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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 #1 : Multiplying And Dividing Fractions

Simplify $\frac{3}{6}\cdot\frac{12}{4}$ .

Possible Answers:

$\text{None of the answers listed.}$

$\frac{3}{2}$

$\frac{36}{24}$

$\frac{6}{4}$

$\frac{2}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

The problem can be made easier by first simplifying each fraction: $\frac{3}{6}=\frac{1}{2}$ and $\frac{12}{4}=\frac{3}{1}$ .

This brings our new problem to $\frac{1}{2}\cdot\frac{3}{1}$ .

Now, the numerators are multiplied by each other then the denomenators are multiplied by each other: $\frac{1\cdot3}{2\cdot1}=\frac{3}{2}$ .

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Example Question #4 : Division With Fractions

Simplify $\frac{5}{3}\div\frac{7}{6}$ .

Possible Answers:

$\frac{21}{3}$

$\frac{10}{7}$

$\frac{30}{21}$

$\frac{35}{18}$

$\frac{3}{10}$

Correct answer:

$\frac{10}{7}$

Explanation:

To solve, we must turn the division problem into a multiplication problem by "flipping" the second fraction (dividing by a fraction is the same as multiplying by its reciprocal):

$\frac{5}{3}\div\frac{7}{6}=\frac{5}{3}\cdot\frac{6}{7}$ .

Then, we multiply the numerators followed by the denomenators:

$\frac{5\cdot6}{3\cdot7}=\frac{30}{21}$ .

Lastly, the fraction must be simplified by a factor of 3:

$\frac{30}{21}=\frac{10}{7}$ , which gives us our final answer.

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Example Question #1 : Multiplying And Dividing Fractions

Multiply:

$\left(\frac{x^2}{z}\right)\cdot \left(\frac{x^2z^2}{y}\right)$

Possible Answers:

$\frac{x^4z}{y}$

x^4z^2y

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

x^4yz

Correct answer:

$\frac{x^4z}{y}$

Explanation:

To multiply fractions, just multiply the numerators, then the denominators, and then simplify.

$(\frac{x^2}{z})(\frac{x^2z^2}{y})=\frac{x^4z^2}{zy}=\frac{x^4z}{y}$

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Example Question #171 : Fractions

Multiply:

$\left(\frac{ab^2c}{a^{\frac{1}{2}}b^4c^3}\right)\cdot \left(\frac{abc^2}{c}\right)$

Possible Answers:

$\frac{a^\frac{3}{2}}{bc}$

$a^{\frac{3}{2}}bc$

$\frac{bc}{a^{\frac{3}{2}}}$

$\frac{a^{\frac{3}{2}}b}{c}$

Correct answer:

$\frac{a^\frac{3}{2}}{bc}$

Explanation:

To multiply fractions, multiply the numerators and denominators together, then simplify.

$(\frac{ab^2c}{a^{\frac{1}{2}}b^4c^3})(\frac{abc^2}{c})=\frac{a^2b^3c^3}{a^{\frac{1}{2}}b^4c^4}=\frac{a^{\frac{3}{2}}}{bc}$

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Example Question #2 : Multiplying And Dividing Fractions

Multiply:

$\left(\frac{4}{5}x\right)\cdot \left(\frac{6}{13}y\right)$

Possible Answers:

$\frac{24}{65}xy$

$\frac{15}{8}xy$

$\frac{8x}{15y}$

$\frac{8}{15xy}$

Correct answer:

$\frac{24}{65}xy$

Explanation:

Multiply the numerators and denominators. Then, simplify.

$(\frac{4}{5}x)(\frac{6}{13}y)=(\frac{4x}{5})(\frac{6y}{13})=\frac{24xy}{65}$

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Example Question #3 : Multiplying And Dividing Fractions

Multiply:

$\left(\frac{15}{7x}\right)\cdot \left(\frac{12x^2}{5}\right)$

Possible Answers:

$\frac{7}{36}x$

$\frac{36}{7x}$

$\frac{36}{7}x$

$\frac{36x^2}{7}$

Correct answer:

$\frac{36}{7}x$

Explanation:

Multiply the numerators and denominators, then simplify.

$(\frac{15}{7x})(\frac{12x^2}{5})=\frac{180x^2}{35x}=\frac{36}{7}x$

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Example Question #4 : Multiplying And Dividing Fractions

Simplify:

$\frac{36x^2y}{5x^5 y^{-2}}\div\frac{9x^{-3}}{25}$

Possible Answers:

20y^3

$\frac{y^3}{20x^4}$

$\frac{20}{y^3}$

20xy^3

Correct answer:

20y^3

Explanation:

In order to divide fractions, you need to multiply the first fraction by the reciprocal of the second one.

$\frac{36x^2y}{5x^5y^{-2}}\div\frac{9x^{-3}}{25}=\frac{36x^2y}{5x^5y^{-2}}\times\frac{25}{9x^{-3}}$

Now, multiply the numerators and denominators together, then simplify.

$\frac{36x^2y}{5x^5y^{-2}}\times\frac{25}{9x^{-3}}=\frac{900x^2y}{45x^2y^{-2}}=20y^3$

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Example Question #8 : Solving Rational And Fractional Functions

Simplify:

$\frac{25st^2}{6s^3t^5}\div\frac{30s^{-9}}{45s^2t^7}$

Possible Answers:

$\frac{25}{4s^9t^4}$

$\frac{4}{25s^2t}$

$\frac{25s^9t^4}{4}$

$\frac{4s^9t^4}{25}$

Correct answer:

$\frac{25s^9t^4}{4}$

Explanation:

To divid fractions, you need to multiply the first fraction by the reciprocal of the second.

$(\frac{25st^2}{6s^3t^5})\div(\frac{30s^{-9}}{45s^2t^7})=(\frac{25st^2}{6s^3t^5})\times(\frac{45s^2t^7}{30s^{-9}})$

Now, multiply the numerators and denominators together, then simplify.

$(\frac{25st^2}{6s^3t^5})\times(\frac{45s^2t^7}{30s^{-9}})=\frac{1125s^3t^9}{180s^{-6}t^5}=\frac{25s^9t^4}{4}$

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Example Question #2 : Multiplying And Dividing Fractions

Simplify:

$\frac{12m^2n}{16m^3n^4}\div\frac{8m^{-4}n}{18m^4n^2}$

Possible Answers:

$\frac{27m^7}{16n^2}$

$\frac{16n^2}{27m^7}$

27m^7n^2

$\frac{27n^2}{16m^7}$

Correct answer:

$\frac{27m^7}{16n^2}$

Explanation:

To divide fractions, you need to multiply the first fraction by the reciprocal of the second.

$(\frac{12m^2n}{16m^3n^4})\div(\frac{8m^{-4}n}{18m^4n^2})=(\frac{12m^2n}{16m^3n^4})\times(\frac{18m^4n^2}{8m^{-4}n})$

Now, multiply the numerators and denominators, then simplify.

$(\frac{12m^2n}{16m^3n^4})\times(\frac{18m^4n^2}{8m^{-4}n})=\frac{216m^6n^3}{128m^{-1}n^5}=\frac{27m^7}{16n^2}$

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Example Question #5 : Division With Fractions

Evaluate: $\frac{7}{6}\div 2\frac{3}{8}$

Possible Answers:

$\frac{17}{41}$

$\frac{28}{57}$

$\frac{133}{48}$

$\frac{48}{133}$

$\frac{57}{28}$

Correct answer:

$\frac{28}{57}$

Explanation:

Change all the fractions to improper fractions.

$\frac{7}{6}\div 2\frac{3}{8}=\frac{7}{6}\div \frac{19}{8}$

Convert the division sign to a multiplication sign, but flip the second term. Simplify.

$\frac{7}{6}\times \frac{8}{19}= \frac{7}{3}\times \frac{4}{19}= \frac{28}{57}$

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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 #1 : Multiplying And Dividing Fractions

Example Question #4 : Division With Fractions

Example Question #1 : Multiplying And Dividing Fractions

Example Question #171 : Fractions

Example Question #2 : Multiplying And Dividing Fractions

Example Question #3 : Multiplying And Dividing Fractions

Example Question #4 : Multiplying And Dividing Fractions

Example Question #8 : Solving Rational And Fractional Functions

Example Question #2 : Multiplying And Dividing Fractions

Example Question #5 : Division With Fractions

All Algebra II Resources

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