Solve (2/8+sqrt{frac{16/9}+4/3)}{5/2}

$$\frac { ( \frac { 2 } { 8 } + \sqrt { \frac { 16 } { 9 } } + \frac { 4 } { 3 } ) } { \frac { 5 } { 2 } }$$

Evaluate

$$\frac{7}{6}\approx 1.166666667$$

Solution Steps

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{4}+\sqrt{\frac{16}{9}}+\frac{4}{3}}{\frac{5}{2}}$$

Rewrite the square root of the division \frac{16}{9} as the division of square roots \frac{\sqrt{16}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{\frac{1}{4}+\frac{4}{3}+\frac{4}{3}}{\frac{5}{2}}$$

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{4}{3} to fractions with denominator 12.

$$\frac{\frac{3}{12}+\frac{16}{12}+\frac{4}{3}}{\frac{5}{2}}$$

Since \frac{3}{12} and \frac{16}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+16}{12}+\frac{4}{3}}{\frac{5}{2}}$$

Add 3 and 16 to get 19.

$$\frac{\frac{19}{12}+\frac{4}{3}}{\frac{5}{2}}$$

Least common multiple of 12 and 3 is 12. Convert \frac{19}{12} and \frac{4}{3} to fractions with denominator 12.

$$\frac{\frac{19}{12}+\frac{16}{12}}{\frac{5}{2}}$$

Since \frac{19}{12} and \frac{16}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{19+16}{12}}{\frac{5}{2}}$$

Add 19 and 16 to get 35.

$$\frac{\frac{35}{12}}{\frac{5}{2}}$$

Divide \frac{35}{12} by \frac{5}{2} by multiplying \frac{35}{12} by the reciprocal of \frac{5}{2}.

$$\frac{35}{12}\times \frac{2}{5}$$

Multiply \frac{35}{12} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 2}{12\times 5}$$

Do the multiplications in the fraction \frac{35\times 2}{12\times 5}.

$$\frac{70}{60}$$

Reduce the fraction \frac{70}{60} to lowest terms by extracting and canceling out 10.

$$\frac{7}{6}$$

Factor

$$\frac{7}{2 \cdot 3} = 1\frac{1}{6} = 1.1666666666666667$$