Solve -1/10+7/8-314/100-782/1000+frac{628}{100}

$$- \frac{ 1 }{ 10 } + \frac{ 7 }{ 8 } - \frac{ 314 }{ 100 } - \frac{ 782 }{ 1000 } + \frac{ 628 }{ 100 }$$

Evaluate

$$\frac{3133}{1000}=3.133$$

Solution Steps

Least common multiple of 10 and 8 is 40. Convert -\frac{1}{10} and \frac{7}{8} to fractions with denominator 40.

$$-\frac{4}{40}+\frac{35}{40}-\frac{314}{100}-\frac{782}{1000}+\frac{628}{100}$$

Since -\frac{4}{40} and \frac{35}{40} have the same denominator, add them by adding their numerators.

$$\frac{-4+35}{40}-\frac{314}{100}-\frac{782}{1000}+\frac{628}{100}$$

Add -4 and 35 to get 31.

$$\frac{31}{40}-\frac{314}{100}-\frac{782}{1000}+\frac{628}{100}$$

Reduce the fraction \frac{314}{100} to lowest terms by extracting and canceling out 2.

$$\frac{31}{40}-\frac{157}{50}-\frac{782}{1000}+\frac{628}{100}$$

Least common multiple of 40 and 50 is 200. Convert \frac{31}{40} and \frac{157}{50} to fractions with denominator 200.

$$\frac{155}{200}-\frac{628}{200}-\frac{782}{1000}+\frac{628}{100}$$

Since \frac{155}{200} and \frac{628}{200} have the same denominator, subtract them by subtracting their numerators.

$$\frac{155-628}{200}-\frac{782}{1000}+\frac{628}{100}$$

Subtract 628 from 155 to get -473.

$$-\frac{473}{200}-\frac{782}{1000}+\frac{628}{100}$$

Reduce the fraction \frac{782}{1000} to lowest terms by extracting and canceling out 2.

$$-\frac{473}{200}-\frac{391}{500}+\frac{628}{100}$$

Least common multiple of 200 and 500 is 1000. Convert -\frac{473}{200} and \frac{391}{500} to fractions with denominator 1000.

$$-\frac{2365}{1000}-\frac{782}{1000}+\frac{628}{100}$$

Since -\frac{2365}{1000} and \frac{782}{1000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2365-782}{1000}+\frac{628}{100}$$

Subtract 782 from -2365 to get -3147.

$$-\frac{3147}{1000}+\frac{628}{100}$$

Reduce the fraction \frac{628}{100} to lowest terms by extracting and canceling out 4.

$$-\frac{3147}{1000}+\frac{157}{25}$$

Least common multiple of 1000 and 25 is 1000. Convert -\frac{3147}{1000} and \frac{157}{25} to fractions with denominator 1000.

$$-\frac{3147}{1000}+\frac{6280}{1000}$$

Since -\frac{3147}{1000} and \frac{6280}{1000} have the same denominator, add them by adding their numerators.

$$\frac{-3147+6280}{1000}$$

Add -3147 and 6280 to get 3133.

$$\frac{3133}{1000}$$

Factor

$$\frac{13 \cdot 241}{2 ^ {3} \cdot 5 ^ {3}} = 3\frac{133}{1000} = 3.133$$