{5}{3}\div\frac{7}{6}=\frac{5}{3}\cdot\frac{6}{7}$ .

Then, we multiply the numerators followed by the denomenators:

$\frac{5\cdot6}{3\cdot7}=\frac{30}{21}$ .

Lastly, the fraction must be simplified by a factor of 3:

$\frac{30}{21}=\frac{10}{7}$ , which gives us our final answer.

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Question

Solve the following equation to find .

$\frac{2}{3}x=\frac{4}{15}+\frac{3}{15}$

Answer

The first step in solving this equation is to add the fractions, giving us:

$\frac{2}{3}x=\frac{7}{15}$

To solve for , we need to divide both sides by $\frac{2}{3}$ .

Remember: When we divide a number by a fraction, we "switch" (find the reciprocal) of the fraction and mulitply it to the number.

$\bigg(\frac{3}{2}\bigg)\bigg(\frac{2}{3}\bigg)x=\bigg(\frac{7}{15}\bigg) \bigg(\frac{3}{2}\bigg)$

The right side of the equation cancels out leaving alone:

$x=\frac{7\times 3}{15\times 2}=\frac{21}{30}$

Notice: Both the numerator and denominator are divisble by so we can simplify this further.

$x=\frac{7}{10}$

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Question

Multiply:

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

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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Question

Simplify:

$\frac{36x^2y}{5x^5 y^{-2}}\div\frac{9x^{-3}}{25}$

Answer

In order to divide fractions, you need to multiply the first fraction by the reciprocal of the second one.

$\frac{36x^2y}{5x^5y^{-2}}\div\frac{9x^{-3}}{25}=\frac{36x^2y}{5x^5y^{-2}}\times\frac{25}{9x^{-3}}$

Now, multiply the numerators and denominators together, then simplify.

$\frac{36x^2y}{5x^5y^{-2}}\times\frac{25}{9x^{-3}}=\frac{900x^2y}{45x^2y^{-2}}=20y^3$

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Question

Simplify:

$\frac{25st^2}{6s^3t^5}\div\frac{30s^{-9}}{45s^2t^7}$

Answer

To divid fractions, you need to multiply the first fraction by the reciprocal of the second.

$(\frac{25st^2}{6s^3t^5})\div(\frac{30s^{-9}}{45s^2t^7})=(\frac{25st^2}{6s^3t^5})\times(\frac{45s^2t^7}{30s^{-9}})$

Now, multiply the numerators and denominators together, then simplify.

$(\frac{25st^2}{6s^3t^5})\times(\frac{45s^2t^7}{30s^{-9}})=\frac{1125s^3t^9}{180s^{-6}t^5}=\frac{25s^9t^4}{4}$

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Question

Simplify:

$\frac{12m^2n}{16m^3n^4}\div\frac{8m^{-4}n}{18m^4n^2}$

Answer

To divide fractions, you need to multiply the first fraction by the reciprocal of the second.

$(\frac{12m^2n}{16m^3n^4})\div(\frac{8m^{-4}n}{18m^4n^2})=(\frac{12m^2n}{16m^3n^4})\times(\frac{18m^4n^2}{8m^{-4}n})$

Now, multiply the numerators and denominators, then simplify.

$(\frac{12m^2n}{16m^3n^4})\times(\frac{18m^4n^2}{8m^{-4}n})=\frac{216m^6n^3}{128m^{-1}n^5}=\frac{27m^7}{16n^2}$

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