Adding Fractions with Unlike Denominators | Free Worksheets ... - Free Printable

To add fractions with different denominators (the bottom numbers), we first need to find a common denominator. This means finding a number that both bottom numbers can divide into evenly. Once the bottom numbers are the same, we can simply add the top numbers together.

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

1. $\frac{3}{5} + \frac{1}{10}$
* The common denominator for 5 and 10 is 10.
* Convert $\frac{3}{5}$: Multiply top and bottom by 2 to get $\frac{6}{10}$.
* Add: $\frac{6}{10} + \frac{1}{10} = \frac{7}{10}$.

2. $\frac{1}{4} + \frac{1}{2}$
* The common denominator for 4 and 2 is 4.
* Convert $\frac{1}{2}$: Multiply top and bottom by 2 to get $\frac{2}{4}$.
* Add: $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$.

3. $\frac{2}{5} + \frac{4}{15}$
* The common denominator for 5 and 15 is 15.
* Convert $\frac{2}{5}$: Multiply top and bottom by 3 to get $\frac{6}{15}$.
* Add: $\frac{6}{15} + \frac{4}{15} = \frac{10}{15}$.
* Simplify: Both numbers divide by 5, so $\frac{10}{15} = \frac{2}{3}$.

4. $\frac{3}{7} + \frac{1}{14}$
* The common denominator for 7 and 14 is 14.
* Convert $\frac{3}{7}$: Multiply top and bottom by 2 to get $\frac{6}{14}$.
* Add: $\frac{6}{14} + \frac{1}{14} = \frac{7}{14}$.
* Simplify: Both numbers divide by 7, so $\frac{7}{14} = \frac{1}{2}$.

5. $\frac{2}{3} + \frac{2}{9}$
* 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: $\frac{6}{9} + \frac{2}{9} = \frac{8}{9}$.

6. $\frac{4}{5} + \frac{3}{20}$
* The common denominator for 5 and 20 is 20.
* Convert $\frac{4}{5}$: Multiply top and bottom by 4 to get $\frac{16}{20}$.
* Add: $\frac{16}{20} + \frac{3}{20} = \frac{19}{20}$.

7. $\frac{1}{4} + \frac{1}{8}$
* The common denominator for 4 and 8 is 8.
* Convert $\frac{1}{4}$: Multiply top and bottom by 2 to get $\frac{2}{8}$.
* Add: $\frac{2}{8} + \frac{1}{8} = \frac{3}{8}$.

8. $\frac{1}{9} + \frac{1}{18}$
* The common denominator for 9 and 18 is 18.
* Convert $\frac{1}{9}$: Multiply top and bottom by 2 to get $\frac{2}{18}$.
* Add: $\frac{2}{18} + \frac{1}{18} = \frac{3}{18}$.
* Simplify: Both numbers divide by 3, so $\frac{3}{18} = \frac{1}{6}$.

9. $\frac{3}{4} + \frac{1}{12}$
* The common denominator for 4 and 12 is 12.
* Convert $\frac{3}{4}$: Multiply top and bottom by 3 to get $\frac{9}{12}$.
* Add: $\frac{9}{12} + \frac{1}{12} = \frac{10}{12}$.
* Simplify: Both numbers divide by 2, so $\frac{10}{12} = \frac{5}{6}$.

10. $\frac{3}{6} + \frac{1}{3}$
* First, simplify $\frac{3}{6}$ to $\frac{1}{2}$. Now the problem is $\frac{1}{2} + \frac{1}{3}$.
* The common denominator for 2 and 3 is 6.
* Convert $\frac{1}{2}$: Multiply top and bottom by 3 to get $\frac{3}{6}$.
* Convert $\frac{1}{3}$: Multiply top and bottom by 2 to get $\frac{2}{6}$.
* Add: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$.
*(Note: If you didn't simplify first, the common denominator for 6 and 3 is 6. $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$. The result is the same.)*

Final Answer:
1. $\frac{7}{10}$
2. $\frac{3}{4}$
3. $\frac{2}{3}$
4. $\frac{1}{2}$
5. $\frac{8}{9}$
6. $\frac{19}{20}$
7. $\frac{3}{8}$
8. $\frac{1}{6}$
9. $\frac{5}{6}$
10. $\frac{5}{6}$