Solve (1/10*(-1/4)+1/5-1/3)*210=

$$( \frac { 1 } { 10 } \cdot ( - \frac { 1 } { 4 } ) + \frac { 1 } { 5 } - \frac { 1 } { 3 } ) \cdot 210 =$$

Evaluate

$$-\frac{133}{4}=-33.25$$

Solution Steps

Multiply \frac{1}{10} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{1\left(-1\right)}{10\times 4}+\frac{1}{5}-\frac{1}{3}\right)\times 210$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{10\times 4}.

$$\left(\frac{-1}{40}+\frac{1}{5}-\frac{1}{3}\right)\times 210$$

Fraction \frac{-1}{40} can be rewritten as -\frac{1}{40} by extracting the negative sign.

$$\left(-\frac{1}{40}+\frac{1}{5}-\frac{1}{3}\right)\times 210$$

Least common multiple of 40 and 5 is 40. Convert -\frac{1}{40} and \frac{1}{5} to fractions with denominator 40.

$$\left(-\frac{1}{40}+\frac{8}{40}-\frac{1}{3}\right)\times 210$$

Since -\frac{1}{40} and \frac{8}{40} have the same denominator, add them by adding their numerators.

$$\left(\frac{-1+8}{40}-\frac{1}{3}\right)\times 210$$

Add -1 and 8 to get 7.

$$\left(\frac{7}{40}-\frac{1}{3}\right)\times 210$$

Least common multiple of 40 and 3 is 120. Convert \frac{7}{40} and \frac{1}{3} to fractions with denominator 120.

$$\left(\frac{21}{120}-\frac{40}{120}\right)\times 210$$

Since \frac{21}{120} and \frac{40}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-40}{120}\times 210$$

Subtract 40 from 21 to get -19.

$$-\frac{19}{120}\times 210$$

Express -\frac{19}{120}\times 210 as a single fraction.

$$\frac{-19\times 210}{120}$$

Multiply -19 and 210 to get -3990.

$$\frac{-3990}{120}$$

Reduce the fraction \frac{-3990}{120} to lowest terms by extracting and canceling out 30.

$$-\frac{133}{4}$$

Factor

$$-\frac{133}{4} = -33\frac{1}{4} = -33.25$$