Solve (3-1/4-5/4)*1/4:[2-(1/5-frac{3}{10})*5]=

$$( 3 - \frac { 1 } { 4 } - \frac { 5 } { 4 } ) \cdot \frac { 1 } { 4 } : [ 2 - ( \frac { 1 } { 5 } - \frac { 3 } { 10 } ) \cdot 5 ] =$$

Evaluate

$$\frac{3}{20}=0.15$$

Solution Steps

Convert 3 to fraction \frac{12}{4}.

$$\frac{\left(\frac{12}{4}-\frac{1}{4}-\frac{5}{4}\right)\times \frac{1}{4}}{2-\left(\frac{1}{5}-\frac{3}{10}\right)\times 5}$$

Since \frac{12}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\frac{12-1}{4}-\frac{5}{4}\right)\times \frac{1}{4}}{2-\left(\frac{1}{5}-\frac{3}{10}\right)\times 5}$$

Subtract 1 from 12 to get 11.

$$\frac{\left(\frac{11}{4}-\frac{5}{4}\right)\times \frac{1}{4}}{2-\left(\frac{1}{5}-\frac{3}{10}\right)\times 5}$$

Since \frac{11}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11-5}{4}\times \frac{1}{4}}{2-\left(\frac{1}{5}-\frac{3}{10}\right)\times 5}$$

Subtract 5 from 11 to get 6.

$$\frac{\frac{6}{4}\times \frac{1}{4}}{2-\left(\frac{1}{5}-\frac{3}{10}\right)\times 5}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{2}\times \frac{1}{4}}{2-\left(\frac{1}{5}-\frac{3}{10}\right)\times 5}$$

Multiply \frac{3}{2} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 1}{2\times 4}}{2-\left(\frac{1}{5}-\frac{3}{10}\right)\times 5}$$

Do the multiplications in the fraction \frac{3\times 1}{2\times 4}.

$$\frac{\frac{3}{8}}{2-\left(\frac{1}{5}-\frac{3}{10}\right)\times 5}$$

Least common multiple of 5 and 10 is 10. Convert \frac{1}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{\frac{3}{8}}{2-\left(\frac{2}{10}-\frac{3}{10}\right)\times 5}$$

Since \frac{2}{10} and \frac{3}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{8}}{2-\frac{2-3}{10}\times 5}$$

Subtract 3 from 2 to get -1.

$$\frac{\frac{3}{8}}{2-\left(-\frac{1}{10}\times 5\right)}$$

Express -\frac{1}{10}\times 5 as a single fraction.

$$\frac{\frac{3}{8}}{2-\frac{-5}{10}}$$

Reduce the fraction \frac{-5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{3}{8}}{2-\left(-\frac{1}{2}\right)}$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\frac{\frac{3}{8}}{2+\frac{1}{2}}$$

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

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

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 4 and 1 to get 5.

$$\frac{\frac{3}{8}}{\frac{5}{2}}$$

Divide \frac{3}{8} by \frac{5}{2} by multiplying \frac{3}{8} by the reciprocal of \frac{5}{2}.

$$\frac{3}{8}\times \frac{2}{5}$$

Multiply \frac{3}{8} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 2}{8\times 5}$$

Do the multiplications in the fraction \frac{3\times 2}{8\times 5}.

$$\frac{6}{40}$$

Reduce the fraction \frac{6}{40} to lowest terms by extracting and canceling out 2.

$$\frac{3}{20}$$

Factor

$$\frac{3}{2 ^ {2} \cdot 5} = 0.15$$