Grade 6 Addition and Subtraction of Fractions Worksheets - free ... - Free Printable

Here are the step-by-step solutions for each problem on the worksheet.

1. $3 \frac{4}{5} + 7 \frac{5}{11}$
* Add the whole numbers: $3 + 7 = 10$.
* Find a common denominator for the fractions $\frac{4}{5}$ and $\frac{5}{11}$. The least common multiple of 5 and 11 is 55.
* Convert fractions: $\frac{4}{5} = \frac{44}{55}$ and $\frac{5}{11} = \frac{25}{55}$.
* Add the fractions: $\frac{44}{55} + \frac{25}{55} = \frac{69}{55}$.
* Since $\frac{69}{55}$ is an improper fraction, convert it to a mixed number: $1 \frac{14}{55}$.
* Add this to the whole number sum: $10 + 1 \frac{14}{55} = 11 \frac{14}{55}$.

2. $4 \frac{10}{12} + 6 \frac{6}{8}$
* First, simplify the fractions to make it easier. $\frac{10}{12}$ simplifies to $\frac{5}{6}$ (divide by 2). $\frac{6}{8}$ simplifies to $\frac{3}{4}$ (divide by 2).
* The problem is now $4 \frac{5}{6} + 6 \frac{3}{4}$.
* Add whole numbers: $4 + 6 = 10$.
* Find a common denominator for 6 and 4, which is 12.
* Convert fractions: $\frac{5}{6} = \frac{10}{12}$ and $\frac{3}{4} = \frac{9}{12}$.
* Add fractions: $\frac{10}{12} + \frac{9}{12} = \frac{19}{12}$.
* Convert improper fraction: $\frac{19}{12} = 1 \frac{7}{12}$.
* Add to whole number sum: $10 + 1 \frac{7}{12} = 11 \frac{7}{12}$.

3. $17 \frac{3}{4} + 13 \frac{1}{3}$
* Add whole numbers: $17 + 13 = 30$.
* Common denominator for 4 and 3 is 12.
* Convert fractions: $\frac{3}{4} = \frac{9}{12}$ and $\frac{1}{3} = \frac{4}{12}$.
* Add fractions: $\frac{9}{12} + \frac{4}{12} = \frac{13}{12}$.
* Convert improper fraction: $\frac{13}{12} = 1 \frac{1}{12}$.
* Add to whole number sum: $30 + 1 \frac{1}{12} = 31 \frac{1}{12}$.

4. $15 \frac{7}{12} + 16 \frac{3}{4}$
* Add whole numbers: $15 + 16 = 31$.
* Common denominator for 12 and 4 is 12.
* Convert fractions: $\frac{7}{12}$ stays the same. $\frac{3}{4} = \frac{9}{12}$.
* Add fractions: $\frac{7}{12} + \frac{9}{12} = \frac{16}{12}$.
* Simplify and convert: $\frac{16}{12}$ simplifies to $\frac{4}{3}$, which is $1 \frac{1}{3}$.
* Add to whole number sum: $31 + 1 \frac{1}{3} = 32 \frac{1}{3}$.

5. $20 \frac{5}{6} + 14 \frac{1}{6}$
* Add whole numbers: $20 + 14 = 34$.
* Add fractions: $\frac{5}{6} + \frac{1}{6} = \frac{6}{6}$.
* $\frac{6}{6}$ equals exactly 1.
* Add to whole number sum: $34 + 1 = 35$.

6. $18 \frac{2}{9} + 8 \frac{7}{9}$
* Add whole numbers: $18 + 8 = 26$.
* Add fractions: $\frac{2}{9} + \frac{7}{9} = \frac{9}{9}$.
* $\frac{9}{9}$ equals exactly 1.
* Add to whole number sum: $26 + 1 = 27$.

7. $3 \frac{2}{10} + 8 \frac{8}{10}$
* Add whole numbers: $3 + 8 = 11$.
* Add fractions: $\frac{2}{10} + \frac{8}{10} = \frac{10}{10}$.
* $\frac{10}{10}$ equals exactly 1.
* Add to whole number sum: $11 + 1 = 12$.

8. $12 \frac{2}{5} + 16 \frac{3}{5}$
* Add whole numbers: $12 + 16 = 28$.
* Add fractions: $\frac{2}{5} + \frac{3}{5} = \frac{5}{5}$.
* $\frac{5}{5}$ equals exactly 1.
* Add to whole number sum: $28 + 1 = 29$.

9. $1 \frac{3}{7} + 11 \frac{5}{7}$
* Add whole numbers: $1 + 11 = 12$.
* Add fractions: $\frac{3}{7} + \frac{5}{7} = \frac{8}{7}$.
* Convert improper fraction: $\frac{8}{7} = 1 \frac{1}{7}$.
* Add to whole number sum: $12 + 1 \frac{1}{7} = 13 \frac{1}{7}$.

10. $14 \frac{6}{7} + 17 \frac{3}{7}$
* Add whole numbers: $14 + 17 = 31$.
* Add fractions: $\frac{6}{7} + \frac{3}{7} = \frac{9}{7}$.
* Convert improper fraction: $\frac{9}{7} = 1 \frac{2}{7}$.
* Add to whole number sum: $31 + 1 \frac{2}{7} = 32 \frac{2}{7}$.

Final Answer:
1. $11 \frac{14}{55}$
2. $11 \frac{7}{12}$
3. $31 \frac{1}{12}$
4. $32 \frac{1}{3}$
5. $35$
6. $27$
7. $12$
8. $29$
9. $13 \frac{1}{7}$
10. $32 \frac{2}{7}$