Solve +(15/4-6/8div(1/2+3/4)]

$$+ ( \frac { 15 } { 4 } - \frac { 6 } { 8 } \div ( \frac { 1 } { 2 } + \frac { 3 } { 4 } ) ]$$

Evaluate

$$\frac{63}{20}=3.15$$

Solution Steps

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{15}{4}-\frac{\frac{3}{4}}{\frac{1}{2}+\frac{3}{4}}$$

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

$$\frac{15}{4}-\frac{\frac{3}{4}}{\frac{2}{4}+\frac{3}{4}}$$

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

$$\frac{15}{4}-\frac{\frac{3}{4}}{\frac{2+3}{4}}$$

Add 2 and 3 to get 5.

$$\frac{15}{4}-\frac{\frac{3}{4}}{\frac{5}{4}}$$

Divide \frac{3}{4} by \frac{5}{4} by multiplying \frac{3}{4} by the reciprocal of \frac{5}{4}.

$$\frac{15}{4}-\frac{3}{4}\times \frac{4}{5}$$

Multiply \frac{3}{4} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15}{4}-\frac{3\times 4}{4\times 5}$$

Cancel out 4 in both numerator and denominator.

$$\frac{15}{4}-\frac{3}{5}$$

Least common multiple of 4 and 5 is 20. Convert \frac{15}{4} and \frac{3}{5} to fractions with denominator 20.

$$\frac{75}{20}-\frac{12}{20}$$

Since \frac{75}{20} and \frac{12}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{75-12}{20}$$

Subtract 12 from 75 to get 63.

$$\frac{63}{20}$$

Factor

$$\frac{3 ^ {2} \cdot 7}{2 ^ {2} \cdot 5} = 3\frac{3}{20} = 3.15$$