Solve (-121/2)-[-(+6.5)-(-6.3)-61/5]

$$( - 12 \frac { 1 } { 2 } ) - [ - ( + 6.5 ) - ( - 6.3 ) - 6 \frac { 1 } { 5 } ]$$

Evaluate

$$-6.1$$

Solution Steps

Multiply 12 and 2 to get 24.

$$-\frac{24+1}{2}-\left(-6.5-\left(-6.3\right)-\frac{6\times 5+1}{5}\right)$$

Add 24 and 1 to get 25.

$$-\frac{25}{2}-\left(-6.5-\left(-6.3\right)-\frac{6\times 5+1}{5}\right)$$

The opposite of -6.3 is 6.3.

$$-\frac{25}{2}-\left(-6.5+6.3-\frac{6\times 5+1}{5}\right)$$

Add -6.5 and 6.3 to get -0.2.

$$-\frac{25}{2}-\left(-0.2-\frac{6\times 5+1}{5}\right)$$

Multiply 6 and 5 to get 30.

$$-\frac{25}{2}-\left(-0.2-\frac{30+1}{5}\right)$$

Add 30 and 1 to get 31.

$$-\frac{25}{2}-\left(-0.2-\frac{31}{5}\right)$$

Convert decimal number -0.2 to fraction -\frac{2}{10}. Reduce the fraction -\frac{2}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{25}{2}-\left(-\frac{1}{5}-\frac{31}{5}\right)$$

Since -\frac{1}{5} and \frac{31}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{25}{2}-\frac{-1-31}{5}$$

Subtract 31 from -1 to get -32.

$$-\frac{25}{2}-\left(-\frac{32}{5}\right)$$

The opposite of -\frac{32}{5} is \frac{32}{5}.

$$-\frac{25}{2}+\frac{32}{5}$$

Least common multiple of 2 and 5 is 10. Convert -\frac{25}{2} and \frac{32}{5} to fractions with denominator 10.

$$-\frac{125}{10}+\frac{64}{10}$$

Since -\frac{125}{10} and \frac{64}{10} have the same denominator, add them by adding their numerators.

$$\frac{-125+64}{10}$$

Add -125 and 64 to get -61.

$$-\frac{61}{10}$$

Factor

$$-6.1$$