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

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

Evaluate

$$\frac{83}{20}=4.15$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

$$\frac{4}{4}+\frac{15}{4}-\frac{\frac{6}{8}}{\frac{1}{2}+\frac{3}{4}}$$

Since \frac{4}{4} and \frac{15}{4} have the same denominator, add them by adding their numerators.

$$\frac{4+15}{4}-\frac{\frac{6}{8}}{\frac{1}{2}+\frac{3}{4}}$$

Add 4 and 15 to get 19.

$$\frac{19}{4}-\frac{\frac{6}{8}}{\frac{1}{2}+\frac{3}{4}}$$

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

$$\frac{19}{4}-\frac{\frac{3}{4}}{\frac{1}{2}+\frac{3}{4}}$$

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

$$\frac{19}{4}-\frac{\frac{3}{4}}{\frac{2}{4}+\frac{3}{4}}$$

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

$$\frac{19}{4}-\frac{\frac{3}{4}}{\frac{2+3}{4}}$$

Add 2 and 3 to get 5.

$$\frac{19}{4}-\frac{\frac{3}{4}}{\frac{5}{4}}$$

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

$$\frac{19}{4}-\frac{3}{4}\times \frac{4}{5}$$

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

$$\frac{19}{4}-\frac{3\times 4}{4\times 5}$$

Cancel out 4 in both numerator and denominator.

$$\frac{19}{4}-\frac{3}{5}$$

Least common multiple of 4 and 5 is 20. Convert \frac{19}{4} and \frac{3}{5} to fractions with denominator 20.

$$\frac{95}{20}-\frac{12}{20}$$

Since \frac{95}{20} and \frac{12}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{95-12}{20}$$

Subtract 12 from 95 to get 83.

$$\frac{83}{20}$$

Factor

$$\frac{83}{2 ^ {2} \cdot 5} = 4\frac{3}{20} = 4.15$$