Solve (-2/3)+(-8.7)-(-32/3)-(-9)

$$( - \frac { 2 } { 3 } ) + ( - 8.7 ) - ( - 3 \frac { 2 } { 3 } ) - ( - 9 )$$

Evaluate

$$3.3$$

Solution Steps

Convert decimal number 8.7 to fraction \frac{87}{10}.

$$-\frac{2}{3}-\frac{87}{10}-\left(-\frac{3\times 3+2}{3}\right)-\left(-9\right)$$

Least common multiple of 3 and 10 is 30. Convert -\frac{2}{3} and \frac{87}{10} to fractions with denominator 30.

$$-\frac{20}{30}-\frac{261}{30}-\left(-\frac{3\times 3+2}{3}\right)-\left(-9\right)$$

Since -\frac{20}{30} and \frac{261}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-20-261}{30}-\left(-\frac{3\times 3+2}{3}\right)-\left(-9\right)$$

Subtract 261 from -20 to get -281.

$$-\frac{281}{30}-\left(-\frac{3\times 3+2}{3}\right)-\left(-9\right)$$

Multiply 3 and 3 to get 9.

$$-\frac{281}{30}-\left(-\frac{9+2}{3}\right)-\left(-9\right)$$

Add 9 and 2 to get 11.

$$-\frac{281}{30}-\left(-\frac{11}{3}\right)-\left(-9\right)$$

The opposite of -\frac{11}{3} is \frac{11}{3}.

$$-\frac{281}{30}+\frac{11}{3}-\left(-9\right)$$

Least common multiple of 30 and 3 is 30. Convert -\frac{281}{30} and \frac{11}{3} to fractions with denominator 30.

$$-\frac{281}{30}+\frac{110}{30}-\left(-9\right)$$

Since -\frac{281}{30} and \frac{110}{30} have the same denominator, add them by adding their numerators.

$$\frac{-281+110}{30}-\left(-9\right)$$

Add -281 and 110 to get -171.

$$\frac{-171}{30}-\left(-9\right)$$

Reduce the fraction \frac{-171}{30} to lowest terms by extracting and canceling out 3.

$$-\frac{57}{10}-\left(-9\right)$$

The opposite of -9 is 9.

$$-\frac{57}{10}+9$$

Convert 9 to fraction \frac{90}{10}.

$$-\frac{57}{10}+\frac{90}{10}$$

Since -\frac{57}{10} and \frac{90}{10} have the same denominator, add them by adding their numerators.

$$\frac{-57+90}{10}$$

Add -57 and 90 to get 33.

$$\frac{33}{10}$$

Factor

$$\frac{3 \cdot 11}{2 \cdot 5} = 3\frac{3}{10} = 3.3$$