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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #4593 : Algebra Ii

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

Possible Answers:

$\frac{5}{12}$

$\frac{24}{5}$

$\frac{3}{10}$

Correct answer:

$\frac{24}{5}$

Explanation:

In order to divide, first simplify the complex fractions.

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

$\frac{\frac{2}{4}}{2} = \frac{2}{4} \div 2 = \frac{2}{4} \times \frac{1}{2} = \frac{1}{4}$

Rewrite the expression.

$\frac{3}{\frac{5}{2}} \div \frac{\frac{2}{4}}{2} = \frac{6}{5} \div \frac{1}{4} = \frac{6}{5} \times 4$

The answer is: $\frac{24}{5}$

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Example Question #4594 : Algebra Ii

Divide: $\frac{9}{4}\div\frac{10}{3}$

Possible Answers:

$\frac{2}{15}$

$\frac{9}{4}$

$\frac{27}{40}$

$\frac{15}{2}$

$\frac{40}{27}$

Correct answer:

$\frac{27}{40}$

Explanation:

Convert the division sign to multiplication and take the reciprocal of the second term. The numerator and denominators can then be multiplied together.

$\frac{9}{4}\div\frac{10}{3}=\frac{9}{4} \times\frac{3}{10} = \frac{27}{40}$

This cannot be simplified any further.

The answer is: $\frac{27}{40}$

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Example Question #4591 : Algebra Ii

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

Possible Answers:

$\frac{30}{7}$

$\frac{27}{70}$

$\frac{17}{3}$

$\frac{70}{27}$

$\frac{7}{30}$

Correct answer:

$\frac{30}{7}$

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: $\frac{30}{7}$

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Example Question #81 : Multiplying And Dividing Fractions

Divide $\frac{3}{5}$ with $\frac{9}{8}$ .

Possible Answers:

$\frac{40}{27}$

$\frac{27}{40}$

$\frac{8}{15}$

$\frac{15}{8}$

$\frac{10}{3}$

Correct answer:

$\frac{8}{15}$

Explanation:

Write the expression of division using a division sign. Avoid writing the expression as a complex fraction.

$\frac{3}{5} \div \frac{9}{8}$

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

$\frac{3}{5} \times \frac{8}{9}$

Simplify the fractions by reducing the numerator and denominator.

$\frac{3}{5} \times \frac{8}{9} = \frac{8}{15}$

The answer is: $\frac{8}{15}$

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Example Question #81 : Multiplying And Dividing Fractions

Multiply: $\frac{9}{5} \times \frac{12}{5}$

Possible Answers:

$\frac{12}{5}$

$\frac{11}{25}$

$\frac{108}{25}$

$\frac{25}{108}$

$\frac{21}{25}$

Correct answer:

$\frac{108}{25}$

Explanation:

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

$\frac{9}{5} \times \frac{12}{5} = \frac{108}{25}$

This fraction cannot be simplified any further.

The answer is: $\frac{108}{25}$

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Example Question #4598 : Algebra Ii

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

Possible Answers:

$\frac{7}{54}$

$\frac{2}{189}$

$\frac{6}{7}$

$\frac{54}{7}$

$\frac{13}{7}$

Correct answer:

$\frac{6}{7}$

Explanation:

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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Example Question #4599 : Algebra Ii

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

Possible Answers:

$\frac{4}{7}$

$\frac{64}{567}$

$\frac{19}{81}$

$\frac{7}{81}$

$\frac{9}{7}$

Correct answer:

$\frac{7}{81}$

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: $\frac{7}{81}$

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Example Question #4600 : Algebra Ii

Multiply the following fractions: $\frac{3}{13}\times \frac{39}{8}\times \frac{64}{27}$

Possible Answers:

$\frac{8}{3}$

$\frac{8}{9}$

$\frac{13}{3}$

$\frac{16}{3}$

Correct answer:

$\frac{8}{3}$

Explanation:

Instead of multiplying the numerators and denominators together, we can rewrite each term by the common factors.

$\frac{3}{13}\times \frac{39}{8}\times \frac{64}{27}=\frac{3}{13}\times \frac{13\cdot 3}{2\times 4}\times \frac{(2\times 2)\times 4\times4}{3\times 3\times 3}$

Cancel all the common terms.

The answer is: $\frac{8}{3}$

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Example Question #90 : Multiplying And Dividing Fractions

Multiply the fractions: $\frac{3}{13}\times \frac{39}{6} \times \frac{1}{4}$

Possible Answers:

$\frac{1}{8}$

$\frac{2}{3}$

$\frac{1}{6}$

$\frac{3}{8}$

$\frac{127}{312}$

Correct answer:

$\frac{3}{8}$

Explanation:

Rewrite the fractions so that the numbers are in terms of their common factors.

$\frac{3}{13}\times \frac{39}{6} \times \frac{1}{4}=\frac{3}{13}\times \frac{13\times 3}{3 \times 2} \times \frac{1}{4}$

Cancel out the common terms.

$\frac{3}{2}\times \frac{1}{4} = \frac{3}{8}$

The answer is: $\frac{3}{8}$

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Example Question #261 : Fractions

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

Possible Answers:

$\frac{10}{3}$

$\frac{54}{5}$

$\frac{3}{10}$

$\frac{2}{15}$

$\frac{15}{2}$

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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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #4593 : Algebra Ii

Example Question #4594 : Algebra Ii

Example Question #4591 : Algebra Ii

Example Question #81 : Multiplying And Dividing Fractions

Example Question #81 : Multiplying And Dividing Fractions

Example Question #4598 : Algebra Ii

Example Question #4599 : Algebra Ii

Example Question #4600 : Algebra Ii

Example Question #90 : Multiplying And Dividing Fractions

Example Question #261 : Fractions

All Algebra II Resources

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