Adding Fractions worksheet with ten equations to solve.

Here are the step-by-step solutions for each fraction addition problem. To add fractions with different bottom numbers (denominators), we first need to find a common denominator so the pieces are the same size. Then, we add the top numbers (numerators).

1. $\frac{1}{2} + \frac{1}{4}$
* The common denominator for 2 and 4 is 4.
* Change $\frac{1}{2}$ to $\frac{2}{4}$ (multiply top and bottom by 2).
* Add: $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$.

2. $\frac{3}{7} + \frac{2}{9}$
* The common denominator for 7 and 9 is 63 ($7 \times 9$).
* Change $\frac{3}{7}$ to $\frac{27}{63}$ ($3 \times 9 = 27$).
* Change $\frac{2}{9}$ to $\frac{14}{63}$ ($2 \times 7 = 14$).
* Add: $\frac{27}{63} + \frac{14}{63} = \frac{41}{63}$.

3. $\frac{3}{5} + \frac{1}{15}$
* The common denominator for 5 and 15 is 15.
* Change $\frac{3}{5}$ to $\frac{9}{15}$ ($3 \times 3 = 9$).
* Add: $\frac{9}{15} + \frac{1}{15} = \frac{10}{15}$.
* Simplify: Both numbers divide by 5. $\frac{10 \div 5}{15 \div 5} = \frac{2}{3}$.

4. $\frac{1}{9} + \frac{7}{8}$
* The common denominator for 9 and 8 is 72 ($9 \times 8$).
* Change $\frac{1}{9}$ to $\frac{8}{72}$ ($1 \times 8 = 8$).
* Change $\frac{7}{8}$ to $\frac{63}{72}$ ($7 \times 9 = 63$).
* Add: $\frac{8}{72} + \frac{63}{72} = \frac{71}{72}$.

5. $\frac{6}{7} + \frac{2}{21}$
* The common denominator for 7 and 21 is 21.
* Change $\frac{6}{7}$ to $\frac{18}{21}$ ($6 \times 3 = 18$).
* Add: $\frac{18}{21} + \frac{2}{21} = \frac{20}{21}$.

6. $\frac{4}{6} + \frac{2}{10}$
* First, simplify the fractions if possible. $\frac{4}{6}$ becomes $\frac{2}{3}$. So, $\frac{2}{3} + \frac{2}{10}$.
* The common denominator for 3 and 10 is 30.
* Change $\frac{2}{3}$ to $\frac{20}{30}$ ($2 \times 10 = 20$).
* Change $\frac{2}{10}$ to $\frac{6}{30}$ ($2 \times 3 = 6$).
* Add: $\frac{20}{30} + \frac{6}{30} = \frac{26}{30}$.
* Simplify: Divide by 2. $\frac{13}{15}$.

7. $\frac{1}{11} + \frac{3}{22}$
* The common denominator for 11 and 22 is 22.
* Change $\frac{1}{11}$ to $\frac{2}{22}$ ($1 \times 2 = 2$).
* Add: $\frac{2}{22} + \frac{3}{22} = \frac{5}{22}$.

8. $\frac{1}{4} + \frac{8}{20}$
* First, simplify $\frac{8}{20}$. Both divide by 4, so it becomes $\frac{2}{5}$. Now we have $\frac{1}{4} + \frac{2}{5}$.
* The common denominator for 4 and 5 is 20.
* Change $\frac{1}{4}$ to $\frac{5}{20}$ ($1 \times 5 = 5$).
* Change $\frac{2}{5}$ to $\frac{8}{20}$ ($2 \times 4 = 8$).
* Add: $\frac{5}{20} + \frac{8}{20} = \frac{13}{20}$.

9. $\frac{4}{7} + \frac{2}{9}$
* The common denominator for 7 and 9 is 63 ($7 \times 9$).
* Change $\frac{4}{7}$ to $\frac{36}{63}$ ($4 \times 9 = 36$).
* Change $\frac{2}{9}$ to $\frac{14}{63}$ ($2 \times 7 = 14$).
* Add: $\frac{36}{63} + \frac{14}{63} = \frac{50}{63}$.

10. $\frac{7}{10} + \frac{2}{30}$
* The common denominator for 10 and 30 is 30.
* Change $\frac{7}{10}$ to $\frac{21}{30}$ ($7 \times 3 = 21$).
* Add: $\frac{21}{30} + \frac{2}{30} = \frac{23}{30}$.

Final Answer:
1. $\frac{3}{4}$
2. $\frac{41}{63}$
3. $\frac{2}{3}$
4. $\frac{71}{72}$
5. $\frac{20}{21}$
6. $\frac{13}{15}$
7. $\frac{5}{22}$
8. $\frac{13}{20}$
9. $\frac{50}{63}$
10. $\frac{23}{30}$