Here are the solutions for the problems on the worksheet. To solve these, we find a common denominator (a number both bottom numbers can go into), change the fractions so they match, and then add or subtract the top numbers.
1) $\frac{4}{3} + \frac{2}{5}$
Common denominator is 15.
$\frac{20}{15} + \frac{6}{15} = \frac{26}{15}$ (or $1 \frac{11}{15}$)
2) $\frac{7}{10} - \frac{2}{5}$
Common denominator is 10. ($\frac{2}{5}$ becomes $\frac{4}{10}$)
$\frac{7}{10} - \frac{4}{10} = \frac{3}{10}$
3) $\frac{5}{9} + \frac{2}{7}$
Common denominator is 63.
$\frac{35}{63} + \frac{18}{63} = \frac{53}{63}$
4) $\frac{4}{8} - \frac{1}{4}$
Common denominator is 8. ($\frac{1}{4}$ becomes $\frac{2}{8}$)
$\frac{4}{8} - \frac{2}{8} = \frac{2}{8}$ which simplifies to $\frac{1}{4}$
5) $\frac{3}{9} + \frac{1}{3}$
Common denominator is 9. ($\frac{1}{3}$ becomes $\frac{3}{9}$)
$\frac{3}{9} + \frac{3}{9} = \frac{6}{9}$ which simplifies to $\frac{2}{3}$
6) $\frac{2}{5} + \frac{1}{10}$
Common denominator is 10. ($\frac{2}{5}$ becomes $\frac{4}{10}$)
$\frac{4}{10} + \frac{1}{10} = \frac{5}{10}$ which simplifies to $\frac{1}{2}$
7) $\frac{4}{5} + \frac{9}{10}$
Common denominator is 10. ($\frac{4}{5}$ becomes $\frac{8}{10}$)
$\frac{8}{10} + \frac{9}{10} = \frac{17}{10}$ (or $1 \frac{7}{10}$)
8) $\frac{4}{6} - \frac{1}{3}$
Common denominator is 6. ($\frac{1}{3}$ becomes $\frac{2}{6}$)
$\frac{4}{6} - \frac{2}{6} = \frac{2}{6}$ which simplifies to $\frac{1}{3}$
9) $\frac{3}{12} + \frac{2}{4}$
Common denominator is 12. ($\frac{2}{4}$ becomes $\frac{6}{12}$)
$\frac{3}{12} + \frac{6}{12} = \frac{9}{12}$ which simplifies to $\frac{3}{4}$
10) $\frac{5}{12} - \frac{1}{6}$
Common denominator is 12. ($\frac{1}{6}$ becomes $\frac{2}{12}$)
$\frac{5}{12} - \frac{2}{12} = \frac{3}{12}$ which simplifies to $\frac{1}{4}$
11) $\frac{2}{8} + \frac{3}{9}$
Common denominator is 72.
$\frac{18}{72} + \frac{24}{72} = \frac{42}{72}$ which simplifies to $\frac{7}{12}$
12) $\frac{1}{4} - \frac{1}{8}$
Common denominator is 8. ($\frac{1}{4}$ becomes $\frac{2}{8}$)
$\frac{2}{8} - \frac{1}{8} = \frac{1}{8}$
13) $\frac{6}{7} + \frac{2}{6}$
Common denominator is 42.
$\frac{36}{42} + \frac{14}{42} = \frac{50}{42}$ which simplifies to $\frac{25}{21}$ (or $1 \frac{4}{21}$)
14) $\frac{1}{3} - \frac{1}{7}$
Common denominator is 21.
$\frac{7}{21} - \frac{3}{21} = \frac{4}{21}$
15) $\frac{7}{8} + \frac{4}{5}$
Common denominator is 40.
$\frac{35}{40} + \frac{32}{40} = \frac{67}{40}$ (or $1 \frac{27}{40}$)
Final Answer:
1) 26/15
2) 3/10
3) 53/63
4) 1/4
5) 2/3
6) 1/2
7) 17/10
8) 1/3
9) 3/4
10) 1/4
11) 7/12
12) 1/8
13) 25/21
14) 4/21
15) 67/40
Parent Tip: Review the logic above to help your child master the concept of worksheet on subtracting like fractions.
