Fractions - Algebra II

Card 0 of 1112

Question

Multiply these fractions:

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

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:

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

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:

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

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

Divide the fractions:

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

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

Divide the fractions:

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

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

Divide the fractions:

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

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:

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

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

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

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

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

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

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

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

$\frac{6}{8}+\frac{5}{7}=$

Answer

Convert each fraction to incorporate a common denominator. The least common denominator of 8 and 7 is 56. Multiply the first fraction by 7 divided by 7 and the second by 8 divided by 8 . Then add or subtract the resulting fractions.

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Question

$\frac{1}{6}+\frac{4}{5}=$

Answer

Convert each fraction to incorporate a common denominator. The least common denominator of 6 and 5 is 30. Multiply the first fraction by 5 divided by 5 and the second by 6 divided by 6 . Then add or subtract the resulting fractions.

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Question

Add the fractions:

$\frac{3}{5}+\frac{1}{10}$

Answer

When adding fractions, the first thing we need to do is get a common denominator.

$\frac{3}{5}\cdot \frac{2}{2}=\frac{6}{10}$

Then when adding, only add the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

$\frac{6}{10}+\frac{1}{10}=\frac{7}{10}$

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Question

$\frac{2}{3}+\frac{3}{8}=$

Answer

Convert each fraction to incorporate a common denominator. The least common denominator of 3 and 8 is 24. Multiply the first fraction by 8 divided by 8 and the second by 3 divided by 3 . Then add or subtract the resulting fractions.

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Question

Add the following fractions: $\frac{2}{a}+\frac{2}{a^3b}$

Answer

To be able to add the fractions, we will need to determine the least common denominator.

The least common denominator is since this is the minimal term that is both divisible by and itself.

Convert only the first fraction with the denominator of .

$\frac{2}{a}+\frac{2}{a^3b}= \frac{2(a^2b)}{a(a^2b)}+\frac{2}{a^3b} = \frac{2a^2b+2}{a^3b}$

The answer is: $\frac{2a^2b+2}{a^3b}$

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Question

Divide the fractions:

$\frac{7}{8}\div \frac{3}{4}$

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.

$\frac{7}{8}\div \frac{3}{4}=\frac{7}{8}\cdot \frac{4}{3}=\frac{28}{24}\div \frac{4}{4}=\frac{7}{6}=1\frac{1}{6}$

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Question

Multiply:

$\frac{5}{6}\cdot \frac{2}{50}$

Answer

Remember, when multiplying fractions, multiply straight across.

But first, try to see if you can reduce diagonally. You can in this case.

Then, multiply across to get your answer of $\frac{1}{30}$ .

Make sure it's in simplest form.

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Question

Subtract the fractions: $\frac{1}{30}- \frac{3}{4}$

Answer

To subtract the fractions, we will need to find the least common denominator.

Write out the factors for both denominators.

Multiply four by 15 to get the least common denominator.

The least common denominator is .

Convert both fractions.

$\frac{1}{30}- \frac{3}{4}= \frac{2}{60}-\frac{45}{60} = -\frac{43}{60}$

The answer is: $-\frac{43}{60}$

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Question

Divide the fractions: $\frac{\frac{1}{3}\div\frac{1}{9}}{\frac{7}{2}}$

Answer

Evaluate the top term first. We can change the sign to multiplication and take the reciprocal of the second term.

$\frac{1}{3}\div\frac{1}{9} = \frac{1}{3}\times \frac{9}{1} = 3$

Rewrite the fraction.

$\frac{\frac{1}{3}\div\frac{1}{9}}{\frac{7}{2}}=\frac{3}{\frac{7}{2}}$

Write the complex fraction using the division sign and repeat the process.

$\frac{3}{\frac{7}{2}}= 3\div \frac{7}{2}= 3\times \frac{2}{7} =\frac{6}{7}$

The answer is: $\frac{6}{7}$

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Question

Simplify $\frac{2}{3}+\frac{1}{4}+\frac{5}{6}$

Answer

Find the least common denominator (LCD) and convert each fraction to the LCD and then add. Simplify as necessary.

$\frac{2}{3}+\frac{1}{4}+\frac{5}{6}=\frac{8}{12}+\frac{3}{12}+\frac{10}{12}=\frac{21}{12}$

The result is an improper fraction because the numerator is larger than the denominator and can be simplified and converted to a mix numeral.

$\frac{21}{12}=\frac{7}{4}=1\frac{3}{4}$

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