Question

add & subtract fractions & mixed numbers
solve by finding a common denominator. simplify
1 $3\frac{2}{5}+2\frac{7}{10}=$
2 $6\frac{7}{8}-2\frac{1}{4}=$
3 $\frac{11}{14}-\frac{3}{7}=$
4 $5\frac{4}{9}+\frac{2}{3}=$
5 $4\frac{3}{8}-1\frac{1}{2}=$
6 $9 - 5\frac{1}{6}=$
7 $2\frac{3}{12}+4\frac{2}{8}=$
8 $\frac{6}{10}+\frac{4}{5}=$
9 $8\frac{1}{2}-1\frac{1}{6}=$
10 $7\frac{1}{3}-3\frac{7}{9}=$

Explanation:

Step1: Convert mixed numbers to improper fractions

1. $3\frac{2}{5} = \frac{17}{5}$, $2\frac{7}{10} = \frac{27}{10}$
2. $6\frac{7}{8} = \frac{55}{8}$, $2\frac{1}{9} = \frac{19}{9}$
3. No conversion needed
4. $5\frac{4}{9} = \frac{49}{9}$
5. $4\frac{3}{8} = \frac{35}{8}$, $1\frac{1}{2} = \frac{3}{2}$
6. $9 = \frac{54}{6}$, $5\frac{1}{6} = \frac{31}{6}$
7. $2\frac{3}{12} = \frac{27}{12}$, $4\frac{2}{6} = \frac{26}{6}$
8. No conversion needed
9. $8\frac{1}{2} = \frac{17}{2}$, $1\frac{1}{6} = \frac{7}{6}$
10. $7\frac{1}{3} = \frac{22}{3}$, $3\frac{7}{9} = \frac{34}{9}$

Step2: Find common denominators

1. $\frac{17}{5} = \frac{34}{10}$
2. $\frac{55}{8} = \frac{495}{72}$, $\frac{19}{9} = \frac{152}{72}$
3. $\frac{3}{7} = \frac{6}{14}$
4. $\frac{2}{3} = \frac{6}{9}$
5. $\frac{3}{2} = \frac{12}{8}$
6. No new denominator needed
7. $\frac{26}{6} = \frac{52}{12}$
8. $\frac{4}{5} = \frac{8}{10}$
9. $\frac{17}{2} = \frac{51}{6}$
10. $\frac{22}{3} = \frac{66}{9}$

Step3: Perform addition/subtraction

1. $\frac{34}{10} + \frac{27}{10} = \frac{61}{10}$
2. $\frac{495}{72} - \frac{152}{72} = \frac{343}{72}$
3. $\frac{11}{14} - \frac{6}{14} = \frac{5}{14}$
4. $\frac{49}{9} + \frac{6}{9} = \frac{55}{9}$
5. $\frac{35}{8} - \frac{12}{8} = \frac{23}{8}$
6. $\frac{54}{6} - \frac{31}{6} = \frac{23}{6}$
7. $\frac{27}{12} + \frac{52}{12} = \frac{79}{12}$
8. $\frac{6}{10} + \frac{8}{10} = \frac{14}{10}$
9. $\frac{51}{6} - \frac{7}{6} = \frac{44}{6}$
10. $\frac{66}{9} - \frac{34}{9} = \frac{32}{9}$

Step4: Simplify/convert to mixed numbers

1. $\frac{61}{10} = 6\frac{1}{10}$
2. $\frac{343}{72} = 4\frac{47}{72}$
3. $\frac{5}{14}$ (already simplified)
4. $\frac{55}{9} = 6\frac{1}{9}$
5. $\frac{23}{8} = 2\frac{3}{8}$
6. $\frac{23}{6} = 3\frac{5}{6}$
7. $\frac{79}{12} = 6\frac{7}{12}$
8. $\frac{14}{10} = 1\frac{2}{5}$
9. $\frac{44}{6} = 7\frac{1}{3}$
10. $\frac{32}{9} = 3\frac{5}{9}$

Answer:

1. $6\frac{1}{10}$
2. $4\frac{47}{72}$
3. $\frac{5}{14}$
4. $6\frac{1}{9}$
5. $2\frac{3}{8}$
6. $3\frac{5}{6}$
7. $6\frac{7}{12}$
8. $1\frac{2}{5}$
9. $7\frac{1}{3}$
10. $3\frac{5}{9}$