Solve 5/11*[(2/5+1/3)div5/6]

$$\frac { 5 } { 11 } \times [ ( \frac { 2 } { 5 } + \frac { 1 } { 3 } ) \div \frac { 5 } { 6 } ]$$

Evaluate

$$\frac{2}{5}=0.4$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{2}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{5}{11}\times \frac{\frac{6}{15}+\frac{5}{15}}{\frac{5}{6}}$$

Since \frac{6}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$\frac{5}{11}\times \frac{\frac{6+5}{15}}{\frac{5}{6}}$$

Add 6 and 5 to get 11.

$$\frac{5}{11}\times \frac{\frac{11}{15}}{\frac{5}{6}}$$

Divide \frac{11}{15} by \frac{5}{6} by multiplying \frac{11}{15} by the reciprocal of \frac{5}{6}.

$$\frac{5}{11}\times \frac{11}{15}\times \frac{6}{5}$$

Multiply \frac{11}{15} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{11}\times \frac{11\times 6}{15\times 5}$$

Do the multiplications in the fraction \frac{11\times 6}{15\times 5}.

$$\frac{5}{11}\times \frac{66}{75}$$

Reduce the fraction \frac{66}{75} to lowest terms by extracting and canceling out 3.

$$\frac{5}{11}\times \frac{22}{25}$$

Multiply \frac{5}{11} times \frac{22}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 22}{11\times 25}$$

Do the multiplications in the fraction \frac{5\times 22}{11\times 25}.

$$\frac{110}{275}$$

Reduce the fraction \frac{110}{275} to lowest terms by extracting and canceling out 55.

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

Factor

$$\frac{2}{5} = 0.4$$