Adding Fractions worksheet with ten problems for practice.

Here are the step-by-step solutions for adding the fractions. To add fractions with different bottom numbers (denominators), we first need to find a common denominator that all the numbers can divide into evenly. Then, we change each fraction so they all have that same bottom number, add the top numbers (numerators), and simplify if needed.

1) $\frac{3}{4} + \frac{3}{5} + \frac{1}{3}$
* The least common multiple for 4, 5, and 3 is 60.
* Convert fractions: $\frac{3 \times 15}{60} + \frac{3 \times 12}{60} + \frac{1 \times 20}{60}$
* This becomes: $\frac{45}{60} + \frac{36}{60} + \frac{20}{60}$
* Add numerators: $45 + 36 + 20 = 101$
* Result: $\frac{101}{60}$ or $1 \frac{41}{60}$

2) $\frac{2}{3} + \frac{4}{5} + \frac{2}{4}$
* First, simplify $\frac{2}{4}$ to $\frac{1}{2}$. Now we have $\frac{2}{3} + \frac{4}{5} + \frac{1}{2}$.
* The least common multiple for 3, 5, and 2 is 30.
* Convert fractions: $\frac{2 \times 10}{30} + \frac{4 \times 6}{30} + \frac{1 \times 15}{30}$
* This becomes: $\frac{20}{30} + \frac{24}{30} + \frac{15}{30}$
* Add numerators: $20 + 24 + 15 = 59$
* Result: $\frac{59}{30}$ or $1 \frac{29}{30}$

3) $\frac{2}{4} + \frac{2}{5} + \frac{2}{10}$
* Simplify $\frac{2}{4}$ to $\frac{1}{2}$ and $\frac{2}{10}$ to $\frac{1}{5}$.
* Now we have: $\frac{1}{2} + \frac{2}{5} + \frac{1}{5}$.
* Combine the fifths: $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$.
* Now add $\frac{1}{2} + \frac{3}{5}$. Common denominator is 10.
* Convert: $\frac{5}{10} + \frac{6}{10} = \frac{11}{10}$
* Result: $\frac{11}{10}$ or $1 \frac{1}{10}$

4) $\frac{7}{10} + \frac{2}{3} + \frac{1}{5}$
* The least common multiple for 10, 3, and 5 is 30.
* Convert fractions: $\frac{7 \times 3}{30} + \frac{2 \times 10}{30} + \frac{1 \times 6}{30}$
* This becomes: $\frac{21}{30} + \frac{20}{30} + \frac{6}{30}$
* Add numerators: $21 + 20 + 6 = 47$
* Result: $\frac{47}{30}$ or $1 \frac{17}{30}$

5) $\frac{3}{4} + \frac{1}{2} + \frac{1}{10}$
* The least common multiple for 4, 2, and 10 is 20.
* Convert fractions: $\frac{3 \times 5}{20} + \frac{1 \times 10}{20} + \frac{1 \times 2}{20}$
* This becomes: $\frac{15}{20} + \frac{10}{20} + \frac{2}{20}$
* Add numerators: $15 + 10 + 2 = 27$
* Result: $\frac{27}{20}$ or $1 \frac{7}{20}$

6) $\frac{8}{10} + \frac{1}{2} + \frac{2}{4}$
* Simplify fractions: $\frac{8}{10} = \frac{4}{5}$, $\frac{2}{4} = \frac{1}{2}$.
* Now we have: $\frac{4}{5} + \frac{1}{2} + \frac{1}{2}$.
* Add the halves: $\frac{1}{2} + \frac{1}{2} = 1$.
* Now add $\frac{4}{5} + 1$.
* Result: $1 \frac{4}{5}$ (or $\frac{9}{5}$)

7) $\frac{2}{5} + \frac{7}{10} + \frac{3}{4}$
* The least common multiple for 5, 10, and 4 is 20.
* Convert fractions: $\frac{2 \times 4}{20} + \frac{7 \times 2}{20} + \frac{3 \times 5}{20}$
* This becomes: $\frac{8}{20} + \frac{14}{20} + \frac{15}{20}$
* Add numerators: $8 + 14 + 15 = 37$
* Result: $\frac{37}{20}$ or $1 \frac{17}{20}$

8) $\frac{5}{10} + \frac{1}{4} + \frac{1}{5}$
* Simplify $\frac{5}{10}$ to $\frac{1}{2}$.
* Now we have: $\frac{1}{2} + \frac{1}{4} + \frac{1}{5}$.
* The least common multiple for 2, 4, and 5 is 20.
* Convert fractions: $\frac{1 \times 10}{20} + \frac{1 \times 5}{20} + \frac{1 \times 4}{20}$
* This becomes: $\frac{10}{20} + \frac{5}{20} + \frac{4}{20}$
* Add numerators: $10 + 5 + 4 = 19$
* Result: $\frac{19}{20}$

9) $\frac{4}{5} + \frac{4}{10} + \frac{1}{2}$
* Simplify $\frac{4}{10}$ to $\frac{2}{5}$. Note that $\frac{1}{2}$ is equal to $\frac{5}{10}$ or $\frac{2.5}{5}$, but let's use 10 as the common denominator for easier math.
* Convert $\frac{4}{5}$ to $\frac{8}{10}$ and $\frac{1}{2}$ to $\frac{5}{10}$.
* Now we have: $\frac{8}{10} + \frac{4}{10} + \frac{5}{10}$
* Add numerators: $8 + 4 + 5 = 17$
* Result: $\frac{17}{10}$ or $1 \frac{7}{10}$

10) $\frac{3}{5} + \frac{3}{4} + \frac{6}{10}$
* Simplify $\frac{6}{10}$ to $\frac{3}{5}$.
* Now we have: $\frac{3}{5} + \frac{3}{4} + \frac{3}{5}$.
* Combine the fifths: $\frac{3}{5} + \frac{3}{5} = \frac{6}{5}$.
* Now add $\frac{6}{5} + \frac{3}{4}$. Common denominator is 20.
* Convert: $\frac{6 \times 4}{20} + \frac{3 \times 5}{20} = \frac{24}{20} + \frac{15}{20}$
* Add numerators: $24 + 15 = 39$
* Result: $\frac{39}{20}$ or $1 \frac{19}{20}$

Final Answer:
1) $1 \frac{41}{60}$
2) $1 \frac{29}{30}$
3) $1 \frac{1}{10}$
4) $1 \frac{17}{30}$
5) $1 \frac{7}{20}$
6) $1 \frac{4}{5}$
7) $1 \frac{17}{20}$
8) $\frac{19}{20}$
9) $1 \frac{7}{10}$
10) $1 \frac{19}{20}$