Here are the step-by-step solutions for each problem on the worksheet. To add fractions with different bottom numbers (denominators), we first need to find a common denominator so the pieces are the same size. Then, we add the top numbers (numerators) and keep the bottom number the same. Finally, we simplify the answer if possible.
1. $\frac{1}{2} + \frac{1}{4}$
* The common denominator for 2 and 4 is 4.
* Change $\frac{1}{2}$ to $\frac{2}{4}$ (multiply top and bottom by 2).
* Add: $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$.
2. $\frac{1}{5} + \frac{7}{10}$
* The common denominator for 5 and 10 is 10.
* Change $\frac{1}{5}$ to $\frac{2}{10}$ (multiply top and bottom by 2).
* Add: $\frac{2}{10} + \frac{7}{10} = \frac{9}{10}$.
3. $\frac{1}{6} + \frac{2}{18}$
* The common denominator for 6 and 18 is 18.
* Change $\frac{1}{6}$ to $\frac{3}{18}$ (multiply top and bottom by 3).
* Add: $\frac{3}{18} + \frac{2}{18} = \frac{5}{18}$.
4. $\frac{1}{4} + \frac{2}{12}$
* The common denominator for 4 and 12 is 12.
* Change $\frac{1}{4}$ to $\frac{3}{12}$ (multiply top and bottom by 3).
* Add: $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$.
5. $\frac{1}{5} + \frac{3}{15}$
* The common denominator for 5 and 15 is 15.
* Change $\frac{1}{5}$ to $\frac{3}{15}$ (multiply top and bottom by 3).
* Add: $\frac{3}{15} + \frac{3}{15} = \frac{6}{15}$.
* Simplify: Both numbers can be divided by 3. $\frac{6 \div 3}{15 \div 3} = \frac{2}{5}$.
6. $\frac{1}{8} + \frac{3}{4}$
* The common denominator for 8 and 4 is 8.
* Change $\frac{3}{4}$ to $\frac{6}{8}$ (multiply top and bottom by 2).
* Add: $\frac{1}{8} + \frac{6}{8} = \frac{7}{8}$.
7. $\frac{1}{2} + \frac{3}{8}$
* The common denominator for 2 and 8 is 8.
* Change $\frac{1}{2}$ to $\frac{4}{8}$ (multiply top and bottom by 4).
* Add: $\frac{4}{8} + \frac{3}{8} = \frac{7}{8}$.
8. $\frac{6}{7} + \frac{2}{21}$
* The common denominator for 7 and 21 is 21.
* Change $\frac{6}{7}$ to $\frac{18}{21}$ (multiply top and bottom by 3).
* Add: $\frac{18}{21} + \frac{2}{21} = \frac{20}{21}$.
9. $\frac{1}{3} + \frac{2}{9}$
* The common denominator for 3 and 9 is 9.
* Change $\frac{1}{3}$ to $\frac{3}{9}$ (multiply top and bottom by 3).
* Add: $\frac{3}{9} + \frac{2}{9} = \frac{5}{9}$.
10. $\frac{5}{16} + \frac{1}{4}$
* The common denominator for 16 and 4 is 16.
* Change $\frac{1}{4}$ to $\frac{4}{16}$ (multiply top and bottom by 4).
* Add: $\frac{5}{16} + \frac{4}{16} = \frac{9}{16}$.
Final Answer:
1. 3/4
2. 9/10
3. 5/18
4. 5/12
5. 2/5
6. 7/8
7. 7/8
8. 20/21
9. 5/9
10. 9/16
Parent Tip: Review the logic above to help your child master the concept of fraction concepts worksheet.
