Solve (38/100-312/100:3/10)*25/1+frac{1}{9}=

$$( \frac { 38 } { 100 } - \frac { 312 } { 100 } : \frac { 3 } { 10 } ) \cdot \frac { 25 } { 1 } + \frac { 1 } { 9 } =$$

Evaluate

$$-\frac{4507}{18}\approx -250.388888889$$

Solution Steps

Reduce the fraction \frac{38}{100} to lowest terms by extracting and canceling out 2.

$$\left(\frac{19}{50}-\frac{\frac{312}{100}}{\frac{3}{10}}\right)\times \frac{25}{1}+\frac{1}{9}$$

Divide \frac{312}{100} by \frac{3}{10} by multiplying \frac{312}{100} by the reciprocal of \frac{3}{10}.

$$\left(\frac{19}{50}-\frac{312\times 10}{100\times 3}\right)\times \frac{25}{1}+\frac{1}{9}$$

Cancel out 3\times 4\times 5 in both numerator and denominator.

$$\left(\frac{19}{50}-\frac{2\times 26}{5}\right)\times \frac{25}{1}+\frac{1}{9}$$

Multiply 2 and 26 to get 52.

$$\left(\frac{19}{50}-\frac{52}{5}\right)\times \frac{25}{1}+\frac{1}{9}$$

Least common multiple of 50 and 5 is 50. Convert \frac{19}{50} and \frac{52}{5} to fractions with denominator 50.

$$\left(\frac{19}{50}-\frac{520}{50}\right)\times \frac{25}{1}+\frac{1}{9}$$

Since \frac{19}{50} and \frac{520}{50} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19-520}{50}\times \frac{25}{1}+\frac{1}{9}$$

Subtract 520 from 19 to get -501.

$$-\frac{501}{50}\times \frac{25}{1}+\frac{1}{9}$$

Anything divided by one gives itself.

$$-\frac{501}{50}\times 25+\frac{1}{9}$$

Express -\frac{501}{50}\times 25 as a single fraction.

$$\frac{-501\times 25}{50}+\frac{1}{9}$$

Multiply -501 and 25 to get -12525.

$$\frac{-12525}{50}+\frac{1}{9}$$

Reduce the fraction \frac{-12525}{50} to lowest terms by extracting and canceling out 25.

$$-\frac{501}{2}+\frac{1}{9}$$

Least common multiple of 2 and 9 is 18. Convert -\frac{501}{2} and \frac{1}{9} to fractions with denominator 18.

$$-\frac{4509}{18}+\frac{2}{18}$$

Since -\frac{4509}{18} and \frac{2}{18} have the same denominator, add them by adding their numerators.

$$\frac{-4509+2}{18}$$

Add -4509 and 2 to get -4507.

$$-\frac{4507}{18}$$

Factor

$$-\frac{4507}{18} = -250\frac{7}{18} = -250.38888888888889$$