Adding Fractions Worksheets with Answer Key - Free Printable

Here are the solutions for each fraction addition problem. To add fractions with different denominators, we first find a common denominator, convert the fractions, add the numerators, and then simplify if needed.

1) $\frac{1}{4} + \frac{1}{2}$
* Common denominator for 4 and 2 is 4.
* Convert $\frac{1}{2}$ to $\frac{2}{4}$.
* Add: $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$.

2) $\frac{3}{4} + \frac{3}{8}$
* Common denominator for 4 and 8 is 8.
* Convert $\frac{3}{4}$ to $\frac{6}{8}$.
* Add: $\frac{6}{8} + \frac{3}{8} = \frac{9}{8}$.
* Simplify to mixed number: $1 \frac{1}{8}$.

3) $\frac{2}{4} + \frac{5}{6}$
* First, simplify $\frac{2}{4}$ to $\frac{1}{2}$. Now we have $\frac{1}{2} + \frac{5}{6}$.
* Common denominator for 2 and 6 is 6.
* Convert $\frac{1}{2}$ to $\frac{3}{6}$.
* Add: $\frac{3}{6} + \frac{5}{6} = \frac{8}{6}$.
* Simplify: $\frac{8}{6}$ reduces to $\frac{4}{3}$, which is $1 \frac{1}{3}$.

4) $\frac{3}{6} + \frac{1}{3}$
* First, simplify $\frac{3}{6}$ to $\frac{1}{2}$. Now we have $\frac{1}{2} + \frac{1}{3}$.
* Common denominator for 2 and 3 is 6.
* Convert $\frac{1}{2}$ to $\frac{3}{6}$ and $\frac{1}{3}$ to $\frac{2}{6}$.
* Add: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$.

5) $\frac{8}{3} + \frac{4}{5}$
* Common denominator for 3 and 5 is 15.
* Convert $\frac{8}{3}$ to $\frac{40}{15}$ ($8 \times 5 = 40$).
* Convert $\frac{4}{5}$ to $\frac{12}{15}$ ($4 \times 3 = 12$).
* Add: $\frac{40}{15} + \frac{12}{15} = \frac{52}{15}$.
* Simplify to mixed number: $3 \frac{7}{15}$ ($15 \times 3 = 45$, remainder 7).

6) $\frac{2}{5} + \frac{5}{10}$
* First, simplify $\frac{5}{10}$ to $\frac{1}{2}$. Now we have $\frac{2}{5} + \frac{1}{2}$.
* Common denominator for 5 and 2 is 10.
* Convert $\frac{2}{5}$ to $\frac{4}{10}$ and $\frac{1}{2}$ to $\frac{5}{10}$.
* Add: $\frac{4}{10} + \frac{5}{10} = \frac{9}{10}$.

7) $\frac{2}{3} + \frac{1}{2}$
* Common denominator for 3 and 2 is 6.
* Convert $\frac{2}{3}$ to $\frac{4}{6}$ and $\frac{1}{2}$ to $\frac{3}{6}$.
* Add: $\frac{4}{6} + \frac{3}{6} = \frac{7}{6}$.
* Simplify to mixed number: $1 \frac{1}{6}$.

8) $\frac{4}{6} + \frac{5}{8}$
* First, simplify $\frac{4}{6}$ to $\frac{2}{3}$. Now we have $\frac{2}{3} + \frac{5}{8}$.
* Common denominator for 3 and 8 is 24.
* Convert $\frac{2}{3}$ to $\frac{16}{24}$ ($2 \times 8 = 16$).
* Convert $\frac{5}{8}$ to $\frac{15}{24}$ ($5 \times 3 = 15$).
* Add: $\frac{16}{24} + \frac{15}{24} = \frac{31}{24}$.
* Simplify to mixed number: $1 \frac{7}{24}$.

9) $\frac{3}{9} + \frac{1}{3}$
* First, simplify $\frac{3}{9}$ to $\frac{1}{3}$. Now we have $\frac{1}{3} + \frac{1}{3}$.
* Add: $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$.

10) $\frac{6}{4} + \frac{5}{12}$
* First, simplify $\frac{6}{4}$ to $\frac{3}{2}$. Now we have $\frac{3}{2} + \frac{5}{12}$.
* Common denominator for 2 and 12 is 12.
* Convert $\frac{3}{2}$ to $\frac{18}{12}$ ($3 \times 6 = 18$).
* Add: $\frac{18}{12} + \frac{5}{12} = \frac{23}{12}$.
* Simplify to mixed number: $1 \frac{11}{12}$.

11) $\frac{4}{6} + \frac{2}{9}$
* First, simplify $\frac{4}{6}$ to $\frac{2}{3}$. Now we have $\frac{2}{3} + \frac{2}{9}$.
* Common denominator for 3 and 9 is 9.
* Convert $\frac{2}{3}$ to $\frac{6}{9}$.
* Add: $\frac{6}{9} + \frac{2}{9} = \frac{8}{9}$.

12) $\frac{9}{2} + \frac{2}{8}$
* First, simplify $\frac{2}{8}$ to $\frac{1}{4}$. Now we have $\frac{9}{2} + \frac{1}{4}$.
* Common denominator for 2 and 4 is 4.
* Convert $\frac{9}{2}$ to $\frac{18}{4}$.
* Add: $\frac{18}{4} + \frac{1}{4} = \frac{19}{4}$.
* Simplify to mixed number: $4 \frac{3}{4}$ ($4 \times 4 = 16$, remainder 3).

Final Answer:
1) $\frac{3}{4}$
2) $1 \frac{1}{8}$
3) $1 \frac{1}{3}$
4) $\frac{5}{6}$
5) $3 \frac{7}{15}$
6) $\frac{9}{10}$
7) $1 \frac{1}{6}$
8) $1 \frac{7}{24}$
9) $\frac{2}{3}$
10) $1 \frac{11}{12}$
11) $\frac{8}{9}$
12) $4 \frac{3}{4}$