Solve 5/14*[(3/4-2/5)div5/4]

$$\frac { 5 } { 14 } \times [ ( \frac { 3 } { 4 } - \frac { 2 } { 5 } ) \div \frac { 5 } { 4 } ]$$

Evaluate

$$\frac{1}{10}=0.1$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{2}{5} to fractions with denominator 20.

$$\frac{5}{14}\times \frac{\frac{15}{20}-\frac{8}{20}}{\frac{5}{4}}$$

Since \frac{15}{20} and \frac{8}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{14}\times \frac{\frac{15-8}{20}}{\frac{5}{4}}$$

Subtract 8 from 15 to get 7.

$$\frac{5}{14}\times \frac{\frac{7}{20}}{\frac{5}{4}}$$

Divide \frac{7}{20} by \frac{5}{4} by multiplying \frac{7}{20} by the reciprocal of \frac{5}{4}.

$$\frac{5}{14}\times \frac{7}{20}\times \frac{4}{5}$$

Multiply \frac{7}{20} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{14}\times \frac{7\times 4}{20\times 5}$$

Do the multiplications in the fraction \frac{7\times 4}{20\times 5}.

$$\frac{5}{14}\times \frac{28}{100}$$

Reduce the fraction \frac{28}{100} to lowest terms by extracting and canceling out 4.

$$\frac{5}{14}\times \frac{7}{25}$$

Multiply \frac{5}{14} times \frac{7}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 7}{14\times 25}$$

Do the multiplications in the fraction \frac{5\times 7}{14\times 25}.

$$\frac{35}{350}$$

Reduce the fraction \frac{35}{350} to lowest terms by extracting and canceling out 35.

$$\frac{1}{10}$$

Factor

$$\frac{1}{2 \cdot 5} = 0.1$$