Solve 9/16+7/12-5/8+1/2-frac{5}{6}+frac{1}{4}

$$\frac { 9 } { 16 } + \frac { 7 } { 12 } - \frac { 5 } { 8 } + \frac { 1 } { 2 } - \frac { 5 } { 6 } + \frac { 1 } { 4 }$$

Evaluate

$$\frac{7}{16}=0.4375$$

Solution Steps

Least common multiple of 16 and 12 is 48. Convert \frac{9}{16} and \frac{7}{12} to fractions with denominator 48.

$$\frac{27}{48}+\frac{28}{48}-\frac{5}{8}+\frac{1}{2}-\frac{5}{6}+\frac{1}{4}$$

Since \frac{27}{48} and \frac{28}{48} have the same denominator, add them by adding their numerators.

$$\frac{27+28}{48}-\frac{5}{8}+\frac{1}{2}-\frac{5}{6}+\frac{1}{4}$$

Add 27 and 28 to get 55.

$$\frac{55}{48}-\frac{5}{8}+\frac{1}{2}-\frac{5}{6}+\frac{1}{4}$$

Least common multiple of 48 and 8 is 48. Convert \frac{55}{48} and \frac{5}{8} to fractions with denominator 48.

$$\frac{55}{48}-\frac{30}{48}+\frac{1}{2}-\frac{5}{6}+\frac{1}{4}$$

Since \frac{55}{48} and \frac{30}{48} have the same denominator, subtract them by subtracting their numerators.

$$\frac{55-30}{48}+\frac{1}{2}-\frac{5}{6}+\frac{1}{4}$$

Subtract 30 from 55 to get 25.

$$\frac{25}{48}+\frac{1}{2}-\frac{5}{6}+\frac{1}{4}$$

Least common multiple of 48 and 2 is 48. Convert \frac{25}{48} and \frac{1}{2} to fractions with denominator 48.

$$\frac{25}{48}+\frac{24}{48}-\frac{5}{6}+\frac{1}{4}$$

Since \frac{25}{48} and \frac{24}{48} have the same denominator, add them by adding their numerators.

$$\frac{25+24}{48}-\frac{5}{6}+\frac{1}{4}$$

Add 25 and 24 to get 49.

$$\frac{49}{48}-\frac{5}{6}+\frac{1}{4}$$

Least common multiple of 48 and 6 is 48. Convert \frac{49}{48} and \frac{5}{6} to fractions with denominator 48.

$$\frac{49}{48}-\frac{40}{48}+\frac{1}{4}$$

Since \frac{49}{48} and \frac{40}{48} have the same denominator, subtract them by subtracting their numerators.

$$\frac{49-40}{48}+\frac{1}{4}$$

Subtract 40 from 49 to get 9.

$$\frac{9}{48}+\frac{1}{4}$$

Reduce the fraction \frac{9}{48} to lowest terms by extracting and canceling out 3.

$$\frac{3}{16}+\frac{1}{4}$$

Least common multiple of 16 and 4 is 16. Convert \frac{3}{16} and \frac{1}{4} to fractions with denominator 16.

$$\frac{3}{16}+\frac{4}{16}$$

Since \frac{3}{16} and \frac{4}{16} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{16}$$

Add 3 and 4 to get 7.

$$\frac{7}{16}$$

Factor

$$\frac{7}{2 ^ {4}} = 0.4375$$