Solve 75-[-1/2+5/6-(1/8-42/3)]

$$75 - [ - \frac { 1 } { 2 } + \frac { 5 } { 6 } - ( \frac { 1 } { 8 } - 4 \frac { 2 } { 3 } ) ]$$

Evaluate

$$\frac{561}{8}=70.125$$

Solution Steps

Least common multiple of 2 and 6 is 6. Convert -\frac{1}{2} and \frac{5}{6} to fractions with denominator 6.

$$75-\left(-\frac{3}{6}+\frac{5}{6}-\left(\frac{1}{8}-\frac{4\times 3+2}{3}\right)\right)$$

Since -\frac{3}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$75-\left(\frac{-3+5}{6}-\left(\frac{1}{8}-\frac{4\times 3+2}{3}\right)\right)$$

Add -3 and 5 to get 2.

$$75-\left(\frac{2}{6}-\left(\frac{1}{8}-\frac{4\times 3+2}{3}\right)\right)$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$75-\left(\frac{1}{3}-\left(\frac{1}{8}-\frac{4\times 3+2}{3}\right)\right)$$

Multiply 4 and 3 to get 12.

$$75-\left(\frac{1}{3}-\left(\frac{1}{8}-\frac{12+2}{3}\right)\right)$$

Add 12 and 2 to get 14.

$$75-\left(\frac{1}{3}-\left(\frac{1}{8}-\frac{14}{3}\right)\right)$$

Least common multiple of 8 and 3 is 24. Convert \frac{1}{8} and \frac{14}{3} to fractions with denominator 24.

$$75-\left(\frac{1}{3}-\left(\frac{3}{24}-\frac{112}{24}\right)\right)$$

Since \frac{3}{24} and \frac{112}{24} have the same denominator, subtract them by subtracting their numerators.

$$75-\left(\frac{1}{3}-\frac{3-112}{24}\right)$$

Subtract 112 from 3 to get -109.

$$75-\left(\frac{1}{3}-\left(-\frac{109}{24}\right)\right)$$

The opposite of -\frac{109}{24} is \frac{109}{24}.

$$75-\left(\frac{1}{3}+\frac{109}{24}\right)$$

Least common multiple of 3 and 24 is 24. Convert \frac{1}{3} and \frac{109}{24} to fractions with denominator 24.

$$75-\left(\frac{8}{24}+\frac{109}{24}\right)$$

Since \frac{8}{24} and \frac{109}{24} have the same denominator, add them by adding their numerators.

$$75-\frac{8+109}{24}$$

Add 8 and 109 to get 117.

$$75-\frac{117}{24}$$

Reduce the fraction \frac{117}{24} to lowest terms by extracting and canceling out 3.

$$75-\frac{39}{8}$$

Convert 75 to fraction \frac{600}{8}.

$$\frac{600}{8}-\frac{39}{8}$$

Since \frac{600}{8} and \frac{39}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{600-39}{8}$$

Subtract 39 from 600 to get 561.

$$\frac{561}{8}$$

Factor

$$\frac{3 \cdot 11 \cdot 17}{2 ^ {3}} = 70\frac{1}{8} = 70.125$$