Solve 10.0002/3-4000-8/27-8000-4/9+240002/3

$$10.000 \frac { 2 } { 3 } - 4000 - \frac { 8 } { 27 } - 8000 - \frac { 4 } { 9 } + 24000 \frac { 2 } { 3 }$$

Evaluate

$$\frac{324286}{27}\approx 12010.592592593$$

Solution Steps

Multiply 10 and 3 to get 30.

$$\frac{30+2}{3}-4000-\frac{8}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Add 30 and 2 to get 32.

$$\frac{32}{3}-4000-\frac{8}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

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

$$\frac{32}{3}-\frac{12000}{3}-\frac{8}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Since \frac{32}{3} and \frac{12000}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32-12000}{3}-\frac{8}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Subtract 12000 from 32 to get -11968.

$$-\frac{11968}{3}-\frac{8}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Least common multiple of 3 and 27 is 27. Convert -\frac{11968}{3} and \frac{8}{27} to fractions with denominator 27.

$$-\frac{107712}{27}-\frac{8}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Since -\frac{107712}{27} and \frac{8}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-107712-8}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Subtract 8 from -107712 to get -107720.

$$-\frac{107720}{27}-8000-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

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

$$-\frac{107720}{27}-\frac{216000}{27}-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Since -\frac{107720}{27} and \frac{216000}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-107720-216000}{27}-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Subtract 216000 from -107720 to get -323720.

$$-\frac{323720}{27}-\frac{4}{9}+\frac{24000\times 3+2}{3}$$

Least common multiple of 27 and 9 is 27. Convert -\frac{323720}{27} and \frac{4}{9} to fractions with denominator 27.

$$-\frac{323720}{27}-\frac{12}{27}+\frac{24000\times 3+2}{3}$$

Since -\frac{323720}{27} and \frac{12}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-323720-12}{27}+\frac{24000\times 3+2}{3}$$

Subtract 12 from -323720 to get -323732.

$$-\frac{323732}{27}+\frac{24000\times 3+2}{3}$$

Multiply 24000 and 3 to get 72000.

$$-\frac{323732}{27}+\frac{72000+2}{3}$$

Add 72000 and 2 to get 72002.

$$-\frac{323732}{27}+\frac{72002}{3}$$

Least common multiple of 27 and 3 is 27. Convert -\frac{323732}{27} and \frac{72002}{3} to fractions with denominator 27.

$$-\frac{323732}{27}+\frac{648018}{27}$$

Since -\frac{323732}{27} and \frac{648018}{27} have the same denominator, add them by adding their numerators.

$$\frac{-323732+648018}{27}$$

Add -323732 and 648018 to get 324286.

$$\frac{324286}{27}$$

Factor

$$\frac{2 \cdot 162143}{3 ^ {3}} = 12010\frac{16}{27} = 12010.592592592593$$