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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

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10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #4581 : Algebra Ii

Divide the fractions: $\frac{12}{7}\div \frac{14}{12}$

Possible Answers:

$\frac{49}{72}$

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{72}{49}$

Correct answer:

$\frac{72}{49}$

Explanation:

In order to divide the fractions, first reduce the second term.

$\frac{14}{12} = \frac{7\times2}{6\times2} = \frac{7}{6}$

Rewrite the expression.

$\frac{12}{7}\div \frac{14}{12}=\frac{12}{7}\div \frac{7}{6}$

Take the reciprocal of the second term and change the division sign to a multiplication sign.

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

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

The answer is: $\frac{72}{49}$

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Example Question #4582 : Algebra Ii

Multiply the fractions: $-\frac{4}{21}\times-\frac{7}{2}\times \frac{3}{13}$

Possible Answers:

$\frac{2}{13}$

$\frac{1}{13}$

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

$-\frac{1}{13}$

$-\frac{2}{13}$

Correct answer:

$\frac{2}{13}$

Explanation:

It is not necessary to multiply out all the terms on the numerator and denominator.

Rewrite the numerator and denominator of non-prime numbers using common factors.

$-\frac{4}{21}\times-\frac{7}{2}\times \frac{3}{13}=-\frac{2(2)}{7(3)}\times-\frac{7}{2}\times \frac{3}{13}$

Notice that the common terms in the numerator and denominator can be simplified.

Cancel out the two, three, and seven. The thirteen in the denominator will remain.

Double negatives will yield a positive.

The answer is: $\frac{2}{13}$

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Example Question #4583 : Algebra Ii

Divide the fraction $\frac{1}{8}$ with $\frac{11}{2}$ .

Possible Answers:

$\frac{11}{16}$

$\frac{10}{11}$

$\frac{16}{11}$

$\frac{1}{44}$

Correct answer:

$\frac{1}{44}$

Explanation:

Set up an expression to divide the fractions. This will be a complex function.

$\frac{\frac{1}{8}}{\frac{11}{2}}$

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

$\frac{1}{8} \div \frac{11}{2}=\frac{1}{8} \times \frac{2}{11} = \frac{2}{88} = \frac{1}{44}$

The answer is: $\frac{1}{44}$

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Example Question #4584 : Algebra Ii

Divide the fractions: $\frac{3}{8}\div \frac{16}{9}$

Possible Answers:

$\frac{27}{128}$

$\frac{13}{72}$

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

$\frac{2}{3}$

$\frac{3}{2}$

Correct answer:

$\frac{27}{128}$

Explanation:

In order to divide these fractions, we will need to rewrite the expression using a multiplication sign, and take the reciprocal of the second term.

$\frac{3}{8}\div \frac{16}{9} = \frac{3}{8}\times\frac{9}{16} = \frac{27}{128}$

The answer is: $\frac{27}{128}$

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Example Question #4585 : Algebra Ii

$\frac{4}{xy}\cdot \frac{x^2y}{16}$

Possible Answers:

$\frac{4}{x}$

$\frac{4x}{11}$

$\frac{x}{8}$

$\frac{x}{4}$

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

Correct answer:

$\frac{x}{4}$

Explanation:

Before multiplying, look diagonally to see if you can reduce anything. It makes simplifying at the end a lot easier. You can simplify here so that it becomes:

$\frac{1}{1}\cdot \frac{x}{4}$

Simplify straight across to get your final answer:

$\frac{x}{4}$

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Example Question #4586 : Algebra Ii

Divide the fractions: $\frac{6}{11}\div\frac{33}{18}$

Possible Answers:

$\frac{36}{121}$

$\frac{1}{3}$

$\frac{3}{11}$

$\frac{18}{121}$

Correct answer:

$\frac{36}{121}$

Explanation:

To divide the fractions, take the reciprocal of the second term and change the division sign to a multiplication sign.

$\frac{6}{11}\div\frac{33}{18}=\frac{6}{11}\times \frac{18}{33}$

Reduce numerator and denominator. Write out the common factors and cancel the common terms.

$\frac{2 \times 3}{11}\times \frac{18}{3\times 11} = \frac{2\times 18}{11\times 11} = \frac{36}{121}$

The answer is: $\frac{36}{121}$

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Example Question #4587 : Algebra Ii

Divide the fractions: $(\frac{3}{2}\div \frac{4}{3})\div \frac{1}{2}$

Possible Answers:

$\frac{9}{4}$

$\frac{4}{9}$

$\frac{16}{9}$

$\frac{9}{16}$

Correct answer:

$\frac{9}{4}$

Explanation:

Rewrite the terms in the parentheses with a multiplication sign and take the reciprocal of the second term.

$(\frac{3}{2}\div \frac{4}{3}) = \frac{3}{2}\times \frac{3}{4} = \frac{9}{8}$

Divide this fraction with the third term.

$\frac{9}{8} \div \frac{1}{2}$

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

$\frac{9}{8} \div \frac{1}{2}=\frac{9}{8} \times \frac{2}{1} = \frac{9}{4}$

The answer is: $\frac{9}{4}$

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Example Question #71 : Multiplying And Dividing Fractions

Divide the fractions: $\frac{18}{7}\div \frac{7}{3}$

Possible Answers:

$\frac{7}{6}$

$\frac{1}{6}$

$\frac{54}{49}$

$\frac{49}{54}$

Correct answer:

$\frac{54}{49}$

Explanation:

To divide the fractions, we will need to take the reciprocal of the second term and change the division sign to a multiplication sign.

$\frac{18}{7}\div \frac{7}{3}=\frac{18}{7}\times \frac{3}{7}=\frac{54}{49}$

The answer is: $\frac{54}{49}$

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Example Question #251 : Fractions

Multiply the fractions: $\frac{33}{16} \times \frac{8}{57}$

Possible Answers:

$\frac{11}{38}$

$\frac{11}{57}$

$\frac{11}{19}$

$\frac{47}{152}$

$\frac{11}{152}$

Correct answer:

$\frac{11}{38}$

Explanation:

Write out the common factors for each number instead of multiplying the numerator with numerator and denominator with denominator.

$\frac{33}{16} \times \frac{8}{57} = \frac{3\times 11}{4\times 2\times 2} \times \frac{4 \times 2}{19\times 3}$

Cancel out the common terms. Write the remaining terms.

$\frac{11}{2\times 19}= \frac{11}{38}$

The answer is: $\frac{11}{38}$

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Example Question #4592 : Algebra Ii

Multiply: $\frac{2}{11}\times \frac{77}{8}\times \frac{4}{5}$

Possible Answers:

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

$\frac{55}{7}$

$\frac{7}{5}$

$\frac{7}{4}$

$\frac{4}{55}$

Correct answer:

$\frac{7}{5}$

Explanation:

Rewrite the fractions with factors so that the common terms in the numerator and denominator can be canceled.

$\frac{2}{11}\times \frac{77}{8}\times \frac{4}{5}=\frac{2}{11}\times \frac{7 \times 11}{2\times 4}\times \frac{4}{5}$

Cancel all common terms.

The answer is: $\frac{7}{5}$

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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 #4581 : Algebra Ii

Example Question #4582 : Algebra Ii

Example Question #4583 : Algebra Ii

Example Question #4584 : Algebra Ii

Example Question #4585 : Algebra Ii

Example Question #4586 : Algebra Ii

Example Question #4587 : Algebra Ii

Example Question #71 : Multiplying And Dividing Fractions

Example Question #251 : Fractions

Example Question #4592 : Algebra Ii

All Algebra II Resources

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