Solve 1/2+1/2/sqrt{frac{1{4}}/5/6}

$$\frac { \frac { 1 } { 2 } + \frac { 1 } { 2 } } { \sqrt { \frac { 1 } { 4 } } / \frac { 5 } { 6 } }$$

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

Since \frac{1}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+1}{2}}{\frac{\sqrt{\frac{1}{4}}}{\frac{5}{6}}}$$

Add 1 and 1 to get 2.

$$\frac{\frac{2}{2}}{\frac{\sqrt{\frac{1}{4}}}{\frac{5}{6}}}$$

Divide 2 by 2 to get 1.

$$\frac{1}{\frac{\sqrt{\frac{1}{4}}}{\frac{5}{6}}}$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{1}{\frac{\frac{1}{2}}{\frac{5}{6}}}$$

Divide \frac{1}{2} by \frac{5}{6} by multiplying \frac{1}{2} by the reciprocal of \frac{5}{6}.

$$\frac{1}{\frac{1}{2}\times \frac{6}{5}}$$

Multiply \frac{1}{2} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{\frac{1\times 6}{2\times 5}}$$

Do the multiplications in the fraction \frac{1\times 6}{2\times 5}.

$$\frac{1}{\frac{6}{10}}$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{\frac{3}{5}}$$

Divide 1 by \frac{3}{5} by multiplying 1 by the reciprocal of \frac{3}{5}.

$$1\times \frac{5}{3}$$

Multiply 1 and \frac{5}{3} to get \frac{5}{3}.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$