Solve 31/2/5+42/3/2=

$$\frac { 3 \frac { 1 } { 2 } } { 5 } + \frac { 4 \frac { 2 } { 3 } } { 2 } =$$

Evaluate

$$\frac{91}{30}\approx 3.033333333$$

Solution Steps

Express \frac{\frac{3\times 2+1}{2}}{5} as a single fraction.

$$\frac{3\times 2+1}{2\times 5}+\frac{\frac{4\times 3+2}{3}}{2}$$

Multiply 3 and 2 to get 6.

$$\frac{6+1}{2\times 5}+\frac{\frac{4\times 3+2}{3}}{2}$$

Add 6 and 1 to get 7.

$$\frac{7}{2\times 5}+\frac{\frac{4\times 3+2}{3}}{2}$$

Multiply 2 and 5 to get 10.

$$\frac{7}{10}+\frac{\frac{4\times 3+2}{3}}{2}$$

Express \frac{\frac{4\times 3+2}{3}}{2} as a single fraction.

$$\frac{7}{10}+\frac{4\times 3+2}{3\times 2}$$

Multiply 4 and 3 to get 12.

$$\frac{7}{10}+\frac{12+2}{3\times 2}$$

Add 12 and 2 to get 14.

$$\frac{7}{10}+\frac{14}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{7}{10}+\frac{14}{6}$$

Reduce the fraction \frac{14}{6} to lowest terms by extracting and canceling out 2.

$$\frac{7}{10}+\frac{7}{3}$$

Least common multiple of 10 and 3 is 30. Convert \frac{7}{10} and \frac{7}{3} to fractions with denominator 30.

$$\frac{21}{30}+\frac{70}{30}$$

Since \frac{21}{30} and \frac{70}{30} have the same denominator, add them by adding their numerators.

$$\frac{21+70}{30}$$

Add 21 and 70 to get 91.

$$\frac{91}{30}$$

Factor

$$\frac{7 \cdot 13}{2 \cdot 3 \cdot 5} = 3\frac{1}{30} = 3.033333333333333$$