Adding Mixed Numbers with Unlike Denominators with Regrouping

$$9\ \frac{5}{7}$$

$$5\ \frac{2}{3}$$

$$10\ \frac{1}{5}$$

$$11\ \frac{5}{6}$$

5    7/12

5    2/24

5    2/12

5    7/24

$$\frac{1}{3}+\frac{1}{5}$$

$$\frac{2}{3}+\frac{4}{5}$$

$$\frac{2}{3}+\frac{1}{5}$$

$$\frac{1}{3}+\frac{4}{5}$$

common numerator

common denominator

equivalent fraction

mixed number

denominators.

4   19/5

4 5/10

4 19/25

4 5/10

4 5/10

4 19/25

$$11\frac{2}{6}$$

$$11\frac{2}{5}$$

$$12\frac{1}{6}$$

$$11\ \frac{5}{6}$$

$$14\frac{17}{30}$$

$$13\frac{17}{30}$$

$$1\frac{17}{30}$$

$$13\frac{11}{13}$$

add the numerators

add the denominators

find a common denominator

find a common numerator

18   7/14

18   12/12

18   24/24

18

18   5/15

17   5/10

17   9/20

17   9/10