Solve (-4)*left(1/3+3/8+2/5right)

$$(-4) \times \left( \frac{ 1 }{ 3 } + \frac{ 3 }{ 8 } + \frac{ 2 }{ 5 } \right)$$

Evaluate

$$-\frac{133}{30}\approx -4.433333333$$

Solution Steps

Least common multiple of 3 and 8 is 24. Convert \frac{1}{3} and \frac{3}{8} to fractions with denominator 24.

$$-4\left(\frac{8}{24}+\frac{9}{24}+\frac{2}{5}\right)$$

Since \frac{8}{24} and \frac{9}{24} have the same denominator, add them by adding their numerators.

$$-4\left(\frac{8+9}{24}+\frac{2}{5}\right)$$

Add 8 and 9 to get 17.

$$-4\left(\frac{17}{24}+\frac{2}{5}\right)$$

Least common multiple of 24 and 5 is 120. Convert \frac{17}{24} and \frac{2}{5} to fractions with denominator 120.

$$-4\left(\frac{85}{120}+\frac{48}{120}\right)$$

Since \frac{85}{120} and \frac{48}{120} have the same denominator, add them by adding their numerators.

$$-4\times \frac{85+48}{120}$$

Add 85 and 48 to get 133.

$$-4\times \frac{133}{120}$$

Express -4\times \frac{133}{120} as a single fraction.

$$\frac{-4\times 133}{120}$$

Multiply -4 and 133 to get -532.

$$\frac{-532}{120}$$

Reduce the fraction \frac{-532}{120} to lowest terms by extracting and canceling out 4.

$$-\frac{133}{30}$$

Factor

$$-\frac{133}{30} = -4\frac{13}{30} = -4.433333333333334$$