Algebra II - Adding and Subtracting 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: $\frac{41}{12}$

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

$\frac{83}{12}$

$\frac{37}{6}$

$\frac{23}{3}$

$\frac{73}{12}$

$\frac{41}{6}$

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: $\frac{83}{12}$

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: $\frac{17}{18}$

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

$1\frac{19}{30}$

$\frac{9}{30}$

$\frac{20}{30}$

$\frac{9}{11}$

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:

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

$\frac{5}{6}$

$\frac{7}{8}$

$\frac{7}{9}$

$1\frac{1}{6}$

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.

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

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

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

Add these fractions:

$\frac{1}{2}+\frac{1}{6}$

$\frac{2}{3}$

$\frac{1}{3}$

$\frac{5}{6}{}$

$\frac{4}{3}$

Explanation

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 3 over 3.

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

Add these fractions together, then reduce it to get the final answer.

$\frac{3}{6}+\frac{1}{6}=\frac{4}{6}=\frac{2\cdot2}{2\cdot 3}=\frac{2}{3}$

Add the fractions: $\frac{3}{7}+\frac{1}{70}+\frac{7}{20}$

$\frac{111}{140}$

$\frac{119}{140}$

$\frac{33}{40}$

$\frac{5}{7}$

$\frac{39}{70}$

Explanation

To solve this expression, determine the least common denominator. There is no need to multiply all the denominators together.

Write the factors for each denominator.

We can see that the LCD is 140.

Convert all fractions.

$\frac{3}{7}+\frac{1}{70}+\frac{7}{20}=\frac{3(20)}{7(20)}+\frac{1(2)}{70(2)}+\frac{7(7)}{20(7)}$

Simplify the fractions.

$\frac{60}{140}+\frac{2}{140}+\frac{49}{140} = \frac{111}{140}$

The answer is: $\frac{111}{140}$

$\frac{1}{14}+\frac{1}{21}$

$\frac{1}{42}$

$\frac{2}{35}$

$\frac{1}{35}$

$\frac{2}{21}$

Explanation

Convert each fraction to incorporate a common denominator. The least common denominator of 14 and 21 is 42. Multiply the first fraction by 3divided by 3 and the second by 2 divided by 2 . Then add or subtract the resulting fractions.

Adding and Subtracting Fractions

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