Solve (-10.9)+3.1-[(-38/9)-81/2-(-8.5)]

$$( - 10.9 ) + 3.1 - [ ( - 3 \frac { 8 } { 9 } ) - 8 \frac { 1 } { 2 } - ( - 8.5 ) ]$$

Evaluate

$$-\frac{176}{45}\approx -3.911111111$$

Solution Steps

Add -10.9 and 3.1 to get -7.8.

$$-7.8-\left(-\frac{3\times 9+8}{9}-\frac{8\times 2+1}{2}-\left(-8.5\right)\right)$$

Multiply 3 and 9 to get 27.

$$-7.8-\left(-\frac{27+8}{9}-\frac{8\times 2+1}{2}-\left(-8.5\right)\right)$$

Add 27 and 8 to get 35.

$$-7.8-\left(-\frac{35}{9}-\frac{8\times 2+1}{2}-\left(-8.5\right)\right)$$

Multiply 8 and 2 to get 16.

$$-7.8-\left(-\frac{35}{9}-\frac{16+1}{2}-\left(-8.5\right)\right)$$

Add 16 and 1 to get 17.

$$-7.8-\left(-\frac{35}{9}-\frac{17}{2}-\left(-8.5\right)\right)$$

Least common multiple of 9 and 2 is 18. Convert -\frac{35}{9} and \frac{17}{2} to fractions with denominator 18.

$$-7.8-\left(-\frac{70}{18}-\frac{153}{18}-\left(-8.5\right)\right)$$

Since -\frac{70}{18} and \frac{153}{18} have the same denominator, subtract them by subtracting their numerators.

$$-7.8-\left(\frac{-70-153}{18}-\left(-8.5\right)\right)$$

Subtract 153 from -70 to get -223.

$$-7.8-\left(-\frac{223}{18}-\left(-8.5\right)\right)$$

The opposite of -8.5 is 8.5.

$$-7.8-\left(-\frac{223}{18}+8.5\right)$$

Convert decimal number 8.5 to fraction \frac{85}{10}. Reduce the fraction \frac{85}{10} to lowest terms by extracting and canceling out 5.

$$-7.8-\left(-\frac{223}{18}+\frac{17}{2}\right)$$

Least common multiple of 18 and 2 is 18. Convert -\frac{223}{18} and \frac{17}{2} to fractions with denominator 18.

$$-7.8-\left(-\frac{223}{18}+\frac{153}{18}\right)$$

Since -\frac{223}{18} and \frac{153}{18} have the same denominator, add them by adding their numerators.

$$-7.8-\frac{-223+153}{18}$$

Add -223 and 153 to get -70.

$$-7.8-\frac{-70}{18}$$

Reduce the fraction \frac{-70}{18} to lowest terms by extracting and canceling out 2.

$$-7.8-\left(-\frac{35}{9}\right)$$

The opposite of -\frac{35}{9} is \frac{35}{9}.

$$-7.8+\frac{35}{9}$$

Convert decimal number -7.8 to fraction -\frac{78}{10}. Reduce the fraction -\frac{78}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{39}{5}+\frac{35}{9}$$

Least common multiple of 5 and 9 is 45. Convert -\frac{39}{5} and \frac{35}{9} to fractions with denominator 45.

$$-\frac{351}{45}+\frac{175}{45}$$

Since -\frac{351}{45} and \frac{175}{45} have the same denominator, add them by adding their numerators.

$$\frac{-351+175}{45}$$

Add -351 and 175 to get -176.

$$-\frac{176}{45}$$

Factor

$$-\frac{176}{45} = -3\frac{41}{45} = -3.911111111111111$$