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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 #62 : Multiplying And Dividing Fractions

Solve: $\frac{3}{7} \div \frac{9}{10}$

Possible Answers:

$\frac{7}{30}$

$\frac{17}{12}$

$\frac{10}{21}$

$\frac{3}{70}$

Correct answer:

$\frac{10}{21}$

Explanation:

To divide the fraction, we will need to rewrite the expression using multiplication.

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

$\frac{3}{7} \div \frac{9}{10}=\frac{3}{7} \times \frac{10}{9}$

The three on the numerator and the nine on the denominator can be reduced.

$\frac{3}{7} \times \frac{10}{9} = \frac{1}{7} \times \frac{10}{3}$

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

The answer is: $\frac{10}{21}$

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Example Question #63 : Multiplying And Dividing Fractions

Multiply the fractions: $\frac{7}{3}\times \frac{33}{6}\times \frac{1}{21}$

Possible Answers:

$\frac{11}{18}$

$\frac{18}{11}$

$\frac{11}{36}$

$\frac{11}{9}$

$\frac{41}{30}$

Correct answer:

$\frac{11}{18}$

Explanation:

Notice that the numerator and denominator have similar terms that can be simplified.

Instead of multiplying all the terms together, rewrite the fractions using common factors.

$\frac{7}{3}\times \frac{3\times 11}{6}\times \frac{1}{3\times 7}$

Cancel the common terms in the numerator and denominator.

$\frac{11}{6\times 3}=\frac{11}{18}$

The answer is: $\frac{11}{18}$

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Example Question #64 : Multiplying And Dividing Fractions

Divide the fractions: $\frac{4}{9} \div\frac{10}{13}$

Possible Answers:

$\frac{9}{19}$

$\frac{40}{117}$

$\frac{26}{45}$

$\frac{3}{2}$

$\frac{45}{26}$

Correct answer:

$\frac{26}{45}$

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.

$\frac{4}{9} \div\frac{10}{13} =\frac{4}{9} \times \frac{13}{10} =\frac{2\times 2}{9}\times \frac{13}{2\times 5}$

Cancel out the common terms on the numerator and denominator.

The fraction becomes:

$\frac{2\times 13}{9\times 5} = \frac{26}{45}$

The answer is: $\frac{26}{45}$

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Example Question #65 : Multiplying And Dividing Fractions

Multiply the fractions: $\frac{25}{12}\times -\frac{24}{5}\times \frac{1}{50}$

Possible Answers:

$-\frac{1}{5}$

$-\frac{1}{2}$

$-\frac{1}{25}$

$-\frac{1}{50}$

Correct answer:

$-\frac{1}{5}$

Explanation:

It is not necessary to multiply all the numerators and denominators.

Rewrite the expression using common factors.

$\frac{25}{12}\times -\frac{24}{5}\times \frac{1}{50}$

$=\frac{25}{12}\times -\frac{2\times 12}{5}\times \frac{1}{25\times 2}$

Cancel the common terms in the numerator and denominator.

The answer is: $-\frac{1}{5}$

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Example Question #1911 : Mathematical Relationships And Basic Graphs

Multiply and simplify the fractions: $\frac{28}{9}\times \frac{270}{63}$

Possible Answers:

$\frac{20}{3}$

$\frac{40}{3}$

$\frac{80}{3}$

Correct answer:

$\frac{40}{3}$

Explanation:

In order to simplify fractions, we will need to rewrite the numbers using common factors instead of multiplying the numerator with numerator and denominator with denominator.

$\frac{28}{9}\times \frac{270}{63} = \frac{7\cdot 4}{9} \times \frac{9 \times 30}{9\times 7}$

Cancel out the common terms in the numerators and denominators.

$\frac{4\times 30}{9} = \frac{4\times 3 \times 10}{3\times 3} = \frac{40}{3}$

The answer is: $\frac{40}{3}$

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Example Question #1912 : Mathematical Relationships And Basic Graphs

Divide the two fractions: $\frac{x}{x-2}\div \frac{x+2}{x}$

Possible Answers:

$\frac{x-2}{x+2}$

$\frac{x^2-4}{x^2}$

$\frac{x+2}{x-2}$

$-\frac{1}{4}$

$\frac{x^2}{x^2-4}$

Correct answer:

$\frac{x^2}{x^2-4}$

Explanation:

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

$\frac{x}{x-2}\div \frac{x+2}{x} = \frac{x}{x-2} \times \frac{x}{x+2}$

Multiply the numerators together.

$x\times x =x^2$

Multiply the denominators together.

(x-2)(x+2) = x^2-4

Divide the numerator with denominator. Do not cancel the x^2 on the numerator and denominator.

The answer is: $\frac{x^2}{x^2-4}$

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Example Question #1911 : Mathematical Relationships And Basic Graphs

Multiply the following fractions: $\frac{4}{9}\times \frac{3}{11}$

Possible Answers:

$\frac{4}{99}$

$\frac{4}{33}$

$\frac{71}{99}$

$\frac{7}{66}$

Correct answer:

$\frac{4}{33}$

Explanation:

The denominators do not have to be common to multiply the fractions.

Notice that the nine is divisible by three. We can rewrite the nine with three times three and cancel one of the threes in the numerator and denominator.

$\frac{4}{9}\times \frac{3}{11}= \frac{4}{3\times 3}\times \frac{3}{11}= \frac{4}{33}$

The answer is: $\frac{4}{33}$

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Example Question #233 : Fractions

Solve: $\frac{\frac{2}{3}}{\frac{9}{8}}$

Possible Answers:

$\frac{4}{3}$

$\frac{3}{4}$

$\frac{16}{27}$

$\frac{1}{12}$

$\frac{27}{16}$

Correct answer:

$\frac{16}{27}$

Explanation:

To simplify the complex fraction, we can rewrite the problem using a division sign.

$\frac{\frac{2}{3}}{\frac{9}{8}}=\frac{2}{3}\div \frac{9}{8}$

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

$\frac{2}{3}\times \frac{8}{9} = \frac{16}{27}$

The answer is: $\frac{16}{27}$

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Example Question #1912 : Mathematical Relationships And Basic Graphs

Multiply these fractions:

$\frac{8}{9}*\frac{3}{4}$

Possible Answers:

$\frac{1}{3}$

$\frac{2}{3}$

$1\frac{2}{3}$

Correct answer:

$\frac{2}{3}$

Explanation:

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

$\frac{8}{9}*\frac{3}{4}=\frac{8*3}{9*4}=\frac{24}{36}$

Simplify the fraction to get the final answer:

$\frac{24}{36}\div \frac{6}{6}=\frac{4}{6}\div \frac{2}{2}=\frac{2}{3}$

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Example Question #71 : Multiplying And Dividing Fractions

Multiply the fractions: $\frac{3}{11}\times \frac{33}{2}\times \frac{1}{9}$

Possible Answers:

$\frac{1089}{2}$

$\frac{2}{11}$

$\frac{1}{9}$

$\frac{9}{11}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

Rewrite the second and third fraction with common factors.

$\frac{3}{11}\times \frac{33}{2}\times \frac{1}{9}=\frac{3}{11}\times \frac{11\times 3}{2}\times \frac{1}{3\times 3}$

Cancel all the common terms on the numerator and denominator.

The term remaining is: $\frac{1}{2}$

The answer is: $\frac{1}{2}$

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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 #62 : Multiplying And Dividing Fractions

Example Question #63 : Multiplying And Dividing Fractions

Example Question #64 : Multiplying And Dividing Fractions

Example Question #65 : Multiplying And Dividing Fractions

Example Question #1911 : Mathematical Relationships And Basic Graphs

Example Question #1912 : Mathematical Relationships And Basic Graphs

Example Question #1911 : Mathematical Relationships And Basic Graphs

Example Question #233 : Fractions

Example Question #1912 : Mathematical Relationships And Basic Graphs

Example Question #71 : Multiplying And Dividing Fractions

All Algebra II Resources

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