Solve 2/7+3/4div5/8-3/2

$$\frac { 2 } { 7 } + \frac { 3 } { 4 } \div \frac { 5 } { 8 } - \frac { 3 } { 2 }$$

Evaluate

$$-\frac{1}{70}\approx -0.014285714$$

Solution Steps

Divide \frac{3}{4} by \frac{5}{8} by multiplying \frac{3}{4} by the reciprocal of \frac{5}{8}.

$$\frac{2}{7}+\frac{3}{4}\times \frac{8}{5}-\frac{3}{2}$$

Multiply \frac{3}{4} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{7}+\frac{3\times 8}{4\times 5}-\frac{3}{2}$$

Do the multiplications in the fraction \frac{3\times 8}{4\times 5}.

$$\frac{2}{7}+\frac{24}{20}-\frac{3}{2}$$

Reduce the fraction \frac{24}{20} to lowest terms by extracting and canceling out 4.

$$\frac{2}{7}+\frac{6}{5}-\frac{3}{2}$$

Least common multiple of 7 and 5 is 35. Convert \frac{2}{7} and \frac{6}{5} to fractions with denominator 35.

$$\frac{10}{35}+\frac{42}{35}-\frac{3}{2}$$

Since \frac{10}{35} and \frac{42}{35} have the same denominator, add them by adding their numerators.

$$\frac{10+42}{35}-\frac{3}{2}$$

Add 10 and 42 to get 52.

$$\frac{52}{35}-\frac{3}{2}$$

Least common multiple of 35 and 2 is 70. Convert \frac{52}{35} and \frac{3}{2} to fractions with denominator 70.

$$\frac{104}{70}-\frac{105}{70}$$

Since \frac{104}{70} and \frac{105}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{104-105}{70}$$

Subtract 105 from 104 to get -1.

$$-\frac{1}{70}$$

Factor

$$-\frac{1}{70} = -0.014285714285714285$$