Adding Fractions worksheet with ten equations to solve, designed for educational practice.

To solve these fraction addition problems, we need to find a common denominator for each pair of fractions. This means finding a number that both bottom numbers (denominators) can divide into evenly. Once the denominators are the same, we add the top numbers (numerators) and keep the bottom number the same. Finally, we simplify the answer if possible.

Here is the step-by-step solution for each problem:

1. $\frac{1}{2} + \frac{1}{4}$
* The common denominator for 2 and 4 is 4.
* Convert $\frac{1}{2}$ to $\frac{2}{4}$.
* 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 $7 \times 9 = 63$.
* Convert $\frac{3}{7}$: multiply top and bottom by 9 $\rightarrow \frac{27}{63}$.
* Convert $\frac{2}{9}$: multiply top and bottom by 7 $\rightarrow \frac{14}{63}$.
* Add: $\frac{27}{63} + \frac{14}{63} = \frac{41}{63}$. (This cannot be simplified further).

3. $\frac{3}{5} + \frac{1}{15}$
* The common denominator for 5 and 15 is 15.
* Convert $\frac{3}{5}$: multiply top and bottom by 3 $\rightarrow \frac{9}{15}$.
* Add: $\frac{9}{15} + \frac{1}{15} = \frac{10}{15}$.
* Simplify: Divide top and bottom by 5 $\rightarrow \frac{2}{3}$.

4. $\frac{1}{9} + \frac{7}{8}$
* The common denominator for 9 and 8 is $9 \times 8 = 72$.
* Convert $\frac{1}{9}$: multiply top and bottom by 8 $\rightarrow \frac{8}{72}$.
* Convert $\frac{7}{8}$: multiply top and bottom by 9 $\rightarrow \frac{63}{72}$.
* 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.
* Convert $\frac{6}{7}$: multiply top and bottom by 3 $\rightarrow \frac{18}{21}$.
* Add: $\frac{18}{21} + \frac{2}{21} = \frac{20}{21}$.

6. $\frac{4}{6} + \frac{2}{10}$
* First, let's simplify the fractions to make it easier. $\frac{4}{6}$ simplifies to $\frac{2}{3}$. So the problem is $\frac{2}{3} + \frac{2}{10}$.
* The common denominator for 3 and 10 is 30.
* Convert $\frac{2}{3}$: multiply top and bottom by 10 $\rightarrow \frac{20}{30}$.
* Convert $\frac{2}{10}$: multiply top and bottom by 3 $\rightarrow \frac{6}{30}$.
* Add: $\frac{20}{30} + \frac{6}{30} = \frac{26}{30}$.
* Simplify: Divide top and bottom by 2 $\rightarrow \frac{13}{15}$.

7. $\frac{1}{11} + \frac{3}{22}$
* The common denominator for 11 and 22 is 22.
* Convert $\frac{1}{11}$: multiply top and bottom by 2 $\rightarrow \frac{2}{22}$.
* Add: $\frac{2}{22} + \frac{3}{22} = \frac{5}{22}$.

8. $\frac{1}{4} + \frac{8}{20}$
* Let's simplify $\frac{8}{20}$ first. Divide top and bottom by 4 $\rightarrow \frac{2}{5}$. So the problem is $\frac{1}{4} + \frac{2}{5}$.
* The common denominator for 4 and 5 is 20.
* Convert $\frac{1}{4}$: multiply top and bottom by 5 $\rightarrow \frac{5}{20}$.
* Convert $\frac{2}{5}$: multiply top and bottom by 4 $\rightarrow \frac{8}{20}$.
* 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 $7 \times 9 = 63$.
* Convert $\frac{4}{7}$: multiply top and bottom by 9 $\rightarrow \frac{36}{63}$.
* Convert $\frac{2}{9}$: multiply top and bottom by 7 $\rightarrow \frac{14}{63}$.
* 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.
* Convert $\frac{7}{10}$: multiply top and bottom by 3 $\rightarrow \frac{21}{30}$.
* 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. $\frac{23}{30}$