Solve 13/4-(5/6-1/8)div52/3

$$1 \frac { 3 } { 4 } - ( \frac { 5 } { 6 } - \frac { 1 } { 8 } ) \div 5 \frac { 2 } { 3 }$$

Evaluate

$$\frac{13}{8}=1.625$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{4+3}{4}-\frac{\frac{5}{6}-\frac{1}{8}}{\frac{5\times 3+2}{3}}$$

Add 4 and 3 to get 7.

$$\frac{7}{4}-\frac{\frac{5}{6}-\frac{1}{8}}{\frac{5\times 3+2}{3}}$$

Least common multiple of 6 and 8 is 24. Convert \frac{5}{6} and \frac{1}{8} to fractions with denominator 24.

$$\frac{7}{4}-\frac{\frac{20}{24}-\frac{3}{24}}{\frac{5\times 3+2}{3}}$$

Since \frac{20}{24} and \frac{3}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{4}-\frac{\frac{20-3}{24}}{\frac{5\times 3+2}{3}}$$

Subtract 3 from 20 to get 17.

$$\frac{7}{4}-\frac{\frac{17}{24}}{\frac{5\times 3+2}{3}}$$

Multiply 5 and 3 to get 15.

$$\frac{7}{4}-\frac{\frac{17}{24}}{\frac{15+2}{3}}$$

Add 15 and 2 to get 17.

$$\frac{7}{4}-\frac{\frac{17}{24}}{\frac{17}{3}}$$

Divide \frac{17}{24} by \frac{17}{3} by multiplying \frac{17}{24} by the reciprocal of \frac{17}{3}.

$$\frac{7}{4}-\frac{17}{24}\times \frac{3}{17}$$

Multiply \frac{17}{24} times \frac{3}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{4}-\frac{17\times 3}{24\times 17}$$

Cancel out 17 in both numerator and denominator.

$$\frac{7}{4}-\frac{3}{24}$$

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

$$\frac{7}{4}-\frac{1}{8}$$

Least common multiple of 4 and 8 is 8. Convert \frac{7}{4} and \frac{1}{8} to fractions with denominator 8.

$$\frac{14}{8}-\frac{1}{8}$$

Since \frac{14}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14-1}{8}$$

Subtract 1 from 14 to get 13.

$$\frac{13}{8}$$

Factor

$$\frac{13}{2 ^ {3}} = 1\frac{5}{8} = 1.625$$