Solve -300*8/27+50*4/9+100*2/9+150*1/27

$$- 300 \times \frac { 8 } { 27 } + 50 \cdot \frac { 4 } { 9 } + 100 \times \frac { 2 } { 9 } + 150 \times \frac { 1 } { 27 }$$

Evaluate

$$-\frac{350}{9}\approx -38.888888889$$

Solution Steps

Express -300\times \frac{8}{27} as a single fraction.

$$\frac{-300\times 8}{27}+50\times \frac{4}{9}+100\times \frac{2}{9}+150\times \frac{1}{27}$$

Multiply -300 and 8 to get -2400.

$$\frac{-2400}{27}+50\times \frac{4}{9}+100\times \frac{2}{9}+150\times \frac{1}{27}$$

Reduce the fraction \frac{-2400}{27} to lowest terms by extracting and canceling out 3.

$$-\frac{800}{9}+50\times \frac{4}{9}+100\times \frac{2}{9}+150\times \frac{1}{27}$$

Express 50\times \frac{4}{9} as a single fraction.

$$-\frac{800}{9}+\frac{50\times 4}{9}+100\times \frac{2}{9}+150\times \frac{1}{27}$$

Multiply 50 and 4 to get 200.

$$-\frac{800}{9}+\frac{200}{9}+100\times \frac{2}{9}+150\times \frac{1}{27}$$

Since -\frac{800}{9} and \frac{200}{9} have the same denominator, add them by adding their numerators.

$$\frac{-800+200}{9}+100\times \frac{2}{9}+150\times \frac{1}{27}$$

Add -800 and 200 to get -600.

$$\frac{-600}{9}+100\times \frac{2}{9}+150\times \frac{1}{27}$$

Reduce the fraction \frac{-600}{9} to lowest terms by extracting and canceling out 3.

$$-\frac{200}{3}+100\times \frac{2}{9}+150\times \frac{1}{27}$$

Express 100\times \frac{2}{9} as a single fraction.

$$-\frac{200}{3}+\frac{100\times 2}{9}+150\times \frac{1}{27}$$

Multiply 100 and 2 to get 200.

$$-\frac{200}{3}+\frac{200}{9}+150\times \frac{1}{27}$$

Least common multiple of 3 and 9 is 9. Convert -\frac{200}{3} and \frac{200}{9} to fractions with denominator 9.

$$-\frac{600}{9}+\frac{200}{9}+150\times \frac{1}{27}$$

Since -\frac{600}{9} and \frac{200}{9} have the same denominator, add them by adding their numerators.

$$\frac{-600+200}{9}+150\times \frac{1}{27}$$

Add -600 and 200 to get -400.

$$-\frac{400}{9}+150\times \frac{1}{27}$$

Multiply 150 and \frac{1}{27} to get \frac{150}{27}.

$$-\frac{400}{9}+\frac{150}{27}$$

Reduce the fraction \frac{150}{27} to lowest terms by extracting and canceling out 3.

$$-\frac{400}{9}+\frac{50}{9}$$

Since -\frac{400}{9} and \frac{50}{9} have the same denominator, add them by adding their numerators.

$$\frac{-400+50}{9}$$

Add -400 and 50 to get -350.

$$-\frac{350}{9}$$

Factor

$$-\frac{350}{9} = -38\frac{8}{9} = -38.888888888888886$$