Solve (1/2+2/5)div(3/4-1/5

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

Evaluate

$$\frac{18}{11}\approx 1.636363636$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{2}{5} to fractions with denominator 10.

$$\frac{\frac{5}{10}+\frac{4}{10}}{\frac{3}{4}-\frac{1}{5}}$$

Since \frac{5}{10} and \frac{4}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+4}{10}}{\frac{3}{4}-\frac{1}{5}}$$

Add 5 and 4 to get 9.

$$\frac{\frac{9}{10}}{\frac{3}{4}-\frac{1}{5}}$$

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{\frac{9}{10}}{\frac{15}{20}-\frac{4}{20}}$$

Since \frac{15}{20} and \frac{4}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9}{10}}{\frac{15-4}{20}}$$

Subtract 4 from 15 to get 11.

$$\frac{\frac{9}{10}}{\frac{11}{20}}$$

Divide \frac{9}{10} by \frac{11}{20} by multiplying \frac{9}{10} by the reciprocal of \frac{11}{20}.

$$\frac{9}{10}\times \frac{20}{11}$$

Multiply \frac{9}{10} times \frac{20}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 20}{10\times 11}$$

Do the multiplications in the fraction \frac{9\times 20}{10\times 11}.

$$\frac{180}{110}$$

Reduce the fraction \frac{180}{110} to lowest terms by extracting and canceling out 10.

$$\frac{18}{11}$$

Factor

$$\frac{2 \cdot 3 ^ {2}}{11} = 1\frac{7}{11} = 1.6363636363636365$$