Solve -17/20(7/3-9/2+21/4)

$$- \frac{ 17 }{ 20 } ( \frac{ 7 }{ 3 } - \frac{ 9 }{ 2 } + \frac{ 21 }{ 4 } )$$

Evaluate

$$-\frac{629}{240}\approx -2.620833333$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{7}{3} and \frac{9}{2} to fractions with denominator 6.

$$-\frac{17}{20}\left(\frac{14}{6}-\frac{27}{6}+\frac{21}{4}\right)$$

Since \frac{14}{6} and \frac{27}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{17}{20}\left(\frac{14-27}{6}+\frac{21}{4}\right)$$

Subtract 27 from 14 to get -13.

$$-\frac{17}{20}\left(-\frac{13}{6}+\frac{21}{4}\right)$$

Least common multiple of 6 and 4 is 12. Convert -\frac{13}{6} and \frac{21}{4} to fractions with denominator 12.

$$-\frac{17}{20}\left(-\frac{26}{12}+\frac{63}{12}\right)$$

Since -\frac{26}{12} and \frac{63}{12} have the same denominator, add them by adding their numerators.

$$-\frac{17}{20}\times \frac{-26+63}{12}$$

Add -26 and 63 to get 37.

$$-\frac{17}{20}\times \frac{37}{12}$$

Multiply -\frac{17}{20} times \frac{37}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-17\times 37}{20\times 12}$$

Do the multiplications in the fraction \frac{-17\times 37}{20\times 12}.

$$\frac{-629}{240}$$

Fraction \frac{-629}{240} can be rewritten as -\frac{629}{240} by extracting the negative sign.

$$-\frac{629}{240}$$

Factor

$$-\frac{629}{240} = -2\frac{149}{240} = -2.620833333333333$$