Solve -33/5left(2/3-2.75right)

$$-3 \frac{ 3 }{ 5 } \left( \frac{ 2 }{ 3 } -2.75 \right)$$

Evaluate

$$7.5$$

Solution Steps

Multiply 3 and 5 to get 15.

$$\left(-\frac{15+3}{5}\right)\left(\frac{2}{3}-2.75\right)$$

Add 15 and 3 to get 18.

$$-\frac{18}{5}\left(\frac{2}{3}-2.75\right)$$

Convert decimal number 2.75 to fraction \frac{275}{100}. Reduce the fraction \frac{275}{100} to lowest terms by extracting and canceling out 25.

$$-\frac{18}{5}\left(\frac{2}{3}-\frac{11}{4}\right)$$

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{11}{4} to fractions with denominator 12.

$$-\frac{18}{5}\left(\frac{8}{12}-\frac{33}{12}\right)$$

Since \frac{8}{12} and \frac{33}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{18}{5}\times \frac{8-33}{12}$$

Subtract 33 from 8 to get -25.

$$-\frac{18}{5}\left(-\frac{25}{12}\right)$$

Multiply -\frac{18}{5} times -\frac{25}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-18\left(-25\right)}{5\times 12}$$

Do the multiplications in the fraction \frac{-18\left(-25\right)}{5\times 12}.

$$\frac{450}{60}$$

Reduce the fraction \frac{450}{60} to lowest terms by extracting and canceling out 30.

$$\frac{15}{2}$$

Factor

$$\frac{3 \cdot 5}{2} = 7\frac{1}{2} = 7.5$$