Solve 3/5:(4/5+11/20)

$$\frac { 3 } { 5 } : ( \frac { 4 } { 5 } + \frac { 11 } { 20 } )$$

Evaluate

$$\frac{4}{9}\approx 0.444444444$$

Solution Steps

Least common multiple of 5 and 20 is 20. Convert \frac{4}{5} and \frac{11}{20} to fractions with denominator 20.

$$\frac{\frac{3}{5}}{\frac{16}{20}+\frac{11}{20}}$$

Since \frac{16}{20} and \frac{11}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{5}}{\frac{16+11}{20}}$$

Add 16 and 11 to get 27.

$$\frac{\frac{3}{5}}{\frac{27}{20}}$$

Divide \frac{3}{5} by \frac{27}{20} by multiplying \frac{3}{5} by the reciprocal of \frac{27}{20}.

$$\frac{3}{5}\times \frac{20}{27}$$

Multiply \frac{3}{5} times \frac{20}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 20}{5\times 27}$$

Do the multiplications in the fraction \frac{3\times 20}{5\times 27}.

$$\frac{60}{135}$$

Reduce the fraction \frac{60}{135} to lowest terms by extracting and canceling out 15.

$$\frac{4}{9}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {2}} = 0.4444444444444444$$