Solve 900*4/9+800*2/9+700*1/27+1000*8/27

$$900 \times \frac { 4 } { 9 } + 800 \times \frac { 2 } { 9 } + 700 \times \frac { 1 } { 27 } + 1000 \times \frac { 8 } { 27 }$$

Evaluate

$$900$$

Solution Steps

Express 900\times \frac{4}{9} as a single fraction.

$$\frac{900\times 4}{9}+800\times \frac{2}{9}+700\times \frac{1}{27}+1000\times \frac{8}{27}$$

Multiply 900 and 4 to get 3600.

$$\frac{3600}{9}+800\times \frac{2}{9}+700\times \frac{1}{27}+1000\times \frac{8}{27}$$

Divide 3600 by 9 to get 400.

$$400+800\times \frac{2}{9}+700\times \frac{1}{27}+1000\times \frac{8}{27}$$

Express 800\times \frac{2}{9} as a single fraction.

$$400+\frac{800\times 2}{9}+700\times \frac{1}{27}+1000\times \frac{8}{27}$$

Multiply 800 and 2 to get 1600.

$$400+\frac{1600}{9}+700\times \frac{1}{27}+1000\times \frac{8}{27}$$

Convert 400 to fraction \frac{3600}{9}.

$$\frac{3600}{9}+\frac{1600}{9}+700\times \frac{1}{27}+1000\times \frac{8}{27}$$

Since \frac{3600}{9} and \frac{1600}{9} have the same denominator, add them by adding their numerators.

$$\frac{3600+1600}{9}+700\times \frac{1}{27}+1000\times \frac{8}{27}$$

Add 3600 and 1600 to get 5200.

$$\frac{5200}{9}+700\times \frac{1}{27}+1000\times \frac{8}{27}$$

Multiply 700 and \frac{1}{27} to get \frac{700}{27}.

$$\frac{5200}{9}+\frac{700}{27}+1000\times \frac{8}{27}$$

Least common multiple of 9 and 27 is 27. Convert \frac{5200}{9} and \frac{700}{27} to fractions with denominator 27.

$$\frac{15600}{27}+\frac{700}{27}+1000\times \frac{8}{27}$$

Since \frac{15600}{27} and \frac{700}{27} have the same denominator, add them by adding their numerators.

$$\frac{15600+700}{27}+1000\times \frac{8}{27}$$

Add 15600 and 700 to get 16300.

$$\frac{16300}{27}+1000\times \frac{8}{27}$$

Express 1000\times \frac{8}{27} as a single fraction.

$$\frac{16300}{27}+\frac{1000\times 8}{27}$$

Multiply 1000 and 8 to get 8000.

$$\frac{16300}{27}+\frac{8000}{27}$$

Since \frac{16300}{27} and \frac{8000}{27} have the same denominator, add them by adding their numerators.

$$\frac{16300+8000}{27}$$

Add 16300 and 8000 to get 24300.

$$\frac{24300}{27}$$

Divide 24300 by 27 to get 900.

$$900$$

Factor

$$2^{2}\times 3^{2}\times 5^{2}$$