Solve 1+(15/4-1/8div11/2+3/4)]

$$1 + ( \frac { 15 } { 4 } - \frac { 1 } { 8 } \div \frac { 11 } { 2 } + \frac { 3 } { 4 } ) ]$$

Evaluate

$$\frac{241}{44}\approx 5.477272727$$

Solution Steps

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

$$\frac{4}{4}+\frac{15}{4}-\frac{\frac{1}{8}}{\frac{11}{2}}+\frac{3}{4}$$

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

$$\frac{4+15}{4}-\frac{\frac{1}{8}}{\frac{11}{2}}+\frac{3}{4}$$

Add 4 and 15 to get 19.

$$\frac{19}{4}-\frac{\frac{1}{8}}{\frac{11}{2}}+\frac{3}{4}$$

Divide \frac{1}{8} by \frac{11}{2} by multiplying \frac{1}{8} by the reciprocal of \frac{11}{2}.

$$\frac{19}{4}-\frac{1}{8}\times \frac{2}{11}+\frac{3}{4}$$

Multiply \frac{1}{8} times \frac{2}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19}{4}-\frac{1\times 2}{8\times 11}+\frac{3}{4}$$

Do the multiplications in the fraction \frac{1\times 2}{8\times 11}.

$$\frac{19}{4}-\frac{2}{88}+\frac{3}{4}$$

Reduce the fraction \frac{2}{88} to lowest terms by extracting and canceling out 2.

$$\frac{19}{4}-\frac{1}{44}+\frac{3}{4}$$

Least common multiple of 4 and 44 is 44. Convert \frac{19}{4} and \frac{1}{44} to fractions with denominator 44.

$$\frac{209}{44}-\frac{1}{44}+\frac{3}{4}$$

Since \frac{209}{44} and \frac{1}{44} have the same denominator, subtract them by subtracting their numerators.

$$\frac{209-1}{44}+\frac{3}{4}$$

Subtract 1 from 209 to get 208.

$$\frac{208}{44}+\frac{3}{4}$$

Reduce the fraction \frac{208}{44} to lowest terms by extracting and canceling out 4.

$$\frac{52}{11}+\frac{3}{4}$$

Least common multiple of 11 and 4 is 44. Convert \frac{52}{11} and \frac{3}{4} to fractions with denominator 44.

$$\frac{208}{44}+\frac{33}{44}$$

Since \frac{208}{44} and \frac{33}{44} have the same denominator, add them by adding their numerators.

$$\frac{208+33}{44}$$

Add 208 and 33 to get 241.

$$\frac{241}{44}$$

Factor

$$\frac{241}{2 ^ {2} \cdot 11} = 5\frac{21}{44} = 5.4772727272727275$$