Solve (-20035/6)+(-20022/3)+(-11/2)+40003/4

$$( - 2003 \frac { 5 } { 6 } ) + ( - 2002 \frac { 2 } { 3 } ) + ( - 1 \frac { 1 } { 2 } ) + 4000 \frac { 3 } { 4 }$$

Evaluate

$$-\frac{29}{4}=-7.25$$

Solution Steps

Multiply 2003 and 6 to get 12018.

$$-\frac{12018+5}{6}-\frac{2002\times 3+2}{3}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Add 12018 and 5 to get 12023.

$$-\frac{12023}{6}-\frac{2002\times 3+2}{3}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Multiply 2002 and 3 to get 6006.

$$-\frac{12023}{6}-\frac{6006+2}{3}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Add 6006 and 2 to get 6008.

$$-\frac{12023}{6}-\frac{6008}{3}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Least common multiple of 6 and 3 is 6. Convert -\frac{12023}{6} and \frac{6008}{3} to fractions with denominator 6.

$$-\frac{12023}{6}-\frac{12016}{6}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Since -\frac{12023}{6} and \frac{12016}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-12023-12016}{6}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Subtract 12016 from -12023 to get -24039.

$$\frac{-24039}{6}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Reduce the fraction \frac{-24039}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{8013}{2}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Multiply 1 and 2 to get 2.

$$-\frac{8013}{2}-\frac{2+1}{2}+\frac{4000\times 4+3}{4}$$

Add 2 and 1 to get 3.

$$-\frac{8013}{2}-\frac{3}{2}+\frac{4000\times 4+3}{4}$$

Since -\frac{8013}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-8013-3}{2}+\frac{4000\times 4+3}{4}$$

Subtract 3 from -8013 to get -8016.

$$\frac{-8016}{2}+\frac{4000\times 4+3}{4}$$

Divide -8016 by 2 to get -4008.

$$-4008+\frac{4000\times 4+3}{4}$$

Multiply 4000 and 4 to get 16000.

$$-4008+\frac{16000+3}{4}$$

Add 16000 and 3 to get 16003.

$$-4008+\frac{16003}{4}$$

Convert -4008 to fraction -\frac{16032}{4}.

$$-\frac{16032}{4}+\frac{16003}{4}$$

Since -\frac{16032}{4} and \frac{16003}{4} have the same denominator, add them by adding their numerators.

$$\frac{-16032+16003}{4}$$

Add -16032 and 16003 to get -29.

$$-\frac{29}{4}$$

Factor

$$-\frac{29}{4} = -7\frac{1}{4} = -7.25$$