Solve 8/16+7/12-5/8+1/2-frac{5}{6}+frac{1}{4}

$$\frac { 8 } { 16 } + \frac { 7 } { 12 } - \frac { 5 } { 8 } + \frac { 1 } { 2 } - \frac { 5 } { 6 } + \frac { 1 } { 4 }$$

Evaluate

$$\frac{3}{8}=0.375$$

Solution Steps

Reduce the fraction \frac{8}{16} to lowest terms by extracting and canceling out 8.

$$\frac{1}{2}+\frac{7}{12}-\frac{5}{8}+\frac{1}{2}-\frac{5}{6}+\frac{1}{4}$$

Least common multiple of 2 and 12 is 12. Convert \frac{1}{2} and \frac{7}{12} to fractions with denominator 12.

$$\frac{6}{12}+\frac{7}{12}-\frac{5}{8}+\frac{1}{2}-\frac{5}{6}+\frac{1}{4}$$

Since \frac{6}{12} and \frac{7}{12} have the same denominator, add them by adding their numerators.

$$\frac{6+7}{12}-\frac{5}{8}+\frac{1}{2}-\frac{5}{6}+\frac{1}{4}$$

Add 6 and 7 to get 13.

$$\frac{13}{12}-\frac{5}{8}+\frac{1}{2}-\frac{5}{6}+\frac{1}{4}$$

Least common multiple of 12 and 8 is 24. Convert \frac{13}{12} and \frac{5}{8} to fractions with denominator 24.

$$\frac{26}{24}-\frac{15}{24}+\frac{1}{2}-\frac{5}{6}+\frac{1}{4}$$

Since \frac{26}{24} and \frac{15}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{26-15}{24}+\frac{1}{2}-\frac{5}{6}+\frac{1}{4}$$

Subtract 15 from 26 to get 11.

$$\frac{11}{24}+\frac{1}{2}-\frac{5}{6}+\frac{1}{4}$$

Least common multiple of 24 and 2 is 24. Convert \frac{11}{24} and \frac{1}{2} to fractions with denominator 24.

$$\frac{11}{24}+\frac{12}{24}-\frac{5}{6}+\frac{1}{4}$$

Since \frac{11}{24} and \frac{12}{24} have the same denominator, add them by adding their numerators.

$$\frac{11+12}{24}-\frac{5}{6}+\frac{1}{4}$$

Add 11 and 12 to get 23.

$$\frac{23}{24}-\frac{5}{6}+\frac{1}{4}$$

Least common multiple of 24 and 6 is 24. Convert \frac{23}{24} and \frac{5}{6} to fractions with denominator 24.

$$\frac{23}{24}-\frac{20}{24}+\frac{1}{4}$$

Since \frac{23}{24} and \frac{20}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23-20}{24}+\frac{1}{4}$$

Subtract 20 from 23 to get 3.

$$\frac{3}{24}+\frac{1}{4}$$

Reduce the fraction \frac{3}{24} to lowest terms by extracting and canceling out 3.

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

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

$$\frac{1}{8}+\frac{2}{8}$$

Since \frac{1}{8} and \frac{2}{8} have the same denominator, add them by adding their numerators.

$$\frac{1+2}{8}$$

Add 1 and 2 to get 3.

$$\frac{3}{8}$$

Factor

$$\frac{3}{2 ^ {3}} = 0.375$$