Solve -7-(1/7-8+1/8)

$$- 7 - ( \frac { 1 } { 7 } - 8 + \frac { 1 } { 8 } )$$

Evaluate

$$\frac{41}{56}\approx 0.732142857$$

Solution Steps

Convert 8 to fraction \frac{56}{7}.

$$-7-\left(\frac{1}{7}-\frac{56}{7}+\frac{1}{8}\right)$$

Since \frac{1}{7} and \frac{56}{7} have the same denominator, subtract them by subtracting their numerators.

$$-7-\left(\frac{1-56}{7}+\frac{1}{8}\right)$$

Subtract 56 from 1 to get -55.

$$-7-\left(-\frac{55}{7}+\frac{1}{8}\right)$$

Least common multiple of 7 and 8 is 56. Convert -\frac{55}{7} and \frac{1}{8} to fractions with denominator 56.

$$-7-\left(-\frac{440}{56}+\frac{7}{56}\right)$$

Since -\frac{440}{56} and \frac{7}{56} have the same denominator, add them by adding their numerators.

$$-7-\frac{-440+7}{56}$$

Add -440 and 7 to get -433.

$$-7-\left(-\frac{433}{56}\right)$$

The opposite of -\frac{433}{56} is \frac{433}{56}.

$$-7+\frac{433}{56}$$

Convert -7 to fraction -\frac{392}{56}.

$$-\frac{392}{56}+\frac{433}{56}$$

Since -\frac{392}{56} and \frac{433}{56} have the same denominator, add them by adding their numerators.

$$\frac{-392+433}{56}$$

Add -392 and 433 to get 41.

$$\frac{41}{56}$$

Factor

$$\frac{41}{2 ^ {3} \cdot 7} = 0.7321428571428571$$