Solve 2/5div[5/11*(9/10+1/5)]

$$\frac { 2 } { 5 } \div [ \frac { 5 } { 11 } \times ( \frac { 9 } { 10 } + \frac { 1 } { 5 } ) ]$$

Evaluate

$$\frac{4}{5}=0.8$$

Solution Steps

Least common multiple of 10 and 5 is 10. Convert \frac{9}{10} and \frac{1}{5} to fractions with denominator 10.

$$\frac{\frac{2}{5}}{\frac{5}{11}\left(\frac{9}{10}+\frac{2}{10}\right)}$$

Since \frac{9}{10} and \frac{2}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{5}}{\frac{5}{11}\times \frac{9+2}{10}}$$

Add 9 and 2 to get 11.

$$\frac{\frac{2}{5}}{\frac{5}{11}\times \frac{11}{10}}$$

Multiply \frac{5}{11} times \frac{11}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2}{5}}{\frac{5\times 11}{11\times 10}}$$

Cancel out 11 in both numerator and denominator.

$$\frac{\frac{2}{5}}{\frac{5}{10}}$$

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

$$\frac{\frac{2}{5}}{\frac{1}{2}}$$

Divide \frac{2}{5} by \frac{1}{2} by multiplying \frac{2}{5} by the reciprocal of \frac{1}{2}.

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

Express \frac{2}{5}\times 2 as a single fraction.

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

Multiply 2 and 2 to get 4.

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

Factor

$$\frac{2 ^ {2}}{5} = 0.8$$