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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 #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 #11 : Multiplying And Dividing Fractions

Multiply and simplify:

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

Possible Answers:

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

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

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

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

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

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:

$\frac{1}{6}$

$\frac{2}{9}$

$\frac{1}{9}$

$\frac{1}{18}$

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 #4 : Operations With Fractions

Multiply these fractions:

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

Possible Answers:

$\frac{3}{14}$

$\frac{1}{4}$

$\frac{5}{27}$

$\frac{5}{28}$

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 #5 : Operations With Fractions

Multiply these fractions:

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

Possible Answers:

$\frac{2}{9}$

$\frac{7}{9}$

$\frac{4}{9}$

$\frac{5}{9}$

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 #191 : Basic Arithmetic

Multiply these fractions:

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

Possible Answers:

$1\frac{1}{3}$

$1\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{6}$

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 #1 : Operations With Fractions

Multiply these fractions:

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

Possible Answers:

$\frac{1}{3}$

$\frac{4}{21}$

$\frac{5}{21}$

$\frac{6}{21}$

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:

$\frac{6}{21}$

$\frac{4}{21}$

$\frac{5}{21}$

$\frac{3}{21}$

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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Example Question #12 : Multiplication With Fractions

Multiply these fractions:

$\frac{1}{10}*\frac{2}{5}$

Possible Answers:

$\frac{3}{25}$

$\frac{1}{50}$

$\frac{1}{25}$

$\frac{2}{25}$

Correct answer:

$\frac{1}{25}$

Explanation:

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

$\frac{1}{10}*\frac{2}{5}=\frac{1*2}{10*5}=\frac{2}{50}$

Simply the fraction to get the final answer:

$\frac{2}{50}\div \frac{2}{2}=\frac{1}{25}$

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Example Question #21 : Multiplying And Dividing Fractions

Multiply these fractions:

$\frac{1}{12}*\frac{4}{5}$

Possible Answers:

$\frac{2}{15}$

$\frac{4}{15}$

$\frac{1}{5}$

$\frac{1}{15}$

Correct answer:

$\frac{1}{15}$

Explanation:

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

$\frac{1}{12}*\frac{4}{5}=\frac{1*4}{12*5}=\frac{4}{60}$

Simply the fraction to get the final answer:

$\frac{4}{60}\div \frac{4}{4}=\frac{1}{15}$

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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 #6 : Division With Fractions

Example Question #11 : Multiplying And Dividing Fractions

Example Question #3 : Operations With Fractions

Example Question #4 : Operations With Fractions

Example Question #5 : Operations With Fractions

Example Question #191 : Basic Arithmetic

Example Question #1 : Operations With Fractions

Example Question #11 : Multiplication With Fractions

Example Question #12 : Multiplication With Fractions

Example Question #21 : Multiplying And Dividing Fractions

All Algebra II Resources

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