Math worksheet for adding fractions and reducing to lowest terms.

Here are the step-by-step solutions for each problem on the worksheet. To solve these, we find a common denominator for the fractions, add them together, and then simplify the result if possible.

1. $8 \frac{1}{6} + \frac{5}{6}$
* The denominators are already the same (6).
* Add the numerators: $1 + 5 = 6$. So, $\frac{6}{6} = 1$.
* Add this to the whole number: $8 + 1 = 9$.
* Answer: $9$

2. $4 \frac{2}{5} + \frac{3}{4}$
* Find a common denominator for 5 and 4, which is 20.
* Convert fractions: $\frac{2}{5} = \frac{8}{20}$ and $\frac{3}{4} = \frac{15}{20}$.
* Add fractions: $\frac{8}{20} + \frac{15}{20} = \frac{23}{20}$. This is an improper fraction, which equals $1 \frac{3}{20}$.
* Add to the whole number: $4 + 1 \frac{3}{20} = 5 \frac{3}{20}$.
* Answer: $5 \frac{3}{20}$

3. $7 \frac{5}{8} + \frac{1}{8}$
* The denominators are the same (8).
* Add numerators: $5 + 1 = 6$. Result is $\frac{6}{8}$.
* Simplify $\frac{6}{8}$ by dividing top and bottom by 2: $\frac{3}{4}$.
* Combine with whole number: $7 \frac{3}{4}$.
* Answer: $7 \frac{3}{4}$

4. $8 \frac{3}{10} + \frac{2}{10}$
* The denominators are the same (10).
* Add numerators: $3 + 2 = 5$. Result is $\frac{5}{10}$.
* Simplify $\frac{5}{10}$ by dividing top and bottom by 5: $\frac{1}{2}$.
* Combine with whole number: $8 \frac{1}{2}$.
* Answer: $8 \frac{1}{2}$

5. $6 \frac{5}{8} + \frac{4}{5}$
* Common denominator for 8 and 5 is 40.
* Convert fractions: $\frac{5}{8} = \frac{25}{40}$ and $\frac{4}{5} = \frac{32}{40}$.
* Add fractions: $\frac{25}{40} + \frac{32}{40} = \frac{57}{40}$.
* Convert improper fraction: $\frac{57}{40} = 1 \frac{17}{40}$.
* Add to whole number: $6 + 1 \frac{17}{40} = 7 \frac{17}{40}$.
* Answer: $7 \frac{17}{40}$

6. $7 \frac{1}{4} + \frac{2}{5}$
* Common denominator for 4 and 5 is 20.
* Convert fractions: $\frac{1}{4} = \frac{5}{20}$ and $\frac{2}{5} = \frac{8}{20}$.
* Add fractions: $\frac{5}{20} + \frac{8}{20} = \frac{13}{20}$.
* This cannot be simplified further.
* Combine with whole number: $7 \frac{13}{20}$.
* Answer: $7 \frac{13}{20}$

7. $1 \frac{1}{3} + \frac{4}{6}$
* Notice that $\frac{4}{6}$ can be simplified first. Divide by 2 to get $\frac{2}{3}$.
* Now add: $1 \frac{1}{3} + \frac{2}{3}$.
* Add fractions: $\frac{1}{3} + \frac{2}{3} = \frac{3}{3} = 1$.
* Add to whole number: $1 + 1 = 2$.
* Answer: $2$

8. $5 \frac{1}{4} + \frac{1}{3}$
* Common denominator for 4 and 3 is 12.
* Convert fractions: $\frac{1}{4} = \frac{3}{12}$ and $\frac{1}{3} = \frac{4}{12}$.
* Add fractions: $\frac{3}{12} + \frac{4}{12} = \frac{7}{12}$.
* Combine with whole number: $5 \frac{7}{12}$.
* Answer: $5 \frac{7}{12}$

9. $1 \frac{1}{3} + \frac{1}{6}$
* Common denominator for 3 and 6 is 6.
* Convert $\frac{1}{3}$ to $\frac{2}{6}$.
* Add fractions: $\frac{2}{6} + \frac{1}{6} = \frac{3}{6}$.
* Simplify $\frac{3}{6}$ to $\frac{1}{2}$.
* Combine with whole number: $1 \frac{1}{2}$.
* Answer: $1 \frac{1}{2}$

10. $3 \frac{2}{5} + \frac{2}{5}$
* Denominators are the same (5).
* Add numerators: $2 + 2 = 4$. Result is $\frac{4}{5}$.
* Combine with whole number: $3 \frac{4}{5}$.
* Answer: $3 \frac{4}{5}$

11. $2 \frac{1}{3} + \frac{2}{8}$
* First, simplify $\frac{2}{8}$ to $\frac{1}{4}$.
* Now add $2 \frac{1}{3} + \frac{1}{4}$.
* Common denominator for 3 and 4 is 12.
* Convert fractions: $\frac{1}{3} = \frac{4}{12}$ and $\frac{1}{4} = \frac{3}{12}$.
* Add fractions: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$.
* Combine with whole number: $2 \frac{7}{12}$.
* Answer: $2 \frac{7}{12}$

12. $3 \frac{2}{5} + \frac{1}{8}$
* Common denominator for 5 and 8 is 40.
* Convert fractions: $\frac{2}{5} = \frac{16}{40}$ and $\frac{1}{8} = \frac{5}{40}$.
* Add fractions: $\frac{16}{40} + \frac{5}{40} = \frac{21}{40}$.
* This cannot be simplified further.
* Combine with whole number: $3 \frac{21}{40}$.
* Answer: $3 \frac{21}{40}$

Final Answer:
1. 9
2. 5 3/20
3. 7 3/4
4. 8 1/2
5. 7 17/40
6. 7 13/20
7. 2
8. 5 7/12
9. 1 1/2
10. 3 4/5
11. 2 7/12
12. 3 21/40