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Algebra II : Fractions

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Example Questions

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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Example Question #6 : Division With Fractions

Divide and simplify:

$\frac{2}{11}\div \frac{9}{22}$ .

Possible Answers:

$\frac{4}{9}$

$\frac{2}{11}$

$\frac{11}{}9$

$\frac{18}{222}$

$\frac{1}{9}$

Correct answer:

$\frac{4}{9}$

Explanation:

Multiplying fractions is a two-step process. First, you must flip the second fraction (make it its reciprocal) and then set up the equation as a multiplication problem:

$\frac{2}{11}\cdot \frac{22}{}9$ .

Then, cross-reduce: 11 goes into both 11 and 22, so you can take that out so it looks like:

$\frac{2}{1}\cdot \frac{2}{9}$ .

Then, multiply straight across so that you get $\frac{4}{}9$ .

You can't simplify any further, so that's your answer!

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Example Question #181 : Fractions

Multiply and simplify:

$\frac{6y^2}{14x^9}\cdot \frac{2x^3}{4y}$

Possible Answers:

$\frac{3y}{x^6}$

$\frac{y}{14x^6}$

$\frac{1}{14x^6}$

$\frac{3y}{4x^6}$

$\frac{3y}{14x^6}$

Correct answer:

$\frac{3y}{14x^6}$

Explanation:

Before multiplying straight across, I would start with some cross-reducing. Look diagonally and see what can be simplified.

Between 6y^2 and , you can take out a 2y.

Between 14x^9 and 2x^3 , you can take out a 2x^3 .

The simplified version looks like:

$\frac{3y}{7x^6}\cdot \frac{1}{2}=\frac{3y}{14x^6}$

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Example Question #3 : Operations With Fractions

Multiply these fractions:

$\frac{7}{9}*\frac{1}{14}$

Possible Answers:

$\frac{2}{9}$

$\frac{1}{6}$

$\frac{1}{18}$

$\frac{1}{9}$

Correct answer:

$\frac{1}{18}$

Explanation:

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

$\frac{7}{9}*\frac{1}{14}=\frac{7*1}{9*14}=\frac{7}{126}$

Simply the fraction to get the final answer:

$\frac{7}{126}\div \frac{7}{7}=\frac{1}{18}$

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Example Question #1 : Multiplication With Fractions

Multiply these fractions:

$\frac{5}{12}*\frac{3}{7}$

Possible Answers:

$\frac{3}{14}$

$\frac{5}{28}$

$\frac{1}{4}$

$\frac{5}{27}$

Correct answer:

$\frac{5}{28}$

Explanation:

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

$\frac{5}{12}*\frac{3}{7}=\frac{5*3}{12*7}=\frac{15}{84}$

Simply the fraction to get the final answer:

$\frac{15}{84}\div \frac{3}{3}=\frac{5}{28}$

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Example Question #11 : Multiplying And Dividing Fractions

Multiply these fractions:

$\frac{2}{3}*\frac{5}{6}$

Possible Answers:

$\frac{7}{9}$

$\frac{4}{9}$

$\frac{2}{9}$

$\frac{5}{9}$

Correct answer:

$\frac{5}{9}$

Explanation:

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

$\frac{2}{3}*\frac{5}{6}=\frac{2*5}{3*6}=\frac{10}{18}$

Simply the fraction to get the final answer:

$\frac{10}{18}\div \frac{2}{2}=\frac{5}{9}$

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Example Question #4521 : Algebra Ii

Multiply these fractions:

$\frac{1}{2}*\frac{2}{3}$

Possible Answers:

$\frac{1}{6}$

$\frac{1}{3}$

$1\frac{1}{3}$

$1\frac{1}{2}$

Correct answer:

$\frac{1}{3}$

Explanation:

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

$\frac{1}{2}*\frac{2}{3}=\frac{1*2}{2*3}=\frac{2}{6}$

Simply the fraction to get the final answer:

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

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Example Question #4 : Operations With Fractions

Multiply these fractions:

$\frac{5}{7}*\frac{1}{3}$

Possible Answers:

$\frac{5}{21}$

$\frac{1}{3}$

$\frac{4}{21}$

$\frac{6}{21}$

Correct answer:

$\frac{5}{21}$

Explanation:

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

$\frac{5}{7}*\frac{1}{3}=\frac{5*1}{7*3}=\frac{5}{21}$

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Example Question #11 : Multiplication With Fractions

Multiply these fractions:

$\frac{4}{9}*\frac{3}{7}$

Possible Answers:

$\frac{5}{21}$

$\frac{3}{21}$

$\frac{4}{21}$

$\frac{6}{21}$

Correct answer:

$\frac{4}{21}$

Explanation:

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

$\frac{4}{9}*\frac{3}{7}=\frac{4*3}{9*7}=\frac{12}{63}$

Simply the fraction to get the final answer:

$\frac{12}{63}\div \frac{3}{3}=\frac{4}{21}$

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Algebra II : Fractions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #2 : Multiplying And Dividing Fractions

Example Question #5 : Division With Fractions

Example Question #6 : Division With Fractions

Example Question #181 : Fractions

Example Question #3 : Operations With Fractions

Example Question #1 : Multiplication With Fractions

Example Question #11 : Multiplying And Dividing Fractions

Example Question #4521 : Algebra Ii

Example Question #4 : Operations With Fractions

Example Question #11 : Multiplication With Fractions

All Algebra II Resources

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