Solve [(2/3-1)*(-1/2)]:[1/4:(2-3/4)]

$$[ ( \frac { 2 } { 3 } - 1 ) \cdot ( - \frac { 1 } { 2 } ) ] : [ \frac { 1 } { 4 } : ( 2 - \frac { 3 } { 4 } ) ]$$

Evaluate

$$\frac{5}{6}\approx 0.833333333$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{\left(\frac{2}{3}-\frac{3}{3}\right)\left(-\frac{1}{2}\right)}{\frac{\frac{1}{4}}{2-\frac{3}{4}}}$$

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

$$\frac{\frac{2-3}{3}\left(-\frac{1}{2}\right)}{\frac{\frac{1}{4}}{2-\frac{3}{4}}}$$

Subtract 3 from 2 to get -1.

$$\frac{-\frac{1}{3}\left(-\frac{1}{2}\right)}{\frac{\frac{1}{4}}{2-\frac{3}{4}}}$$

Multiply -\frac{1}{3} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-\left(-1\right)}{3\times 2}.

$$\frac{\frac{1}{6}}{\frac{\frac{1}{4}}{2-\frac{3}{4}}}$$

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

$$\frac{\frac{1}{6}}{\frac{\frac{1}{4}}{\frac{8}{4}-\frac{3}{4}}}$$

Since \frac{8}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{6}}{\frac{\frac{1}{4}}{\frac{8-3}{4}}}$$

Subtract 3 from 8 to get 5.

$$\frac{\frac{1}{6}}{\frac{\frac{1}{4}}{\frac{5}{4}}}$$

Divide \frac{1}{4} by \frac{5}{4} by multiplying \frac{1}{4} by the reciprocal of \frac{5}{4}.

$$\frac{\frac{1}{6}}{\frac{1}{4}\times \frac{4}{5}}$$

Multiply \frac{1}{4} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{6}}{\frac{1\times 4}{4\times 5}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{1}{6}}{\frac{1}{5}}$$

Divide \frac{1}{6} by \frac{1}{5} by multiplying \frac{1}{6} by the reciprocal of \frac{1}{5}.

$$\frac{1}{6}\times 5$$

Multiply \frac{1}{6} and 5 to get \frac{5}{6}.

$$\frac{5}{6}$$

Factor

$$\frac{5}{2 \cdot 3} = 0.8333333333333334$$