Solve (-1/2)-4.1-(-11/2)-(-10.1)-7

$$( - \frac { 1 } { 2 } ) - 4.1 - ( - 1 \frac { 1 } { 2 } ) - ( - 10.1 ) - 7$$

Evaluate

$$0$$

Solution Steps

Convert decimal number 4.1 to fraction \frac{41}{10}.

$$-\frac{1}{2}-\frac{41}{10}-\left(-\frac{1\times 2+1}{2}\right)-\left(-10.1\right)-7$$

Least common multiple of 2 and 10 is 10. Convert -\frac{1}{2} and \frac{41}{10} to fractions with denominator 10.

$$-\frac{5}{10}-\frac{41}{10}-\left(-\frac{1\times 2+1}{2}\right)-\left(-10.1\right)-7$$

Since -\frac{5}{10} and \frac{41}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-41}{10}-\left(-\frac{1\times 2+1}{2}\right)-\left(-10.1\right)-7$$

Subtract 41 from -5 to get -46.

$$\frac{-46}{10}-\left(-\frac{1\times 2+1}{2}\right)-\left(-10.1\right)-7$$

Reduce the fraction \frac{-46}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{23}{5}-\left(-\frac{1\times 2+1}{2}\right)-\left(-10.1\right)-7$$

Multiply 1 and 2 to get 2.

$$-\frac{23}{5}-\left(-\frac{2+1}{2}\right)-\left(-10.1\right)-7$$

Add 2 and 1 to get 3.

$$-\frac{23}{5}-\left(-\frac{3}{2}\right)-\left(-10.1\right)-7$$

The opposite of -\frac{3}{2} is \frac{3}{2}.

$$-\frac{23}{5}+\frac{3}{2}-\left(-10.1\right)-7$$

Least common multiple of 5 and 2 is 10. Convert -\frac{23}{5} and \frac{3}{2} to fractions with denominator 10.

$$-\frac{46}{10}+\frac{15}{10}-\left(-10.1\right)-7$$

Since -\frac{46}{10} and \frac{15}{10} have the same denominator, add them by adding their numerators.

$$\frac{-46+15}{10}-\left(-10.1\right)-7$$

Add -46 and 15 to get -31.

$$-\frac{31}{10}-\left(-10.1\right)-7$$

The opposite of -10.1 is 10.1.

$$-\frac{31}{10}+10.1-7$$

Convert decimal number 10.1 to fraction \frac{101}{10}.

$$-\frac{31}{10}+\frac{101}{10}-7$$

Since -\frac{31}{10} and \frac{101}{10} have the same denominator, add them by adding their numerators.

$$\frac{-31+101}{10}-7$$

Add -31 and 101 to get 70.

$$\frac{70}{10}-7$$

Divide 70 by 10 to get 7.

$$7-7$$

Subtract 7 from 7 to get 0.

$$0$$

Factor

$$0$$