Adding mixed numbers and fractions worksheet for Grade 5 students.

Here are the step-by-step solutions for each problem on the worksheet. To add mixed numbers with unlike denominators, we first find a common denominator for the fractions, add them together, and then add the whole numbers. If the resulting fraction is improper (top number is bigger than the bottom), we convert it to a mixed number and add it to the whole number sum.

1. $5 \frac{2}{9} + 6 \frac{6}{7}$
* Common Denominator: The least common multiple for 9 and 7 is 63.
* Convert Fractions: $\frac{2}{9} = \frac{14}{63}$ and $\frac{6}{7} = \frac{54}{63}$.
* Add Fractions: $\frac{14}{63} + \frac{54}{63} = \frac{68}{63}$. This is an improper fraction, which equals $1 \frac{5}{63}$.
* Add Whole Numbers: $5 + 6 = 11$.
* Total Sum: $11 + 1 \frac{5}{63} = 12 \frac{5}{63}$.

2. $7 \frac{2}{6} + \frac{1}{12}$
* Simplify First: $\frac{2}{6}$ simplifies to $\frac{1}{3}$. So the problem is $7 \frac{1}{3} + \frac{1}{12}$.
* Common Denominator: The least common multiple for 3 and 12 is 12.
* Convert Fractions: $\frac{1}{3} = \frac{4}{12}$. The second fraction is already $\frac{1}{12}$.
* Add Fractions: $\frac{4}{12} + \frac{1}{12} = \frac{5}{12}$.
* Add Whole Numbers: $7 + 0 = 7$.
* Total Sum: $7 \frac{5}{12}$.

3. $1 \frac{1}{10} + \frac{7}{8}$
* Common Denominator: The least common multiple for 10 and 8 is 40.
* Convert Fractions: $\frac{1}{10} = \frac{4}{40}$ and $\frac{7}{8} = \frac{35}{40}$.
* Add Fractions: $\frac{4}{40} + \frac{35}{40} = \frac{39}{40}$.
* Add Whole Numbers: $1 + 0 = 1$.
* Total Sum: $1 \frac{39}{40}$.

4. $6 \frac{7}{9} + \frac{1}{9}$
* Common Denominator: The denominators are already the same (9).
* Add Fractions: $\frac{7}{9} + \frac{1}{9} = \frac{8}{9}$.
* Add Whole Numbers: $6 + 0 = 6$.
* Total Sum: $6 \frac{8}{9}$.

5. $2 \frac{1}{2} + \frac{1}{5}$
* Common Denominator: The least common multiple for 2 and 5 is 10.
* Convert Fractions: $\frac{1}{2} = \frac{5}{10}$ and $\frac{1}{5} = \frac{2}{10}$.
* Add Fractions: $\frac{5}{10} + \frac{2}{10} = \frac{7}{10}$.
* Add Whole Numbers: $2 + 0 = 2$.
* Total Sum: $2 \frac{7}{10}$.

6. $1 \frac{8}{11} + \frac{2}{8}$
* Simplify First: $\frac{2}{8}$ simplifies to $\frac{1}{4}$. So the problem is $1 \frac{8}{11} + \frac{1}{4}$.
* Common Denominator: The least common multiple for 11 and 4 is 44.
* Convert Fractions: $\frac{8}{11} = \frac{32}{44}$ and $\frac{1}{4} = \frac{11}{44}$.
* Add Fractions: $\frac{32}{44} + \frac{11}{44} = \frac{43}{44}$.
* Add Whole Numbers: $1 + 0 = 1$.
* Total Sum: $1 \frac{43}{44}$.

7. $10 \frac{5}{16} + \frac{1}{2}$
* Common Denominator: The least common multiple for 16 and 2 is 16.
* Convert Fractions: $\frac{5}{16}$ stays the same. $\frac{1}{2} = \frac{8}{16}$.
* Add Fractions: $\frac{5}{16} + \frac{8}{16} = \frac{13}{16}$.
* Add Whole Numbers: $10 + 0 = 10$.
* Total Sum: $10 \frac{13}{16}$.

8. $2 \frac{1}{6} + \frac{5}{8}$
* Common Denominator: The least common multiple for 6 and 8 is 24.
* Convert Fractions: $\frac{1}{6} = \frac{4}{24}$ and $\frac{5}{8} = \frac{15}{24}$.
* Add Fractions: $\frac{4}{24} + \frac{15}{24} = \frac{19}{24}$.
* Add Whole Numbers: $2 + 0 = 2$.
* Total Sum: $2 \frac{19}{24}$.

9. $6 \frac{6}{7} + \frac{3}{9}$
* Simplify First: $\frac{3}{9}$ simplifies to $\frac{1}{3}$. So the problem is $6 \frac{6}{7} + \frac{1}{3}$.
* Common Denominator: The least common multiple for 7 and 3 is 21.
* Convert Fractions: $\frac{6}{7} = \frac{18}{21}$ and $\frac{1}{3} = \frac{7}{21}$.
* Add Fractions: $\frac{18}{21} + \frac{7}{21} = \frac{25}{21}$. This is an improper fraction, which equals $1 \frac{4}{21}$.
* Add Whole Numbers: $6 + 1 = 7$.
* Total Sum: $7 \frac{4}{21}$.

10. $10 \frac{2}{6} + \frac{5}{12}$
* Simplify First: $\frac{2}{6}$ simplifies to $\frac{1}{3}$. So the problem is $10 \frac{1}{3} + \frac{5}{12}$.
* Common Denominator: The least common multiple for 3 and 12 is 12.
* Convert Fractions: $\frac{1}{3} = \frac{4}{12}$. The second fraction is $\frac{5}{12}$.
* Add Fractions: $\frac{4}{12} + \frac{5}{12} = \frac{9}{12}$.
* Simplify Result: $\frac{9}{12}$ simplifies to $\frac{3}{4}$ (divide top and bottom by 3).
* Add Whole Numbers: $10 + 0 = 10$.
* Total Sum: $10 \frac{3}{4}$.

11. $1 \frac{4}{11} + \frac{2}{5}$
* Common Denominator: The least common multiple for 11 and 5 is 55.
* Convert Fractions: $\frac{4}{11} = \frac{20}{55}$ and $\frac{2}{5} = \frac{22}{55}$.
* Add Fractions: $\frac{20}{55} + \frac{22}{55} = \frac{42}{55}$.
* Add Whole Numbers: $1 + 0 = 1$.
* Total Sum: $1 \frac{42}{55}$.

12. $7 \frac{8}{11} + \frac{3}{3}$
* Simplify First: $\frac{3}{3}$ equals exactly 1.
* Add Whole Numbers: $7 + 1 = 8$.
* Add Fractions: The remaining fraction is $\frac{8}{11}$.
* Total Sum: $8 \frac{8}{11}$.

13. $7 \frac{3}{10} + \frac{5}{12}$
* Common Denominator: The least common multiple for 10 and 12 is 60.
* Convert Fractions: $\frac{3}{10} = \frac{18}{60}$ and $\frac{5}{12} = \frac{25}{60}$.
* Add Fractions: $\frac{18}{60} + \frac{25}{60} = \frac{43}{60}$.
* Add Whole Numbers: $7 + 0 = 7$.
* Total Sum: $7 \frac{43}{60}$.

14. $7 \frac{2}{6} + \frac{1}{4}$
* Simplify First: $\frac{2}{6}$ simplifies to $\frac{1}{3}$. So the problem is $7 \frac{1}{3} + \frac{1}{4}$.
* Common Denominator: The least common multiple for 3 and 4 is 12.
* Convert Fractions: $\frac{1}{3} = \frac{4}{12}$ and $\frac{1}{4} = \frac{3}{12}$.
* Add Fractions: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$.
* Add Whole Numbers: $7 + 0 = 7$.
* Total Sum: $7 \frac{7}{12}$.

Final Answer:
1. $12 \frac{5}{63}$
2. $7 \frac{5}{12}$
3. $1 \frac{39}{40}$
4. $6 \frac{8}{9}$
5. $2 \frac{7}{10}$
6. $1 \frac{43}{44}$
7. $10 \frac{13}{16}$
8. $2 \frac{19}{24}$
9. $7 \frac{4}{21}$
10. $10 \frac{3}{4}$
11. $1 \frac{42}{55}$
12. $8 \frac{8}{11}$
13. $7 \frac{43}{60}$
14. $7 \frac{7}{12}$