Worksheet 2: Adding Fractions - Solve the equations.

To add fractions with different denominators, we first need to find a common denominator. This is a number that both bottom numbers can divide into evenly. Once the denominators are the same, we add the top numbers (numerators) and keep the bottom number (denominator) the same. Finally, we simplify the fraction if possible.

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

1. $\frac{1}{6} + \frac{5}{12}$
* The common denominator for 6 and 12 is 12.
* Convert $\frac{1}{6}$: multiply top and bottom by 2 to get $\frac{2}{12}$.
* Add: $\frac{2}{12} + \frac{5}{12} = \frac{7}{12}$.
* This cannot be simplified further.

2. $\frac{1}{8} + \frac{12}{24}$
* The common denominator for 8 and 24 is 24.
* Convert $\frac{1}{8}$: multiply top and bottom by 3 to get $\frac{3}{24}$.
* Add: $\frac{3}{24} + \frac{12}{24} = \frac{15}{24}$.
* Simplify: Both numbers divide by 3. $15 \div 3 = 5$ and $24 \div 3 = 8$.
* Result: $\frac{5}{8}$.

3. $\frac{2}{3} + \frac{1}{15}$
* The common denominator for 3 and 15 is 15.
* Convert $\frac{2}{3}$: multiply top and bottom by 5 to get $\frac{10}{15}$.
* Add: $\frac{10}{15} + \frac{1}{15} = \frac{11}{15}$.
* This cannot be simplified further.

4. $\frac{3}{9} + \frac{7}{18}$
* The common denominator for 9 and 18 is 18.
* Convert $\frac{3}{9}$: multiply top and bottom by 2 to get $\frac{6}{18}$.
* Add: $\frac{6}{18} + \frac{7}{18} = \frac{13}{18}$.
* This cannot be simplified further.

5. $\frac{1}{6} + \frac{3}{12}$
* The common denominator for 6 and 12 is 12.
* Convert $\frac{1}{6}$: multiply top and bottom by 2 to get $\frac{2}{12}$.
* Add: $\frac{2}{12} + \frac{3}{12} = \frac{5}{12}$.
* This cannot be simplified further.

6. $\frac{2}{3} + \frac{2}{9}$
* The common denominator for 3 and 9 is 9.
* Convert $\frac{2}{3}$: multiply top and bottom by 3 to get $\frac{6}{9}$.
* Add: $\frac{6}{9} + \frac{2}{9} = \frac{8}{9}$.
* This cannot be simplified further.

7. $\frac{4}{5} + \frac{2}{15}$
* The common denominator for 5 and 15 is 15.
* Convert $\frac{4}{5}$: multiply top and bottom by 3 to get $\frac{12}{15}$.
* Add: $\frac{12}{15} + \frac{2}{15} = \frac{14}{15}$.
* This cannot be simplified further.

8. $\frac{6}{8} + \frac{3}{16}$
* The common denominator for 8 and 16 is 16.
* Convert $\frac{6}{8}$: multiply top and bottom by 2 to get $\frac{12}{16}$.
* Add: $\frac{12}{16} + \frac{3}{16} = \frac{15}{16}$.
* This cannot be simplified further.

9. $\frac{1}{4} + \frac{3}{16}$
* The common denominator for 4 and 16 is 16.
* Convert $\frac{1}{4}$: multiply top and bottom by 4 to get $\frac{4}{16}$.
* Add: $\frac{4}{16} + \frac{3}{16} = \frac{7}{16}$.
* This cannot be simplified further.

10. $\frac{1}{2} + \frac{2}{6}$
* The common denominator for 2 and 6 is 6.
* Convert $\frac{1}{2}$: multiply top and bottom by 3 to get $\frac{3}{6}$.
* Add: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$.
* This cannot be simplified further.

Final Answer:
1. $\frac{7}{12}$
2. $\frac{5}{8}$
3. $\frac{11}{15}$
4. $\frac{13}{18}$
5. $\frac{5}{12}$
6. $\frac{8}{9}$
7. $\frac{14}{15}$
8. $\frac{15}{16}$
9. $\frac{7}{16}$
10. $\frac{5}{6}$