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

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

Evaluate

$$\frac{7}{2}=3.5$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

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

Since \frac{6}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

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

Add 6 and 1 to get 7.

$$\frac{\frac{7}{4}}{\frac{5}{6}-\frac{1}{3}}$$

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{1}{3} to fractions with denominator 6.

$$\frac{\frac{7}{4}}{\frac{5}{6}-\frac{2}{6}}$$

Since \frac{5}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{4}}{\frac{5-2}{6}}$$

Subtract 2 from 5 to get 3.

$$\frac{\frac{7}{4}}{\frac{3}{6}}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{7}{4}}{\frac{1}{2}}$$

Divide \frac{7}{4} by \frac{1}{2} by multiplying \frac{7}{4} by the reciprocal of \frac{1}{2}.

$$\frac{7}{4}\times 2$$

Express \frac{7}{4}\times 2 as a single fraction.

$$\frac{7\times 2}{4}$$

Multiply 7 and 2 to get 14.

$$\frac{14}{4}$$

Reduce the fraction \frac{14}{4} to lowest terms by extracting and canceling out 2.

$$\frac{7}{2}$$

Factor

$$\frac{7}{2} = 3\frac{1}{2} = 3.5$$