Solve 5/8+1/4/frac{3{4}-1/2}

$$\frac { \frac { 5 } { 8 } + \frac { 1 } { 4 } } { \frac { 3 } { 4 } - \frac { 1 } { 2 } }$$

Evaluate

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

Solution Steps

Least common multiple of 8 and 4 is 8. Convert \frac{5}{8} and \frac{1}{4} to fractions with denominator 8.

$$\frac{\frac{5}{8}+\frac{2}{8}}{\frac{3}{4}-\frac{1}{2}}$$

Since \frac{5}{8} and \frac{2}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+2}{8}}{\frac{3}{4}-\frac{1}{2}}$$

Add 5 and 2 to get 7.

$$\frac{\frac{7}{8}}{\frac{3}{4}-\frac{1}{2}}$$

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

$$\frac{\frac{7}{8}}{\frac{3}{4}-\frac{2}{4}}$$

Since \frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{8}}{\frac{3-2}{4}}$$

Subtract 2 from 3 to get 1.

$$\frac{\frac{7}{8}}{\frac{1}{4}}$$

Divide \frac{7}{8} by \frac{1}{4} by multiplying \frac{7}{8} by the reciprocal of \frac{1}{4}.

$$\frac{7}{8}\times 4$$

Express \frac{7}{8}\times 4 as a single fraction.

$$\frac{7\times 4}{8}$$

Multiply 7 and 4 to get 28.

$$\frac{28}{8}$$

Reduce the fraction \frac{28}{8} to lowest terms by extracting and canceling out 4.

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

Factor

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