Solve 5/4:(-20035/6)+(-20022/3)+(-11/2)+4000frac{3}{4}

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

Evaluate

$$\frac{288058967}{144276}\approx 1996.582709529$$

Solution Steps

Multiply 2003 and 6 to get 12018.

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

Add 12018 and 5 to get 12023.

$$\frac{\frac{5}{4}}{-\frac{12023}{6}}-\frac{2002\times 3+2}{3}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Divide \frac{5}{4} by -\frac{12023}{6} by multiplying \frac{5}{4} by the reciprocal of -\frac{12023}{6}.

$$\frac{5}{4}\left(-\frac{6}{12023}\right)-\frac{2002\times 3+2}{3}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Multiply \frac{5}{4} times -\frac{6}{12023} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-6\right)}{4\times 12023}-\frac{2002\times 3+2}{3}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Do the multiplications in the fraction \frac{5\left(-6\right)}{4\times 12023}.

$$\frac{-30}{48092}-\frac{2002\times 3+2}{3}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Reduce the fraction \frac{-30}{48092} to lowest terms by extracting and canceling out 2.

$$-\frac{15}{24046}-\frac{2002\times 3+2}{3}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Multiply 2002 and 3 to get 6006.

$$-\frac{15}{24046}-\frac{6006+2}{3}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Add 6006 and 2 to get 6008.

$$-\frac{15}{24046}-\frac{6008}{3}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Least common multiple of 24046 and 3 is 72138. Convert -\frac{15}{24046} and \frac{6008}{3} to fractions with denominator 72138.

$$-\frac{45}{72138}-\frac{144468368}{72138}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Since -\frac{45}{72138} and \frac{144468368}{72138} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-45-144468368}{72138}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Subtract 144468368 from -45 to get -144468413.

$$-\frac{144468413}{72138}-\frac{1\times 2+1}{2}+\frac{4000\times 4+3}{4}$$

Multiply 1 and 2 to get 2.

$$-\frac{144468413}{72138}-\frac{2+1}{2}+\frac{4000\times 4+3}{4}$$

Add 2 and 1 to get 3.

$$-\frac{144468413}{72138}-\frac{3}{2}+\frac{4000\times 4+3}{4}$$

Least common multiple of 72138 and 2 is 72138. Convert -\frac{144468413}{72138} and \frac{3}{2} to fractions with denominator 72138.

$$-\frac{144468413}{72138}-\frac{108207}{72138}+\frac{4000\times 4+3}{4}$$

Since -\frac{144468413}{72138} and \frac{108207}{72138} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-144468413-108207}{72138}+\frac{4000\times 4+3}{4}$$

Subtract 108207 from -144468413 to get -144576620.

$$\frac{-144576620}{72138}+\frac{4000\times 4+3}{4}$$

Reduce the fraction \frac{-144576620}{72138} to lowest terms by extracting and canceling out 2.

$$-\frac{72288310}{36069}+\frac{4000\times 4+3}{4}$$

Multiply 4000 and 4 to get 16000.

$$-\frac{72288310}{36069}+\frac{16000+3}{4}$$

Add 16000 and 3 to get 16003.

$$-\frac{72288310}{36069}+\frac{16003}{4}$$

Least common multiple of 36069 and 4 is 144276. Convert -\frac{72288310}{36069} and \frac{16003}{4} to fractions with denominator 144276.

$$-\frac{289153240}{144276}+\frac{577212207}{144276}$$

Since -\frac{289153240}{144276} and \frac{577212207}{144276} have the same denominator, add them by adding their numerators.

$$\frac{-289153240+577212207}{144276}$$

Add -289153240 and 577212207 to get 288058967.

$$\frac{288058967}{144276}$$

Factor

$$\frac{7 \cdot 103 \cdot 399527}{2 ^ {2} \cdot 3 \cdot 11 \cdot 1093} = 1996\frac{84071}{144276} = 1996.5827095289583$$