Solve 1/2+1/4/frac{5{6}-2/3}

$$\frac { \frac { 1 } { 2 } + \frac { 1 } { 4 } } { \frac { 5 } { 6 } - \frac { 2 } { 3 } }$$

Evaluate

$$\frac{9}{2}=4.5$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{\frac{2}{4}+\frac{1}{4}}{\frac{5}{6}-\frac{2}{3}}$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2+1}{4}}{\frac{5}{6}-\frac{2}{3}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{3}{4}}{\frac{5}{6}-\frac{2}{3}}$$

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{2}{3} to fractions with denominator 6.

$$\frac{\frac{3}{4}}{\frac{5}{6}-\frac{4}{6}}$$

Since \frac{5}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{4}}{\frac{5-4}{6}}$$

Subtract 4 from 5 to get 1.

$$\frac{\frac{3}{4}}{\frac{1}{6}}$$

Divide \frac{3}{4} by \frac{1}{6} by multiplying \frac{3}{4} by the reciprocal of \frac{1}{6}.

$$\frac{3}{4}\times 6$$

Express \frac{3}{4}\times 6 as a single fraction.

$$\frac{3\times 6}{4}$$

Multiply 3 and 6 to get 18.

$$\frac{18}{4}$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$