Solve (-20115/6)+(-20122/3)+4023+(-11/2)

$$( - 2011 \frac { 5 } { 6 } ) + ( - 2012 \frac { 2 } { 3 } ) + 4023 + ( - 1 \frac { 1 } { 2 } )$$

Evaluate

$$-3$$

Solution Steps

Multiply 2011 and 6 to get 12066.

$$-\frac{12066+5}{6}-\frac{2012\times 3+2}{3}+4023-\frac{1\times 2+1}{2}$$

Add 12066 and 5 to get 12071.

$$-\frac{12071}{6}-\frac{2012\times 3+2}{3}+4023-\frac{1\times 2+1}{2}$$

Multiply 2012 and 3 to get 6036.

$$-\frac{12071}{6}-\frac{6036+2}{3}+4023-\frac{1\times 2+1}{2}$$

Add 6036 and 2 to get 6038.

$$-\frac{12071}{6}-\frac{6038}{3}+4023-\frac{1\times 2+1}{2}$$

Least common multiple of 6 and 3 is 6. Convert -\frac{12071}{6} and \frac{6038}{3} to fractions with denominator 6.

$$-\frac{12071}{6}-\frac{12076}{6}+4023-\frac{1\times 2+1}{2}$$

Since -\frac{12071}{6} and \frac{12076}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-12071-12076}{6}+4023-\frac{1\times 2+1}{2}$$

Subtract 12076 from -12071 to get -24147.

$$\frac{-24147}{6}+4023-\frac{1\times 2+1}{2}$$

Reduce the fraction \frac{-24147}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{8049}{2}+4023-\frac{1\times 2+1}{2}$$

Convert 4023 to fraction \frac{8046}{2}.

$$-\frac{8049}{2}+\frac{8046}{2}-\frac{1\times 2+1}{2}$$

Since -\frac{8049}{2} and \frac{8046}{2} have the same denominator, add them by adding their numerators.

$$\frac{-8049+8046}{2}-\frac{1\times 2+1}{2}$$

Add -8049 and 8046 to get -3.

$$-\frac{3}{2}-\frac{1\times 2+1}{2}$$

Multiply 1 and 2 to get 2.

$$-\frac{3}{2}-\frac{2+1}{2}$$

Add 2 and 1 to get 3.

$$-\frac{3}{2}-\frac{3}{2}$$

Since -\frac{3}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3-3}{2}$$

Subtract 3 from -3 to get -6.

$$\frac{-6}{2}$$

Divide -6 by 2 to get -3.

$$-3$$

Factor

$$-3$$