Solve -7/8+1/2-[-3/8-(3/5-frac{2}{3})]

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

Evaluate

$$-\frac{1}{15}\approx -0.066666667$$

Solution Steps

Fraction \frac{-7}{8} can be rewritten as -\frac{7}{8} by extracting the negative sign.

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

Least common multiple of 8 and 2 is 8. Convert -\frac{7}{8} and \frac{1}{2} to fractions with denominator 8.

$$-\frac{7}{8}+\frac{4}{8}-\left(-\frac{3}{8}-\left(\frac{3}{5}-\frac{2}{3}\right)\right)$$

Since -\frac{7}{8} and \frac{4}{8} have the same denominator, add them by adding their numerators.

$$\frac{-7+4}{8}-\left(-\frac{3}{8}-\left(\frac{3}{5}-\frac{2}{3}\right)\right)$$

Add -7 and 4 to get -3.

$$-\frac{3}{8}-\left(-\frac{3}{8}-\left(\frac{3}{5}-\frac{2}{3}\right)\right)$$

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

$$-\frac{3}{8}-\left(-\frac{3}{8}-\left(\frac{9}{15}-\frac{10}{15}\right)\right)$$

Since \frac{9}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{8}-\left(-\frac{3}{8}-\frac{9-10}{15}\right)$$

Subtract 10 from 9 to get -1.

$$-\frac{3}{8}-\left(-\frac{3}{8}-\left(-\frac{1}{15}\right)\right)$$

The opposite of -\frac{1}{15} is \frac{1}{15}.

$$-\frac{3}{8}-\left(-\frac{3}{8}+\frac{1}{15}\right)$$

Least common multiple of 8 and 15 is 120. Convert -\frac{3}{8} and \frac{1}{15} to fractions with denominator 120.

$$-\frac{3}{8}-\left(-\frac{45}{120}+\frac{8}{120}\right)$$

Since -\frac{45}{120} and \frac{8}{120} have the same denominator, add them by adding their numerators.

$$-\frac{3}{8}-\frac{-45+8}{120}$$

Add -45 and 8 to get -37.

$$-\frac{3}{8}-\left(-\frac{37}{120}\right)$$

The opposite of -\frac{37}{120} is \frac{37}{120}.

$$-\frac{3}{8}+\frac{37}{120}$$

Least common multiple of 8 and 120 is 120. Convert -\frac{3}{8} and \frac{37}{120} to fractions with denominator 120.

$$-\frac{45}{120}+\frac{37}{120}$$

Since -\frac{45}{120} and \frac{37}{120} have the same denominator, add them by adding their numerators.

$$\frac{-45+37}{120}$$

Add -45 and 37 to get -8.

$$\frac{-8}{120}$$

Reduce the fraction \frac{-8}{120} to lowest terms by extracting and canceling out 8.

$$-\frac{1}{15}$$

Factor

$$-\frac{1}{15} = -0.06666666666666667$$