To solve these fraction addition problems, we need to find a common denominator for each pair of fractions. This means making the bottom numbers (denominators) the same so we can add the top numbers (numerators).
Here is the step-by-step solution for each problem:
1. $\frac{1}{2} + \frac{1}{4}$
* The common denominator for 2 and 4 is 4.
* Convert $\frac{1}{2}$ to $\frac{2}{4}$.
* 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.
* Convert $\frac{1}{5}$ to $\frac{2}{10}$.
* 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.
* Convert $\frac{1}{6}$ to $\frac{3}{18}$.
* 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.
* Convert $\frac{1}{4}$ to $\frac{3}{12}$.
* 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.
* Convert $\frac{1}{5}$ to $\frac{3}{15}$.
* Add: $\frac{3}{15} + \frac{3}{15} = \frac{6}{15}$
* Simplify: Both numbers divide by 3, so $\frac{6 \div 3}{15 \div 3} = \frac{2}{5}$
6. $\frac{1}{8} + \frac{3}{4}$
* The common denominator for 8 and 4 is 8.
* Convert $\frac{3}{4}$ to $\frac{6}{8}$.
* 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.
* Convert $\frac{1}{2}$ to $\frac{4}{8}$.
* 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.
* Convert $\frac{6}{7}$ to $\frac{18}{21}$.
* 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.
* Convert $\frac{1}{3}$ to $\frac{3}{9}$.
* 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.
* Convert $\frac{1}{4}$ to $\frac{4}{16}$.
* 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 5th grade adding and subtracting fractions worksheet.
