Solve (1/4-2/5*1/2)div3/5

$$( \frac{ 1 }{ 4 } - \frac{ 2 }{ 5 } \times \frac{ 1 }{ 2 } ) \div \frac{ 3 }{ 5 }$$

Evaluate

$$\frac{1}{12}\approx 0.083333333$$

Solution Steps

Multiply \frac{2}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{1}{4}-\frac{1}{5}}{\frac{3}{5}}$$

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{\frac{5}{20}-\frac{4}{20}}{\frac{3}{5}}$$

Since \frac{5}{20} and \frac{4}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-4}{20}}{\frac{3}{5}}$$

Subtract 4 from 5 to get 1.

$$\frac{\frac{1}{20}}{\frac{3}{5}}$$

Divide \frac{1}{20} by \frac{3}{5} by multiplying \frac{1}{20} by the reciprocal of \frac{3}{5}.

$$\frac{1}{20}\times \frac{5}{3}$$

Multiply \frac{1}{20} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5}{20\times 3}$$

Do the multiplications in the fraction \frac{1\times 5}{20\times 3}.

$$\frac{5}{60}$$

Reduce the fraction \frac{5}{60} to lowest terms by extracting and canceling out 5.

$$\frac{1}{12}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 3} = 0.08333333333333333$$