Solve 100002/3-4000-8/27-8000-4/9+240002/3

$$10000 \frac { 2 } { 3 } - 4000 - \frac { 8 } { 27 } - 8000 - \frac { 4 } { 9 } + 24000 \frac { 2 } { 3 }$$

Evaluate

$$\frac{594016}{27}\approx 22000.592592593$$

Solution Steps

Multiply 10000 and 3 to get 30000.

$$\frac{30000+2}{3}-4000-\frac{8}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Add 30000 and 2 to get 30002.

$$\frac{30002}{3}-4000-\frac{8}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Convert 4000 to fraction \frac{12000}{3}.

$$\frac{30002}{3}-\frac{12000}{3}-\frac{8}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Since \frac{30002}{3} and \frac{12000}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30002-12000}{3}-\frac{8}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Subtract 12000 from 30002 to get 18002.

$$\frac{18002}{3}-\frac{8}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Least common multiple of 3 and 27 is 27. Convert \frac{18002}{3} and \frac{8}{27} to fractions with denominator 27.

$$\frac{162018}{27}-\frac{8}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Since \frac{162018}{27} and \frac{8}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{162018-8}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Subtract 8 from 162018 to get 162010.

$$\frac{162010}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Convert 8000 to fraction \frac{216000}{27}.

$$\frac{162010}{27}-\frac{216000}{27}-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Since \frac{162010}{27} and \frac{216000}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{162010-216000}{27}-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Subtract 216000 from 162010 to get -53990.

$$-\frac{53990}{27}-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Least common multiple of 27 and 9 is 27. Convert -\frac{53990}{27} and \frac{4}{9} to fractions with denominator 27.

$$-\frac{53990}{27}-\frac{12}{27}+\frac{24000\times 3+2}{3}$$

Since -\frac{53990}{27} and \frac{12}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-53990-12}{27}+\frac{24000\times 3+2}{3}$$

Subtract 12 from -53990 to get -54002.

$$-\frac{54002}{27}+\frac{24000\times 3+2}{3}$$

Multiply 24000 and 3 to get 72000.

$$-\frac{54002}{27}+\frac{72000+2}{3}$$

Add 72000 and 2 to get 72002.

$$-\frac{54002}{27}+\frac{72002}{3}$$

Least common multiple of 27 and 3 is 27. Convert -\frac{54002}{27} and \frac{72002}{3} to fractions with denominator 27.

$$-\frac{54002}{27}+\frac{648018}{27}$$

Since -\frac{54002}{27} and \frac{648018}{27} have the same denominator, add them by adding their numerators.

$$\frac{-54002+648018}{27}$$

Add -54002 and 648018 to get 594016.

$$\frac{594016}{27}$$

Factor

$$\frac{2 ^ {5} \cdot 19 \cdot 977}{3 ^ {3}} = 22000\frac{16}{27} = 22000.59259259259$$