Solve 23/6-0.5-31/4-11/2+19/6+7.75

$$\frac{ 23 }{ 6 } -0.5- \frac{ 31 }{ 4 } - \frac{ 11 }{ 2 } + \frac{ 19 }{ 6 } +7.75$$

Evaluate

$$1$$

Solution Steps

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{23}{6}-\frac{1}{2}-\frac{31}{4}-\frac{11}{2}+\frac{19}{6}+7.75$$

Least common multiple of 6 and 2 is 6. Convert \frac{23}{6} and \frac{1}{2} to fractions with denominator 6.

$$\frac{23}{6}-\frac{3}{6}-\frac{31}{4}-\frac{11}{2}+\frac{19}{6}+7.75$$

Since \frac{23}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23-3}{6}-\frac{31}{4}-\frac{11}{2}+\frac{19}{6}+7.75$$

Subtract 3 from 23 to get 20.

$$\frac{20}{6}-\frac{31}{4}-\frac{11}{2}+\frac{19}{6}+7.75$$

Reduce the fraction \frac{20}{6} to lowest terms by extracting and canceling out 2.

$$\frac{10}{3}-\frac{31}{4}-\frac{11}{2}+\frac{19}{6}+7.75$$

Least common multiple of 3 and 4 is 12. Convert \frac{10}{3} and \frac{31}{4} to fractions with denominator 12.

$$\frac{40}{12}-\frac{93}{12}-\frac{11}{2}+\frac{19}{6}+7.75$$

Since \frac{40}{12} and \frac{93}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{40-93}{12}-\frac{11}{2}+\frac{19}{6}+7.75$$

Subtract 93 from 40 to get -53.

$$-\frac{53}{12}-\frac{11}{2}+\frac{19}{6}+7.75$$

Least common multiple of 12 and 2 is 12. Convert -\frac{53}{12} and \frac{11}{2} to fractions with denominator 12.

$$-\frac{53}{12}-\frac{66}{12}+\frac{19}{6}+7.75$$

Since -\frac{53}{12} and \frac{66}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-53-66}{12}+\frac{19}{6}+7.75$$

Subtract 66 from -53 to get -119.

$$-\frac{119}{12}+\frac{19}{6}+7.75$$

Least common multiple of 12 and 6 is 12. Convert -\frac{119}{12} and \frac{19}{6} to fractions with denominator 12.

$$-\frac{119}{12}+\frac{38}{12}+7.75$$

Since -\frac{119}{12} and \frac{38}{12} have the same denominator, add them by adding their numerators.

$$\frac{-119+38}{12}+7.75$$

Add -119 and 38 to get -81.

$$\frac{-81}{12}+7.75$$

Reduce the fraction \frac{-81}{12} to lowest terms by extracting and canceling out 3.

$$-\frac{27}{4}+7.75$$

Convert decimal number 7.75 to fraction \frac{775}{100}. Reduce the fraction \frac{775}{100} to lowest terms by extracting and canceling out 25.

$$-\frac{27}{4}+\frac{31}{4}$$

Since -\frac{27}{4} and \frac{31}{4} have the same denominator, add them by adding their numerators.

$$\frac{-27+31}{4}$$

Add -27 and 31 to get 4.

$$\frac{4}{4}$$

Divide 4 by 4 to get 1.

$$1$$

Factor

$$1$$