To add fractions with different denominators, we need to find a common denominator. This is a number that both bottom numbers (denominators) can divide into evenly. Once the denominators are the same, we just add the top numbers (numerators).
Here is the step-by-step solution for each problem:
1. $\frac{1}{4} + \frac{2}{12}$
* The common denominator for 4 and 12 is 12.
* Convert $\frac{1}{4}$: Multiply top and bottom by 3 to get $\frac{3}{12}$.
* Add: $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$.
2. $\frac{2}{6} + \frac{1}{2}$
* The common denominator for 6 and 2 is 6.
* Convert $\frac{1}{2}$: Multiply top and bottom by 3 to get $\frac{3}{6}$.
* Add: $\frac{2}{6} + \frac{3}{6} = \frac{5}{6}$.
3. $\frac{1}{3} + \frac{2}{9}$
* The common denominator for 3 and 9 is 9.
* Convert $\frac{1}{3}$: Multiply top and bottom by 3 to get $\frac{3}{9}$.
* Add: $\frac{3}{9} + \frac{2}{9} = \frac{5}{9}$.
4. $\frac{5}{8} + \frac{1}{16}$
* The common denominator for 8 and 16 is 16.
* Convert $\frac{5}{8}$: Multiply top and bottom by 2 to get $\frac{10}{16}$.
* Add: $\frac{10}{16} + \frac{1}{16} = \frac{11}{16}$.
5. $\frac{2}{9} + \frac{1}{27}$
* The common denominator for 9 and 27 is 27.
* Convert $\frac{2}{9}$: Multiply top and bottom by 3 to get $\frac{6}{27}$.
* Add: $\frac{6}{27} + \frac{1}{27} = \frac{7}{27}$.
6. $\frac{1}{3} + \frac{3}{21}$
* The common denominator for 3 and 21 is 21.
* Convert $\frac{1}{3}$: Multiply top and bottom by 7 to get $\frac{7}{21}$.
* Add: $\frac{7}{21} + \frac{3}{21} = \frac{10}{21}$.
7. $\frac{3}{4} + \frac{1}{16}$
* The common denominator for 4 and 16 is 16.
* Convert $\frac{3}{4}$: Multiply top and bottom by 4 to get $\frac{12}{16}$.
* Add: $\frac{12}{16} + \frac{1}{16} = \frac{13}{16}$.
8. $\frac{1}{5} + \frac{1}{10}$
* The common denominator for 5 and 10 is 10.
* Convert $\frac{1}{5}$: Multiply top and bottom by 2 to get $\frac{2}{10}$.
* Add: $\frac{2}{10} + \frac{1}{10} = \frac{3}{10}$.
9. $\frac{3}{7} + \frac{1}{28}$
* The common denominator for 7 and 28 is 28.
* Convert $\frac{3}{7}$: Multiply top and bottom by 4 to get $\frac{12}{28}$.
* Add: $\frac{12}{28} + \frac{1}{28} = \frac{13}{28}$.
10. $\frac{3}{5} + \frac{1}{10}$
* The common denominator for 5 and 10 is 10.
* Convert $\frac{3}{5}$: Multiply top and bottom by 2 to get $\frac{6}{10}$.
* Add: $\frac{6}{10} + \frac{1}{10} = \frac{7}{10}$.
Final Answer:
1. 5/12
2. 5/6
3. 5/9
4. 11/16
5. 7/27
6. 10/21
7. 13/16
8. 3/10
9. 13/28
10. 7/10
Parent Tip: Review the logic above to help your child master the concept of same demominators.
