Here are the solutions to the fraction addition problems. To solve these, we find a common denominator for each pair of fractions, add the numerators, and then simplify the result if possible.
1. $\frac{1}{2} + \frac{1}{4}$
* Common denominator is 4.
* $\frac{1}{2} = \frac{2}{4}$
* $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$
2. $\frac{3}{7} + \frac{2}{9}$
* Common denominator is $7 \times 9 = 63$.
* $\frac{3 \times 9}{63} + \frac{2 \times 7}{63} = \frac{27}{63} + \frac{14}{63}$
* $\frac{27 + 14}{63} = \frac{41}{63}$
3. $\frac{3}{5} + \frac{1}{15}$
* Common denominator is 15.
* $\frac{3 \times 3}{15} + \frac{1}{15} = \frac{9}{15} + \frac{1}{15}$
* $\frac{10}{15}$ simplifies to $\frac{2}{3}$ (divide top and bottom by 5).
4. $\frac{1}{9} + \frac{7}{8}$
* Common denominator is $9 \times 8 = 72$.
* $\frac{1 \times 8}{72} + \frac{7 \times 9}{72} = \frac{8}{72} + \frac{63}{72}$
* $\frac{8 + 63}{72} = \frac{71}{72}$
5. $\frac{6}{7} + \frac{2}{21}$
* Common denominator is 21.
* $\frac{6 \times 3}{21} + \frac{2}{21} = \frac{18}{21} + \frac{2}{21}$
* $\frac{20}{21}$
6. $\frac{4}{6} + \frac{2}{10}$
* Simplify first: $\frac{4}{6} = \frac{2}{3}$ and $\frac{2}{10} = \frac{1}{5}$.
* New problem: $\frac{2}{3} + \frac{1}{5}$. Common denominator is 15.
* $\frac{2 \times 5}{15} + \frac{1 \times 3}{15} = \frac{10}{15} + \frac{3}{15}$
* $\frac{13}{15}$
7. $\frac{1}{11} + \frac{3}{22}$
* Common denominator is 22.
* $\frac{1 \times 2}{22} + \frac{3}{22} = \frac{2}{22} + \frac{3}{22}$
* $\frac{5}{22}$
8. $\frac{1}{4} + \frac{8}{20}$
* Simplify $\frac{8}{20}$ to $\frac{2}{5}$ (divide by 4). Or use 20 as common denominator. Let's use 20.
* $\frac{1 \times 5}{20} + \frac{8}{20} = \frac{5}{20} + \frac{8}{20}$
* $\frac{13}{20}$
9. $\frac{4}{7} + \frac{2}{9}$
* Common denominator is $7 \times 9 = 63$.
* $\frac{4 \times 9}{63} + \frac{2 \times 7}{63} = \frac{36}{63} + \frac{14}{63}$
* $\frac{36 + 14}{63} = \frac{50}{63}$
10. $\frac{7}{10} + \frac{2}{30}$
* Common denominator is 30.
* $\frac{7 \times 3}{30} + \frac{2}{30} = \frac{21}{30} + \frac{2}{30}$
* $\frac{23}{30}$
Final Answer:
1. 3/4
2. 41/63
3. 2/3
4. 71/72
5. 20/21
6. 13/15
7. 5/22
8. 13/20
9. 50/63
10. 23/30
Parent Tip: Review the logic above to help your child master the concept of fraction math worksheet for sixth grade.
