Solve (-2+5/4):(1/2-1/3)]:[5/7:(frac{1}{3}-frac{5}{21}+frac{1}{3}:frac{1}{6})]

$$( - 2 + \frac { 5 } { 4 } ) : ( \frac { 1 } { 2 } - \frac { 1 } { 3 } ) ] : [ \frac { 5 } { 7 } : ( \frac { 1 } { 3 } - \frac { 5 } { 21 } + \frac { 1 } { 3 } : \frac { 1 } { 6 } ) ]$$

Evaluate

$$-\frac{9}{2}=-4.5$$

Solution Steps

Convert -2 to fraction -\frac{8}{4}.

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

Since -\frac{8}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

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

Add -8 and 5 to get -3.

$$\frac{-\frac{3}{4}}{\frac{1}{2}-\frac{1}{3}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{-\frac{3}{4}}{\frac{3}{6}-\frac{2}{6}}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{3}{4}}{\frac{3-2}{6}}$$

Subtract 2 from 3 to get 1.

$$\frac{-\frac{3}{4}}{\frac{1}{6}}$$

Divide -\frac{3}{4} by \frac{1}{6} by multiplying -\frac{3}{4} by the reciprocal of \frac{1}{6}.

$$-\frac{3}{4}\times 6$$

Express -\frac{3}{4}\times 6 as a single fraction.

$$\frac{-3\times 6}{4}$$

Multiply -3 and 6 to get -18.

$$\frac{-18}{4}$$

Reduce the fraction \frac{-18}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{9}{2}$$

Factor

$$-\frac{9}{2} = -4\frac{1}{2} = -4.5$$