Fractions - Algebra 2

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Question

Multiply these fractions:

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

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Answer

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

$\frac{5}{7}\frac{1}{3}=\frac{51}{7*3}=\frac{5}{21}$

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Question

Multiply the fractions:

$\frac{3}{5}\cdot \frac{5}{7}$

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Answer

When multiplying fractions, multiply the numbers on the top together and the numbers on the bottom together. Then simplify accordingly.

$\frac{3}{5}\cdot \frac{5}{7}=\frac{15}{35}\div \frac{5}{5}=\frac{3}{7}$

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Question

Divide the fractions:

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

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Answer

When dividing fractions, first we flip the second fraction in the problem. Then we multiply the numbers on the top together and the numbers on the bottom together. Finally simplify accordingly.

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

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Question

Solve: $\frac{3}{5}-\frac{2}{7} -\frac{1}{2}$

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Answer

Identify the least common denominator.

Convert the fractions.

$\frac{3}{5}-\frac{2}{7} -\frac{1}{2} =\frac{3(7)(2)}{5(7)(2)}-\frac{2(5)(2)}{7(5)(2)} -\frac{1(5)(7)}{2(5)(7)}$

Simplify the terms.

$\frac{42}{70}-\frac{20}{70}-\frac{35}{70} = -\frac{13}{70}$

The answer is: $-\frac{13}{70}$

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Question

Add the following fractions: $\frac{1}{5x}+\frac{3}{7}+\frac{10}{x^2}$

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Answer

Determine the least common denominator.

The first two denominators do not have an . After all denominators have an term, the coefficients of the three denominators are:

The least common denominator would be:

Convert all fractions.

$\frac{1}{5x}+\frac{3}{7}+\frac{10}{x^2}=\frac{1(7x)}{5x(7x)}+\frac{3(5x^2)}{7(5x^2)}+\frac{10(35)}{x^2 (35)}$

Simplify the fractions.

The answer is: $\frac{15x^2+7x+350}{35x^2}$

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Question

Add the fractions: $\frac{4}{9}+\frac{1}{3}+\frac{5}{6}$

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Answer

To add the fractions we need the least common denominator. Write the multiples for each denominator.

Convert the fractions with a denominator of 18, since this is the least common denominator.

$\frac{4}{9}+\frac{1}{3}+\frac{5}{6}=\frac{4(2)}{9(2)}+\frac{1(6)}{3(6)}+\frac{5(3)}{6(3)}$

Simplify the fractions.

$\frac{8}{18}+\frac{6}{18}+\frac{15}{18} = \frac{29}{18}$

The answer is: $\frac{29}{18}$

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Question

Divide the fractions:

$\frac{7}{9}\div \frac{5}{6}$

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Answer

When dividing fractions, first we flip the second fraction in the problem. Then we multiply the numbers on the top together and the numbers on the bottom together. Finally simplify accordingly.

$\frac{7}{9}\div \frac{5}{6}=\frac{7}{9}\cdot \frac{6}{5}=\frac{42}{45}\div \frac{3}{3}=\frac{14}{15}$

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Question

Multiply:

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

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Answer

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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Question

Divide the fractions:

$\frac{2}{5}\div \frac{3}{4}$

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Answer

When dividing fractions, first we flip the second fraction in the problem. Then we multiply the numbers on the top together and the numbers on the bottom together. Finally simplify accordingly.

$\frac{2}{5}\div \frac{3}{4}=\frac{2}{5}\cdot \frac{4}{3}=\frac{8}{15}$

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Question

Subtract: $\frac{3}{27}-\frac{9}{30}-\frac{12}{60}$

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Answer

In order to subtract the fractions, we should reduce all the fractions first.

$\frac{3}{27}-\frac{9}{30}-\frac{12}{60} = \frac{1}{9}-\frac{3}{10}-\frac{1}{5}$

Convert the reduced fractions to a common denominator. By visualization, the common denominator is 90, since this value is divisible by all three numbers.

$\frac{1(10)}{9(10)}-\frac{3(9)}{10(9)}-\frac{1(18)}{5(18)}$

Simplify the top and bottom.

$\frac{10}{90}-\frac{27}{90}-\frac{18}{90} = -\frac{35}{90}$

Reduce this fraction.

$-\frac{35}{90} = -\frac{7\times 5}{18\times 5} = -\frac{7}{18}$

The answer is: $-\frac{7}{18}$

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Question

Divide the fractions:

$\frac{3}{5}\div \frac{4}{7}$

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Answer

When dividing fractions, first we flip the second fraction in the problem. Then we multiply the numbers on the top together and the numbers on the bottom together. Finally simplify accordingly.

$\frac{3}{5}\div \frac{4}{7}=\frac{3}{5}\cdot \frac{7}{4}=\frac{21}{20}=1\frac{1}{20}$

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Question

Divide the fractions:

$\frac{2}{7}\div \frac{3}{21}$

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Answer

When dividing fractions, first we flip the second fraction in the problem. Then we multiply the numbers on the top together and the numbers on the bottom together. Finally simplify accordingly.

$\frac{2}{7}\div \frac{3}{21}=\frac{2}{7}\cdot \frac{21}{3}=\frac{42}{21}=2$

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Question

$\frac{4}{11}+\frac{7}{13}=$

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Answer

Convert each fraction to incorporate a common denominator. The least common denominator of 11 and 13 is 143. Multiply the first fraction by 13 divided by 13 and the second by 11 divided by 11 . Then add or subtract the resulting fractions.

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Question

$\frac{3}{7}-\frac{5}{13}=$

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Answer

Convert each fraction to incorporate a common denominator. The least common denominator of 7 and 13 is 91. Multiply the first fraction by 13 divided by 13 and the second by 7 divided by 7 . Then add or subtract the resulting fractions.

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Question

$\frac{4}{9}-\frac{2}{7}=$

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Answer

Convert each fraction to incorporate a common denominator. The least common denominator of 9 and 7 is 63. Multiply the first fraction by 7 divided by 7 and the second by 9 divided by 9 . Then add or subtract the resulting fractions.

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Question

Add the fractions: $\frac{8}{11}+\frac{1}{66}$

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Answer

Change the first fraction so that both fractions have the same denominator.

Multiply the first fraction by $\frac{6}{6}$ in order to change the fraction.

$\frac{8}{11}(\frac{6}{6})+\frac{1}{66} = \frac{48}{66}+\frac{1}{66} = \frac{49}{66}$

The answer is: $\frac{49}{66}$

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Question

Add the fractions: $\frac{2}{3}+\frac{8}{9}+2\frac{1}{6}$

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Answer

Change the mixed fraction to an improper fraction.

$1\frac{1}{6} = \frac{6(2)+1}{6} = \frac{13}{6}$

Rewrite the expression.

$\frac{2}{3}+\frac{8}{9}+\frac{13}{6}$

Convert all of the terms to common denominator. A common denominator is 18 since this value is divisible by all denominators given.

$\frac{2(6)}{3(6)}+\frac{8(2)}{9(2)}+\frac{13(3)}{6(3)}$

Simplify all the terms.

$\frac{12}{18}+\frac{16}{18}+\frac{39}{18} = \frac{67}{18}$

The answer is: $\frac{67}{18}$

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Question

Compute the fractions: $\frac{7}{2}-\frac{3}{8}+\frac{3}{4}$

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Answer

Convert the fractions to a common denominator.

The least common denominator is eight.

$\frac{7(4)}{2(4)}-\frac{3}{8}+\frac{3(2)}{4(2)} = \frac{28}{8}-\frac{3}{8}+\frac{6}{8}$

Find the sum now that the denominators are equal.

The answer is: $\frac{31}{8}$

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Question

Multiply:

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

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Answer

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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Question

Add the fractions: $\frac{7}{4}+\frac{9}{8}+\frac{1}{12}$

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Answer

Determine the least common denominator. Write out the multiples of each denominator.

Convert all fractions to a common denominator of 24.

$\frac{7}{4}+\frac{9}{8}+\frac{1}{12} = \frac{7(6)}{4(6)}+\frac{9(3)}{8(3)}+\frac{1(2)}{12(2)}$

Simplify the fractions.

$\frac{42}{24}+\frac{27}{24}+\frac{2}{24} = \frac{71}{24}$

The answer is: $\frac{71}{24}$

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