Solve (2/3-1/5)*5/7+13/8

$$( \frac { 2 } { 3 } - \frac { 1 } { 5 } ) \times \frac { 5 } { 7 } + 1 \frac { 3 } { 8 }$$

Evaluate

$$\frac{41}{24}\approx 1.708333333$$

Solution Steps

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

$$\left(\frac{10}{15}-\frac{3}{15}\right)\times \frac{5}{7}+\frac{1\times 8+3}{8}$$

Since \frac{10}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-3}{15}\times \frac{5}{7}+\frac{1\times 8+3}{8}$$

Subtract 3 from 10 to get 7.

$$\frac{7}{15}\times \frac{5}{7}+\frac{1\times 8+3}{8}$$

Multiply \frac{7}{15} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 5}{15\times 7}+\frac{1\times 8+3}{8}$$

Cancel out 7 in both numerator and denominator.

$$\frac{5}{15}+\frac{1\times 8+3}{8}$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$\frac{1}{3}+\frac{1\times 8+3}{8}$$

Multiply 1 and 8 to get 8.

$$\frac{1}{3}+\frac{8+3}{8}$$

Add 8 and 3 to get 11.

$$\frac{1}{3}+\frac{11}{8}$$

Least common multiple of 3 and 8 is 24. Convert \frac{1}{3} and \frac{11}{8} to fractions with denominator 24.

$$\frac{8}{24}+\frac{33}{24}$$

Since \frac{8}{24} and \frac{33}{24} have the same denominator, add them by adding their numerators.

$$\frac{8+33}{24}$$

Add 8 and 33 to get 41.

$$\frac{41}{24}$$

Factor

$$\frac{41}{2 ^ {3} \cdot 3} = 1\frac{17}{24} = 1.7083333333333333$$