Solve 9/20div[1/2*(2/3+4/5)]

$$\frac { 9 } { 20 } \div [ \frac { 1 } { 2 } \times ( \frac { 2 } { 3 } + \frac { 4 } { 5 } ) ]$$

Evaluate

$$\frac{27}{44}\approx 0.613636364$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{\frac{9}{20}}{\frac{1}{2}\left(\frac{10}{15}+\frac{12}{15}\right)}$$

Since \frac{10}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9}{20}}{\frac{1}{2}\times \frac{10+12}{15}}$$

Add 10 and 12 to get 22.

$$\frac{\frac{9}{20}}{\frac{1}{2}\times \frac{22}{15}}$$

Multiply \frac{1}{2} times \frac{22}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9}{20}}{\frac{1\times 22}{2\times 15}}$$

Do the multiplications in the fraction \frac{1\times 22}{2\times 15}.

$$\frac{\frac{9}{20}}{\frac{22}{30}}$$

Reduce the fraction \frac{22}{30} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{9}{20}}{\frac{11}{15}}$$

Divide \frac{9}{20} by \frac{11}{15} by multiplying \frac{9}{20} by the reciprocal of \frac{11}{15}.

$$\frac{9}{20}\times \frac{15}{11}$$

Multiply \frac{9}{20} times \frac{15}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 15}{20\times 11}$$

Do the multiplications in the fraction \frac{9\times 15}{20\times 11}.

$$\frac{135}{220}$$

Reduce the fraction \frac{135}{220} to lowest terms by extracting and canceling out 5.

$$\frac{27}{44}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {2} \cdot 11} = 0.6136363636363636$$