Adding Fractions worksheet with ten equations for practice.

To solve these fraction addition problems, we need to find a common denominator for the two fractions in each equation. This allows us to add the numerators together while keeping the denominator the same. After adding, we should check if the resulting fraction can be simplified (reduced) to its lowest terms.

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

1. $\frac{1}{2} + \frac{1}{3}$
* The least common multiple for 2 and 3 is 6.
* Convert $\frac{1}{2}$ to $\frac{3}{6}$ (multiply top and bottom by 3).
* Convert $\frac{1}{3}$ to $\frac{2}{6}$ (multiply top and bottom by 2).
* Add: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$.

2. $\frac{4}{5} + \frac{1}{6}$
* The least common multiple for 5 and 6 is 30.
* Convert $\frac{4}{5}$ to $\frac{24}{30}$ ($4 \times 6 = 24$).
* Convert $\frac{1}{6}$ to $\frac{5}{30}$ ($1 \times 5 = 5$).
* Add: $\frac{24}{30} + \frac{5}{30} = \frac{29}{30}$.

3. $\frac{3}{5} + \frac{2}{7}$
* The least common multiple for 5 and 7 is 35.
* Convert $\frac{3}{5}$ to $\frac{21}{35}$ ($3 \times 7 = 21$).
* Convert $\frac{2}{7}$ to $\frac{10}{35}$ ($2 \times 5 = 10$).
* Add: $\frac{21}{35} + \frac{10}{35} = \frac{31}{35}$.

4. $\frac{4}{5} + \frac{1}{8}$
* The least common multiple for 5 and 8 is 40.
* Convert $\frac{4}{5}$ to $\frac{32}{40}$ ($4 \times 8 = 32$).
* Convert $\frac{1}{8}$ to $\frac{5}{40}$ ($1 \times 5 = 5$).
* Add: $\frac{32}{40} + \frac{5}{40} = \frac{37}{40}$.

5. $\frac{5}{8} + \frac{2}{11}$
* The least common multiple for 8 and 11 is 88.
* Convert $\frac{5}{8}$ to $\frac{55}{88}$ ($5 \times 11 = 55$).
* Convert $\frac{2}{11}$ to $\frac{16}{88}$ ($2 \times 8 = 16$).
* Add: $\frac{55}{88} + \frac{16}{88} = \frac{71}{88}$.

6. $\frac{5}{8} + \frac{2}{9}$
* The least common multiple for 8 and 9 is 72.
* Convert $\frac{5}{8}$ to $\frac{45}{72}$ ($5 \times 9 = 45$).
* Convert $\frac{2}{9}$ to $\frac{16}{72}$ ($2 \times 8 = 16$).
* Add: $\frac{45}{72} + \frac{16}{72} = \frac{61}{72}$.

7. $\frac{4}{7} + \frac{5}{14}$
* Since 14 is a multiple of 7, the common denominator is 14.
* Convert $\frac{4}{7}$ to $\frac{8}{14}$ ($4 \times 2 = 8$).
* Keep $\frac{5}{14}$ as is.
* Add: $\frac{8}{14} + \frac{5}{14} = \frac{13}{14}$.

8. $\frac{3}{5} + \frac{4}{12}$
* First, simplify $\frac{4}{12}$ to $\frac{1}{3}$ (divide top and bottom by 4). Now the problem is $\frac{3}{5} + \frac{1}{3}$.
* The least common multiple for 5 and 3 is 15.
* Convert $\frac{3}{5}$ to $\frac{9}{15}$ ($3 \times 3 = 9$).
* Convert $\frac{1}{3}$ to $\frac{5}{15}$ ($1 \times 5 = 5$).
* Add: $\frac{9}{15} + \frac{5}{15} = \frac{14}{15}$.

9. $\frac{7}{9} + \frac{1}{18}$
* Since 18 is a multiple of 9, the common denominator is 18.
* Convert $\frac{7}{9}$ to $\frac{14}{18}$ ($7 \times 2 = 14$).
* Keep $\frac{1}{18}$ as is.
* Add: $\frac{14}{18} + \frac{1}{18} = \frac{15}{18}$.
* Simplify: Both numbers are divisible by 3. $\frac{15 \div 3}{18 \div 3} = \frac{5}{6}$.

10. $\frac{2}{10} + \frac{8}{30}$
* First, simplify $\frac{2}{10}$ to $\frac{1}{5}$ (divide top and bottom by 2). Now the problem is $\frac{1}{5} + \frac{8}{30}$.
* The least common multiple for 5 and 30 is 30.
* Convert $\frac{1}{5}$ to $\frac{6}{30}$ ($1 \times 6 = 6$).
* Keep $\frac{8}{30}$ as is.
* Add: $\frac{6}{30} + \frac{8}{30} = \frac{14}{30}$.
* Simplify: Both numbers are divisible by 2. $\frac{14 \div 2}{30 \div 2} = \frac{7}{15}$.

Final Answer:
1. $\frac{5}{6}$
2. $\frac{29}{30}$
3. $\frac{31}{35}$
4. $\frac{37}{40}$
5. $\frac{71}{88}$
6. $\frac{61}{72}$
7. $\frac{13}{14}$
8. $\frac{14}{15}$
9. $\frac{5}{6}$
10. $\frac{7}{15}$