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Algebra II : Multiplying and Dividing Fractions

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Example Question #41 : Multiplying And Dividing Fractions

A recipe for a cake calls for two-thirds a cup of flower per cake. If you have 12 cups of flour, how many cakes can you make?

Possible Answers:

Can not be determined

Correct answer:

Explanation:

The key here is to recognize that you are dividing twelve by two-thirds because that will give you the total number of cakes that twelve cups of flour.

So:

$\frac{\frac{12}{1}}{\frac{2}{3}}$

When you divide fractions, it is equivalent to multiplying by the reciprocal of one of the divisor.

Which looks like this:

$\frac{12}{1}*\frac{3}{2}=18$

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Example Question #42 : Multiplying And Dividing Fractions

Simplify the following fraction operation:

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

Possible Answers:

$\frac{14}{3}$

$\frac{3}{7}$

Correct answer:

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.

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Example Question #42 : Multiplying And Dividing Fractions

$\frac{9}{11}\cdot \frac{121}{108}$

Possible Answers:

$\frac{5}{12}$

$\frac{1}{11}$

$\frac{12}{11}$

$\frac{11}{12}$

$\frac{1}{12}$

Correct answer:

$\frac{11}{12}$

Explanation:

Remember to simplify before multiplying straight across--it makes finding your final answer much easier. 9 goes into both 9 and 108, while 11 goes into both 11 and 121. Multiply straight across to get your answer: $\frac{11}{12}$

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Example Question #43 : Multiplying And Dividing Fractions

$\frac{4x}{y}\div \frac{22}{y^2}$

Possible Answers:

$\frac{xy}{11}$

2xy

$\frac{2y}{11}$

$\frac{2xy}{11}$

Correct answer:

$\frac{2xy}{11}$

Explanation:

Recall that when dividing fractions, you have to flip the second fraction (use its reciprocal) and then multiply the two: $\frac{4x}{y}\times \frac{y^2}{22}$ . See if you can simplify diagonally before you multiply straight across to get your answer of $\frac{2xy}{11}$ .

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Example Question #45 : Multiplying And Dividing Fractions

Simplify the following:

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

Possible Answers:

$\frac{7}{3}$

$\frac{144}{17}$

$\frac{13}{14}$

$\frac{3}{5}$

Correct answer:

$\frac{7}{3}$

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:

$\frac{7}{3}$

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Example Question #46 : Multiplying And Dividing Fractions

Simplify the following fraction expression:

$(\frac{4}{7}*\frac{12}{13})\div \frac{100}{91}$

Possible Answers:

$4\frac{4}{7}$

$\frac{12}{25}$

$2\frac{1}{12}$

$\frac{13}{33}$

Correct answer:

$\frac{12}{25}$

Explanation:

Simplify the following fraction expression:

$(\frac{4}{7}*\frac{12}{13})\div \frac{100}{91}$

Let's begin by simplifying the multiplication inside the parentheses.

$(\frac{48}{91})\div \frac{100}{91}$

Next, take the reciprocal of the second fraction and multiply (because when dividing fractions we really want to multiply by the reciprocal)

$(\frac{48}{91})\div \frac{100}{91}=\frac{48}{91}*\frac{91}{100}$

Which will become:

$\frac{48}{91}*\frac{91}{100}=\frac{48}{100}=\frac{12}{25}$

So our answer is:

$\frac{12}{25}$

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Example Question #47 : Multiplying And Dividing Fractions

Simplify the following:

$\frac{\frac{3}{4}}{\frac{4}{3}}$

Possible Answers:

$\frac{9}{16}$

$\frac{4}{9}$

$\frac{16}{9}$

Correct answer:

$\frac{9}{16}$

Explanation:

This is a dividing fractions problem. The trick here is to know that you need to flip one of your fractions and then multiply straight across.

When you do this it will look like this:

$\frac{3}{4}*\frac{3}{4}$ $=\frac{9}{16}$

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Example Question #44 : Multiplying And Dividing Fractions

Multiply the fractions:

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

Possible Answers:

$\frac{8}{15}$

$\frac{4}{15}$

$\frac{6}{15}$

$\frac{1}{5}$

Correct answer:

$\frac{4}{15}$

Explanation:

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

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

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Example Question #45 : Multiplying And Dividing Fractions

Multiply the fractions:

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

Possible Answers:

$\frac{9}{23}$

$\frac{7}{23}$

$\frac{10}{23}$

$\frac{6}{23}$

Correct answer:

$\frac{6}{23}$

Explanation:

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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Example Question #46 : Multiplying And Dividing Fractions

Multiply the fractions:

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

Possible Answers:

$\frac{3}{14}$

$\frac{7}{14}$

$\frac{5}{14}$

$\frac{11}{14}$

Correct answer:

$\frac{3}{14}$

Explanation:

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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Algebra II : Multiplying and Dividing Fractions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #41 : Multiplying And Dividing Fractions

Example Question #42 : Multiplying And Dividing Fractions

Example Question #42 : Multiplying And Dividing Fractions

Example Question #43 : Multiplying And Dividing Fractions

Example Question #45 : Multiplying And Dividing Fractions

Example Question #46 : Multiplying And Dividing Fractions

Example Question #47 : Multiplying And Dividing Fractions

Example Question #44 : Multiplying And Dividing Fractions

Example Question #45 : Multiplying And Dividing Fractions

Example Question #46 : Multiplying And Dividing Fractions

All Algebra II Resources

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