Solve 4/5div2(1/3+2/5)*4/11

$$\frac { 4 } { 5 } \div 2 ( \frac { 1 } { 3 } + \frac { 2 } { 5 } ) \times \frac { 4 } { 11 }$$

Evaluate

$$\frac{8}{75}\approx 0.106666667$$

Solution Steps

Express \frac{\frac{4}{5}}{2} as a single fraction.

$$\frac{4}{5\times 2}\left(\frac{1}{3}+\frac{2}{5}\right)\times \frac{4}{11}$$

Multiply 5 and 2 to get 10.

$$\frac{4}{10}\left(\frac{1}{3}+\frac{2}{5}\right)\times \frac{4}{11}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{2}{5}\left(\frac{1}{3}+\frac{2}{5}\right)\times \frac{4}{11}$$

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

$$\frac{2}{5}\left(\frac{5}{15}+\frac{6}{15}\right)\times \frac{4}{11}$$

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

$$\frac{2}{5}\times \frac{5+6}{15}\times \frac{4}{11}$$

Add 5 and 6 to get 11.

$$\frac{2}{5}\times \frac{11}{15}\times \frac{4}{11}$$

Multiply \frac{2}{5} times \frac{11}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 11}{5\times 15}\times \frac{4}{11}$$

Do the multiplications in the fraction \frac{2\times 11}{5\times 15}.

$$\frac{22}{75}\times \frac{4}{11}$$

Multiply \frac{22}{75} times \frac{4}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22\times 4}{75\times 11}$$

Do the multiplications in the fraction \frac{22\times 4}{75\times 11}.

$$\frac{88}{825}$$

Reduce the fraction \frac{88}{825} to lowest terms by extracting and canceling out 11.

$$\frac{8}{75}$$

Factor

$$\frac{2 ^ {3}}{3 \cdot 5 ^ {2}} = 0.10666666666666667$$