Solve 1/2.7+1/2.7+1/2.7+1/2.7+frac{1}{2.7}+frac{1}{2.7}=

$$\frac{ 1 }{ 2.7 } + \frac{ 1 }{ 2.7 } + \frac{ 1 }{ 2.7 } + \frac{ 1 }{ 2.7 } + \frac{ 1 }{ 2.7 } + \frac{ 1 }{ 2.7 } =$$

Evaluate

$$\frac{20}{9}\approx 2.222222222$$

Solution Steps

Expand \frac{1}{2.7} by multiplying both numerator and the denominator by 10.

$$\frac{10}{27}+\frac{1}{2.7}+\frac{1}{2.7}+\frac{1}{2.7}+\frac{1}{2.7}+\frac{1}{2.7}$$

Expand \frac{1}{2.7} by multiplying both numerator and the denominator by 10.

$$\frac{10}{27}+\frac{10}{27}+\frac{1}{2.7}+\frac{1}{2.7}+\frac{1}{2.7}+\frac{1}{2.7}$$

Since \frac{10}{27} and \frac{10}{27} have the same denominator, add them by adding their numerators.

$$\frac{10+10}{27}+\frac{1}{2.7}+\frac{1}{2.7}+\frac{1}{2.7}+\frac{1}{2.7}$$

Add 10 and 10 to get 20.

$$\frac{20}{27}+\frac{1}{2.7}+\frac{1}{2.7}+\frac{1}{2.7}+\frac{1}{2.7}$$

Expand \frac{1}{2.7} by multiplying both numerator and the denominator by 10.

$$\frac{20}{27}+\frac{10}{27}+\frac{1}{2.7}+\frac{1}{2.7}+\frac{1}{2.7}$$

Since \frac{20}{27} and \frac{10}{27} have the same denominator, add them by adding their numerators.

$$\frac{20+10}{27}+\frac{1}{2.7}+\frac{1}{2.7}+\frac{1}{2.7}$$

Add 20 and 10 to get 30.

$$\frac{30}{27}+\frac{1}{2.7}+\frac{1}{2.7}+\frac{1}{2.7}$$

Reduce the fraction \frac{30}{27} to lowest terms by extracting and canceling out 3.

$$\frac{10}{9}+\frac{1}{2.7}+\frac{1}{2.7}+\frac{1}{2.7}$$

Expand \frac{1}{2.7} by multiplying both numerator and the denominator by 10.

$$\frac{10}{9}+\frac{10}{27}+\frac{1}{2.7}+\frac{1}{2.7}$$

Least common multiple of 9 and 27 is 27. Convert \frac{10}{9} and \frac{10}{27} to fractions with denominator 27.

$$\frac{30}{27}+\frac{10}{27}+\frac{1}{2.7}+\frac{1}{2.7}$$

Since \frac{30}{27} and \frac{10}{27} have the same denominator, add them by adding their numerators.

$$\frac{30+10}{27}+\frac{1}{2.7}+\frac{1}{2.7}$$

Add 30 and 10 to get 40.

$$\frac{40}{27}+\frac{1}{2.7}+\frac{1}{2.7}$$

Expand \frac{1}{2.7} by multiplying both numerator and the denominator by 10.

$$\frac{40}{27}+\frac{10}{27}+\frac{1}{2.7}$$

Since \frac{40}{27} and \frac{10}{27} have the same denominator, add them by adding their numerators.

$$\frac{40+10}{27}+\frac{1}{2.7}$$

Add 40 and 10 to get 50.

$$\frac{50}{27}+\frac{1}{2.7}$$

Expand \frac{1}{2.7} by multiplying both numerator and the denominator by 10.

$$\frac{50}{27}+\frac{10}{27}$$

Since \frac{50}{27} and \frac{10}{27} have the same denominator, add them by adding their numerators.

$$\frac{50+10}{27}$$

Add 50 and 10 to get 60.

$$\frac{60}{27}$$

Reduce the fraction \frac{60}{27} to lowest terms by extracting and canceling out 3.

$$\frac{20}{9}$$

Factor

$$\frac{5 \cdot 2 ^ {2}}{3 ^ {2}} = 2\frac{2}{9} = 2.2222222222222223$$