Solve 68*(3/17-3/4)-1/3div22/3

$$68 \times ( \frac { 3 } { 17 } - \frac { 3 } { 4 } ) - \frac { 1 } { 3 } \div 2 \frac { 2 } { 3 }$$

Evaluate

$$-\frac{313}{8}=-39.125$$

Solution Steps

Least common multiple of 17 and 4 is 68. Convert \frac{3}{17} and \frac{3}{4} to fractions with denominator 68.

$$68\left(\frac{12}{68}-\frac{51}{68}\right)-\frac{\frac{1}{3}}{\frac{2\times 3+2}{3}}$$

Since \frac{12}{68} and \frac{51}{68} have the same denominator, subtract them by subtracting their numerators.

$$68\times \frac{12-51}{68}-\frac{\frac{1}{3}}{\frac{2\times 3+2}{3}}$$

Subtract 51 from 12 to get -39.

$$68\left(-\frac{39}{68}\right)-\frac{\frac{1}{3}}{\frac{2\times 3+2}{3}}$$

Cancel out 68 and 68.

$$-39-\frac{\frac{1}{3}}{\frac{2\times 3+2}{3}}$$

Divide \frac{1}{3} by \frac{2\times 3+2}{3} by multiplying \frac{1}{3} by the reciprocal of \frac{2\times 3+2}{3}.

$$-39-\frac{3}{3\left(2\times 3+2\right)}$$

Multiply 2 and 3 to get 6.

$$-39-\frac{3}{3\left(6+2\right)}$$

Add 6 and 2 to get 8.

$$-39-\frac{3}{3\times 8}$$

Multiply 3 and 8 to get 24.

$$-39-\frac{3}{24}$$

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

$$-39-\frac{1}{8}$$

Convert -39 to fraction -\frac{312}{8}.

$$-\frac{312}{8}-\frac{1}{8}$$

Since -\frac{312}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-312-1}{8}$$

Subtract 1 from -312 to get -313.

$$-\frac{313}{8}$$

Factor

$$-\frac{313}{8} = -39\frac{1}{8} = -39.125$$