Solve [194/900-244/99]*(3/7-(-5/2))

$$[ \frac { 194 } { 900 } - \frac { 244 } { 99 } ] \cdot ( \frac { 3 } { 7 } - ( - \frac { 5 } { 2 } ) )$$

Evaluate

$$-\frac{50717}{7700}\approx -6.586623377$$

Solution Steps

Reduce the fraction \frac{194}{900} to lowest terms by extracting and canceling out 2.

$$\left(\frac{97}{450}-\frac{244}{99}\right)\left(\frac{3}{7}-\left(-\frac{5}{2}\right)\right)$$

Least common multiple of 450 and 99 is 4950. Convert \frac{97}{450} and \frac{244}{99} to fractions with denominator 4950.

$$\left(\frac{1067}{4950}-\frac{12200}{4950}\right)\left(\frac{3}{7}-\left(-\frac{5}{2}\right)\right)$$

Since \frac{1067}{4950} and \frac{12200}{4950} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1067-12200}{4950}\left(\frac{3}{7}-\left(-\frac{5}{2}\right)\right)$$

Subtract 12200 from 1067 to get -11133.

$$\frac{-11133}{4950}\left(\frac{3}{7}-\left(-\frac{5}{2}\right)\right)$$

Reduce the fraction \frac{-11133}{4950} to lowest terms by extracting and canceling out 9.

$$-\frac{1237}{550}\left(\frac{3}{7}-\left(-\frac{5}{2}\right)\right)$$

The opposite of -\frac{5}{2} is \frac{5}{2}.

$$-\frac{1237}{550}\left(\frac{3}{7}+\frac{5}{2}\right)$$

Least common multiple of 7 and 2 is 14. Convert \frac{3}{7} and \frac{5}{2} to fractions with denominator 14.

$$-\frac{1237}{550}\left(\frac{6}{14}+\frac{35}{14}\right)$$

Since \frac{6}{14} and \frac{35}{14} have the same denominator, add them by adding their numerators.

$$-\frac{1237}{550}\times \frac{6+35}{14}$$

Add 6 and 35 to get 41.

$$-\frac{1237}{550}\times \frac{41}{14}$$

Multiply -\frac{1237}{550} times \frac{41}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-1237\times 41}{550\times 14}$$

Do the multiplications in the fraction \frac{-1237\times 41}{550\times 14}.

$$\frac{-50717}{7700}$$

Fraction \frac{-50717}{7700} can be rewritten as -\frac{50717}{7700} by extracting the negative sign.

$$-\frac{50717}{7700}$$

Factor

$$-\frac{50717}{7700} = -6\frac{4517}{7700} = -6.586623376623376$$