Algebra II - Fractions | Practice Hub

Divide the fractions: $\frac{10}{3}\div\frac{7}{9}$

$\frac{30}{7}$

$\frac{70}{27}$

$\frac{27}{70}$

$\frac{7}{30}$

$\frac{17}{3}$

Explanation

Change the division sign in the expression and take the reciprocal of the second term.

$\frac{10}{3}\div\frac{7}{9} = \frac{10}{3}\times\frac{9}{7}$

Reduce the three and nine in the numerator and denominator.

The fractions become:

$\frac{10}{1} \times \frac{3}{7} = \frac{30}{7}$

The answer is: $\frac{30}{7}$

Divide the following fractions: $\frac{\frac{4}{9}}{\frac{8}{7}} \div \frac{3}{\frac{2}{3}}$

$\frac{7}{81}$

$\frac{64}{567}$

$\frac{4}{7}$

$\frac{9}{7}$

$\frac{19}{81}$

Explanation

In order to solve this, we will need to evaluate term by term. First rewrite the complex fractions by using a division sign.

$\frac{\frac{4}{9}}{\frac{8}{7}} =\frac{4}{9} \div\frac{8}{7}$

Change the sign from a division to multiplication and take the reciprocal of the second term.

$\frac{4}{9} \div\frac{8}{7} = \frac{4}{9} \times\frac{7}{8} = \frac{28}{72} =\frac{7\times 4}{18\times 4}=\frac{7}{18}$

Evaluate the second complex fraction.

$\frac{3}{\frac{2}{3}} = 3\div \frac{2}{3} = 3\times \frac{3}{2} = \frac{9}{2}$

This means that:

$\frac{\frac{4}{9}}{\frac{8}{7}} \div \frac{3}{\frac{2}{3}} = \frac{7}{18}\div \frac{9}{2}=\frac{7}{18}\times \frac{2}{9} = \frac{7}{9}\times\frac{1}{9}$

The answer is: $\frac{7}{81}$

Divide the fractions: $\frac{\frac{2}{3}}{5}\div \frac{\frac{1}{2}}{3}$

$\frac{4}{5}$

$\frac{5}{4}$

$\frac{1}{45}$

$\textup{The answer is not given.}$

Explanation

We will need to solve each complex fraction first.

Rewrite the complex fractions using a division sign, change the sign to a multiplication sign, and then take the reciprocal of the second term.

$\frac{\frac{2}{3}}{5} = \frac{2}{3}\div 5 =\frac{2}{3}\times \frac{1}{5} = \frac{2}{15}$

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

Divide the two fractions.

$\frac{2}{15}\div \frac{1}{6} = \frac{2}{15}\times \frac{6}{1} = \frac{12}{15}$

Reduce this fraction.

The answer is: $\frac{4}{5}$

Add these fractions:

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

$1\frac{7}{15}$

$1\frac{4}{15}$

$\frac{7}{15}$

$1\frac{15}{22}$

Explanation

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 5 on the top and bottom and the second fraction by 3 on the top and bottom.

$\frac{2}{3}*\frac{5}{5}=\frac{10}{15}$

$\frac{4}{5}*\frac{3}{3}=\frac{12}{15}$

Add these fractions together, then write it as a mixed number

$\frac{10}{15}+\frac{12}{15}=\frac{22}{15}=1\frac{7}{15}$

Sum the fractions: $\frac{7}{11}+\frac{1}{44}$

$\frac{29}{44}$

$\frac{8}{44}$

$\frac{29}{88}$

$\frac{8}{11}$

$\frac{5}{22}$

Explanation

In order to add the fractions, determine the least common denominator.

The LCD is 44 since this number is divisible by both 11 and 44.

Convert the fractions.

$\frac{7}{11}+\frac{1}{44} = \frac{7(4)}{11(4)}+\frac{1}{44}$

Add the numerator. The denominator remains the same.

The answer is: $\frac{29}{44}$

Add the fractions: $\frac{5}{9}+\frac{7}{18}$

$\frac{17}{18}$

$\frac{17}{9}$

$\frac{2}{3}$

$\frac{5}{6}$

$\frac{8}{9}$

Explanation

In order to add the fractions, change the denominator of the first fraction so that both denominators are common.

$\frac{5(2)}{9(2)}+\frac{7}{18}$

Simplify the fractions.

$= \frac{10}{18}+\frac{7}{18} = \frac{17}{18}$

The answer is: $\frac{17}{18}$

Add the fractions: $\frac{5}{2}+\frac{9}{4}+\frac{13}{6}$

$\frac{83}{12}$

$\frac{37}{6}$

$\frac{23}{3}$

$\frac{73}{12}$

$\frac{41}{6}$

Explanation

Convert the fractions to a least common denominator in order to add the numerators. Write out the factors for each denominator to determine the LCD.

The LCD is 12.

$\frac{5}{2}+\frac{9}{4}+\frac{13}{6} =\frac{5(6)}{2(6)}+\frac{9(3)}{4(3)}+\frac{13(2)}{6(2)}$

Simplify the fractions.

$\frac{30}{12}+\frac{27}{12}+\frac{26}{12} = \frac{83}{12}$

The answer is: $\frac{83}{12}$

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

$1\frac{19}{30}$

$\frac{9}{30}$

$\frac{20}{30}$

$\frac{9}{11}$

Explanation

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

Add the fractions: $\frac{3}{4}+\frac{8}{3}$

$\frac{41}{12}$

$\frac{21}{12}$

$\frac{31}{12}$

$\frac{38}{12}$

Explanation

Find the least common denominator to these fractions.

Multiply both denominators together.

$4\times3=12$

Convert the fractions using this denominator.

$\frac{3}{4}+\frac{8}{3} = \frac{9}{12}+\frac{32}{12} = \frac{41}{12}$

The answer is: $\frac{41}{12}$

Add the fractions:

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

$\frac{5}{6}$

$\frac{7}{8}$

$\frac{7}{9}$

$1\frac{1}{6}$

Explanation

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

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

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

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.

$\frac{3}{6}+\frac{2}{6}=\frac{5}{6}$

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