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Algebra II : Multiplying and Dividing Fractions

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Example Question #262 : Fractions

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

Possible Answers:

$\frac{54}{5}$

$\frac{2}{15}$

$\frac{3}{10}$

$\frac{15}{2}$

$\frac{10}{3}$

Correct answer:

$\frac{10}{3}$

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: $\frac{10}{3}$

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Example Question #263 : Fractions

Solve: $-\frac{-6}{-7}\cdot -\frac{3}{5}$

Possible Answers:

$\frac{51}{35}$

$\frac{18}{35}$

$-\frac{18}{35}$

$-\frac{51}{35}$

$\frac{9}{35}$

Correct answer:

$\frac{18}{35}$

Explanation:

Double negatives will simplify to a positive. Since there are four negative signs, the answer will become a positive.

$-\frac{-6}{-7}\cdot -\frac{3}{5}=\frac{6}{7}\cdot \frac{3}{5}$

Multiply the numerator with the numerator and the denominator with the denominator.

The answer is: $\frac{18}{35}$

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Example Question #264 : Fractions

Divide: $2\frac{4}{9}\div 3\frac{2}{5}$

Possible Answers:

$\frac{110}{153}$

$\frac{20}{27}$

$\frac{374}{45}$

$\frac{16}{15}$

$\frac{15}{16}$

Correct answer:

$\frac{110}{153}$

Explanation:

In order to divide this expression, we will need to convert both fractions to improper fractions.

Leaving the denominators the same, the numerator can be determined by multiplying the denominator with the whole number, and then add the numerator.

$2\frac{4}{9}\div 3\frac{2}{5} = \frac{22}{9}\div \frac{17}{5}$

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

$\frac{22}{9}\div \frac{17}{5} = \frac{22}{9}\times \frac{5}{17} =\frac{110}{153}$

The answer is: $\frac{110}{153}$

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Example Question #265 : Fractions

Divide: $\frac{\frac{3}{4}}{\frac{6}{5}}\div \frac{2}{\frac{3}{5}}$

Possible Answers:

$\frac{1}{3}$

$\frac{4}{3}$

$\frac{3}{16}$

$\frac{25}{27}$

$\frac{25}{12}$

Correct answer:

$\frac{3}{16}$

Explanation:

In order to simplify this, we will need to evaluate each complex fraction first.

Rewrite each complex fraction using a division sign, and then convert the division sign to a multiplication sign and take the reciprocal of the second term. This will avoid confusion while flipping the numerator and denominator.

$\frac{\frac{3}{4}}{\frac{6}{5}}= \frac{3}{4} \div\frac{6}{5} = \frac{3}{4} \times \frac{5}{6} = \frac{5}{8}$

$\frac{2}{\frac{3}{5}} = 2\div \frac{3}{5} = 2\times \frac{5}{3} =\frac{10}{3}$

Divide the two fractions.

$\frac{\frac{3}{4}}{\frac{6}{5}}\div \frac{2}{\frac{3}{5}} = \frac{5}{8}\div \frac{10}{3} =\frac{5}{8}\times \frac{3}{10}$

Reduce the fraction.

$\frac{5}{8}\times \frac{3}{10} = \frac{1}{8}\times \frac{3}{2} = \frac{3}{16}$

The answer is: $\frac{3}{16}$

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Example Question #266 : Fractions

Solve: $\frac{2}{7}\cdot \frac{5}{8}\cdot \frac{7}{4}$

Possible Answers:

$\frac{5}{64}$

$\frac{149}{56}$

$\frac{5}{32}$

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

$\frac{5}{16}$

Correct answer:

$\frac{5}{16}$

Explanation:

In order to simplify this, we do not need to multiply the numerators and denominators. We can save calculation by eliminating the common terms.

We do not need common denominators to multiply.

$\frac{2}{7}\cdot \frac{5}{8}\cdot \frac{7}{4}=\frac{2}{7}\cdot \frac{5}{8}\cdot \frac{7}{2\times 2}$

Cancel the common twos and sevens. Rewrite the remaining terms.

$\frac{5}{8\times 2} = \frac{5}{16}$

The answer is: $\frac{5}{16}$

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Example Question #267 : Fractions

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

Possible Answers:

$\frac{1}{45}$

$\frac{5}{4}$

$\frac{4}{5}$

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

Correct answer:

$\frac{4}{5}$

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: $\frac{4}{5}$

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Example Question #268 : Fractions

Divide the fractions: $\frac{8}{3}\div \frac{9}{24}$

Possible Answers:

$\frac{2}{3}$

$\frac{64}{3}$

$\frac{64}{9}$

$\frac{8}{3}$

Correct answer:

$\frac{64}{9}$

Explanation:

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

$\frac{8}{3}\div \frac{9}{24} = \frac{8}{3}\times \frac{24}{9}$

Reduce the fractions instead of multiplying the numerator with numerator and denominator with denominator.

$\frac{8}{1}\times \frac{8}{9} = \frac{64}{9}$

The answer is: $\frac{64}{9}$

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Example Question #269 : Fractions

Divide the fractions: $\frac{\frac{7}{8}}{3} \div \frac{2}{5}$

Possible Answers:

$\frac{35}{48}$

$\frac{60}{7}$

$\frac{21}{20}$

$\frac{3}{5}$

$\frac{48}{35}$

Correct answer:

$\frac{35}{48}$

Explanation:

Simplify the complex fraction by using a division sign.

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

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

$\frac{7}{8} \div 3 = \frac{7}{8} \times\frac{ 1 }{3 }=\frac{7}{24}$

Replace the term and repeat the process for the second fraction.

$\frac{\frac{7}{8}}{3} \div \frac{2}{5} = \frac{7}{24} \times \frac{5}{2} = \frac{35}{48}$

The answer is: $\frac{35}{48}$

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Example Question #270 : Fractions

Evaluate: $\frac{\frac{3}{7}}{\frac{1}{2}} \div \frac{\frac{1}{3}}{4}$

Possible Answers:

$\frac{7}{18}$

$\frac{72}{7}$

$\frac{1}{14}$

$\frac{18}{7}$

Correct answer:

$\frac{72}{7}$

Explanation:

Evaluate each complex fraction. Rewrite each using the division sign and then use the reciprocal property of division to evaluate the expression.

$\frac{\frac{3}{7}}{\frac{1}{2}} = \frac{3}{7} \div \frac{1}{2} = \frac{3}{7} \times \frac{2}{1}=\frac{6}{7}$

$\frac{\frac{1}{3}}{4} = \frac{1}{3}\div 4 =\frac{1}{3}\times \frac{1}{4} =\frac{1}{12}$

Divide both fractions.

$\frac{6}{7} \div \frac{1}{12} = \frac{6}{7} \times \frac{12} {1} = \frac{72}{7}$

The answer is: $\frac{72}{7}$

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Example Question #271 : Fractions

Divide the fractions: $\frac{3}{12}\div \frac{1}{\frac{3}{5}}$

Possible Answers:

$\frac{1}{10}$

$\frac{12}{5}$

$\frac{3}{20}$

$\frac{20}{3}$

$\frac{3}{10}$

Correct answer:

$\frac{3}{20}$

Explanation:

Reduce the first fraction.

$\frac{1}{4}\div \frac{1}{\frac{3}{5}}$

Simplify the complex fraction by using first using a division sign to rewrite the terms. Convert the division sign to a multiplication sign and take the reciprocal of the second term.

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

Divide the fractions.

$\frac{1}{4}\div \frac{5}{3} = \frac{1}{4}\times \frac{3}{5}$

Simplify the fractions.

The answer is: $\frac{3}{20}$

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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 #262 : Fractions

Example Question #263 : Fractions

Example Question #264 : Fractions

Example Question #265 : Fractions

Example Question #266 : Fractions

Example Question #267 : Fractions

Example Question #268 : Fractions

Example Question #269 : Fractions

Example Question #270 : Fractions

Example Question #271 : Fractions

All Algebra II Resources

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