Solve 7/8-3/2:(1/2+5/14)

$$\frac { 7 } { 8 } - \frac { 3 } { 2 } : ( \frac { 1 } { 2 } + \frac { 5 } { 14 } )$$

Evaluate

$$-\frac{7}{8}=-0.875$$

Solution Steps

Least common multiple of 2 and 14 is 14. Convert \frac{1}{2} and \frac{5}{14} to fractions with denominator 14.

$$\frac{7}{8}-\frac{\frac{3}{2}}{\frac{7}{14}+\frac{5}{14}}$$

Since \frac{7}{14} and \frac{5}{14} have the same denominator, add them by adding their numerators.

$$\frac{7}{8}-\frac{\frac{3}{2}}{\frac{7+5}{14}}$$

Add 7 and 5 to get 12.

$$\frac{7}{8}-\frac{\frac{3}{2}}{\frac{12}{14}}$$

Reduce the fraction \frac{12}{14} to lowest terms by extracting and canceling out 2.

$$\frac{7}{8}-\frac{\frac{3}{2}}{\frac{6}{7}}$$

Divide \frac{3}{2} by \frac{6}{7} by multiplying \frac{3}{2} by the reciprocal of \frac{6}{7}.

$$\frac{7}{8}-\frac{3}{2}\times \frac{7}{6}$$

Multiply \frac{3}{2} times \frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{8}-\frac{3\times 7}{2\times 6}$$

Do the multiplications in the fraction \frac{3\times 7}{2\times 6}.

$$\frac{7}{8}-\frac{21}{12}$$

Reduce the fraction \frac{21}{12} to lowest terms by extracting and canceling out 3.

$$\frac{7}{8}-\frac{7}{4}$$

Least common multiple of 8 and 4 is 8. Convert \frac{7}{8} and \frac{7}{4} to fractions with denominator 8.

$$\frac{7}{8}-\frac{14}{8}$$

Since \frac{7}{8} and \frac{14}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-14}{8}$$

Subtract 14 from 7 to get -7.

$$-\frac{7}{8}$$

Factor

$$-\frac{7}{8} = -0.875$$