Solve 1/5(2-3/4)/1+frac{1{6}:2/3}=

$$\frac { \frac { 1 } { 5 } ( 2 - \frac { 3 } { 4 } ) } { 1 + \frac { 1 } { 6 } : \frac { 2 } { 3 } } =$$

Evaluate

$$\frac{1}{5}=0.2$$

Solution Steps

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

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

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

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

Subtract 3 from 8 to get 5.

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

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

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

Cancel out 5 in both numerator and denominator.

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

Divide \frac{1}{6} by \frac{2}{3} by multiplying \frac{1}{6} by the reciprocal of \frac{2}{3}.

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

Multiply \frac{1}{6} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 3}{6\times 2}.

$$\frac{\frac{1}{4}}{1+\frac{3}{12}}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{4}}{1+\frac{1}{4}}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{\frac{1}{4}}{\frac{4}{4}+\frac{1}{4}}$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{4}}{\frac{4+1}{4}}$$

Add 4 and 1 to get 5.

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

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

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

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

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

Cancel out 4 in both numerator and denominator.

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

Factor

$$\frac{1}{5} = 0.2$$