Here are the step-by-step solutions for each problem on the worksheet.
1) $\frac{4}{3} + \frac{2}{5}$
* Find the common denominator for 3 and 5, which is 15.
* Convert fractions: $\frac{4 \times 5}{3 \times 5} = \frac{20}{15}$ and $\frac{2 \times 3}{5 \times 3} = \frac{6}{15}$.
* Add numerators: $20 + 6 = 26$.
* Result: $\frac{26}{15}$ (or $1 \frac{11}{15}$).
2) $\frac{7}{10} - \frac{2}{5}$
* The common denominator is 10.
* Convert $\frac{2}{5}$ to $\frac{4}{10}$.
* Subtract: $\frac{7}{10} - \frac{4}{10} = \frac{3}{10}$.
3) $\frac{5}{9} + \frac{2}{7}$
* Common denominator for 9 and 7 is 63.
* Convert fractions: $\frac{5 \times 7}{63} = \frac{35}{63}$ and $\frac{2 \times 9}{63} = \frac{18}{63}$.
* Add numerators: $35 + 18 = 53$.
* Result: $\frac{53}{63}$.
4) $\frac{4}{8} - \frac{1}{4}$
* Simplify $\frac{4}{8}$ to $\frac{1}{2}$. Now solve $\frac{1}{2} - \frac{1}{4}$.
* Common denominator is 4. Convert $\frac{1}{2}$ to $\frac{2}{4}$.
* Subtract: $\frac{2}{4} - \frac{1}{4} = \frac{1}{4}$.
5) $\frac{3}{9} + \frac{1}{3}$
* Simplify $\frac{3}{9}$ to $\frac{1}{3}$.
* Add: $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$.
6) $\frac{2}{5} + \frac{1}{10}$
* Common denominator is 10.
* Convert $\frac{2}{5}$ to $\frac{4}{10}$.
* Add: $\frac{4}{10} + \frac{1}{10} = \frac{5}{10}$.
* Simplify: $\frac{1}{2}$.
7) $\frac{4}{5} + \frac{9}{10}$
* Common denominator is 10.
* Convert $\frac{4}{5}$ to $\frac{8}{10}$.
* Add: $\frac{8}{10} + \frac{9}{10} = \frac{17}{10}$ (or $1 \frac{7}{10}$).
8) $\frac{4}{6} - \frac{1}{3}$
* Simplify $\frac{4}{6}$ to $\frac{2}{3}$.
* Subtract: $\frac{2}{3} - \frac{1}{3} = \frac{1}{3}$.
9) $\frac{3}{12} + \frac{2}{4}$
* Simplify $\frac{3}{12}$ to $\frac{1}{4}$.
* Add: $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$.
10) $\frac{5}{12} - \frac{1}{6}$
* Common denominator is 12.
* Convert $\frac{1}{6}$ to $\frac{2}{12}$.
* Subtract: $\frac{5}{12} - \frac{2}{12} = \frac{3}{12}$.
* Simplify: $\frac{1}{4}$.
11) $\frac{2}{8} + \frac{3}{9}$
* Simplify first: $\frac{2}{8} = \frac{1}{4}$ and $\frac{3}{9} = \frac{1}{3}$.
* Problem becomes $\frac{1}{4} + \frac{1}{3}$. Common denominator is 12.
* Convert: $\frac{3}{12} + \frac{4}{12} = \frac{7}{12}$.
12) $\frac{1}{4} - \frac{1}{8}$
* Common denominator is 8.
* Convert $\frac{1}{4}$ to $\frac{2}{8}$.
* Subtract: $\frac{2}{8} - \frac{1}{8} = \frac{1}{8}$.
13) $\frac{6}{7} + \frac{2}{6}$
* Simplify $\frac{2}{6}$ to $\frac{1}{3}$. Problem is $\frac{6}{7} + \frac{1}{3}$.
* Common denominator is 21.
* Convert: $\frac{18}{21} + \frac{7}{21} = \frac{25}{21}$ (or $1 \frac{4}{21}$).
14) $\frac{1}{3} - \frac{1}{7}$
* Common denominator is 21.
* Convert: $\frac{7}{21} - \frac{3}{21}$.
* Subtract: $\frac{4}{21}$.
15) $\frac{7}{8} + \frac{4}{5}$
* Common denominator is 40.
* Convert: $\frac{35}{40} + \frac{32}{40}$.
* Add: $\frac{67}{40}$ (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 adding and subtracting unlike fractions worksheet.
