Solve (1/3+2/5)+(5/3-2/4)5

$$( \frac { 1 } { 3 } + \frac { 2 } { 5 } ) + ( \frac { 5 } { 3 } - \frac { 2 } { 4 } ) 5$$

Evaluate

$$\frac{197}{30}\approx 6.566666667$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{5}{15}+\frac{6}{15}+\left(\frac{5}{3}-\frac{2}{4}\right)\times 5$$

Since \frac{5}{15} and \frac{6}{15} have the same denominator, add them by adding their numerators.

$$\frac{5+6}{15}+\left(\frac{5}{3}-\frac{2}{4}\right)\times 5$$

Add 5 and 6 to get 11.

$$\frac{11}{15}+\left(\frac{5}{3}-\frac{2}{4}\right)\times 5$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{11}{15}+\left(\frac{5}{3}-\frac{1}{2}\right)\times 5$$

Least common multiple of 3 and 2 is 6. Convert \frac{5}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{11}{15}+\left(\frac{10}{6}-\frac{3}{6}\right)\times 5$$

Since \frac{10}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{15}+\frac{10-3}{6}\times 5$$

Subtract 3 from 10 to get 7.

$$\frac{11}{15}+\frac{7}{6}\times 5$$

Express \frac{7}{6}\times 5 as a single fraction.

$$\frac{11}{15}+\frac{7\times 5}{6}$$

Multiply 7 and 5 to get 35.

$$\frac{11}{15}+\frac{35}{6}$$

Least common multiple of 15 and 6 is 30. Convert \frac{11}{15} and \frac{35}{6} to fractions with denominator 30.

$$\frac{22}{30}+\frac{175}{30}$$

Since \frac{22}{30} and \frac{175}{30} have the same denominator, add them by adding their numerators.

$$\frac{22+175}{30}$$

Add 22 and 175 to get 197.

$$\frac{197}{30}$$

Factor

$$\frac{197}{2 \cdot 3 \cdot 5} = 6\frac{17}{30} = 6.566666666666666$$