Solve 11/8-(5/12-1/4)+5/8

$$\frac{ 11 }{ 8 } -( \frac{ 5 }{ 12 } - \frac{ 1 }{ 4 } )+ \frac{ 5 }{ 8 }$$

Evaluate

$$\frac{11}{6}\approx 1.833333333$$

Solution Steps

Least common multiple of 12 and 4 is 12. Convert \frac{5}{12} and \frac{1}{4} to fractions with denominator 12.

$$\frac{11}{8}-\left(\frac{5}{12}-\frac{3}{12}\right)+\frac{5}{8}$$

Since \frac{5}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{8}-\frac{5-3}{12}+\frac{5}{8}$$

Subtract 3 from 5 to get 2.

$$\frac{11}{8}-\frac{2}{12}+\frac{5}{8}$$

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$\frac{11}{8}-\frac{1}{6}+\frac{5}{8}$$

Least common multiple of 8 and 6 is 24. Convert \frac{11}{8} and \frac{1}{6} to fractions with denominator 24.

$$\frac{33}{24}-\frac{4}{24}+\frac{5}{8}$$

Since \frac{33}{24} and \frac{4}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{33-4}{24}+\frac{5}{8}$$

Subtract 4 from 33 to get 29.

$$\frac{29}{24}+\frac{5}{8}$$

Least common multiple of 24 and 8 is 24. Convert \frac{29}{24} and \frac{5}{8} to fractions with denominator 24.

$$\frac{29}{24}+\frac{15}{24}$$

Since \frac{29}{24} and \frac{15}{24} have the same denominator, add them by adding their numerators.

$$\frac{29+15}{24}$$

Add 29 and 15 to get 44.

$$\frac{44}{24}$$

Reduce the fraction \frac{44}{24} to lowest terms by extracting and canceling out 4.

$$\frac{11}{6}$$

Factor

$$\frac{11}{2 \cdot 3} = 1\frac{5}{6} = 1.8333333333333333$$