Solve 1/1.1+2/1.1+2/1.1^3+2/1.1+frac{2}{1.1}+frac{0.5}{1.1}-4

$$\frac{ 1 }{ 1.1 } + \frac{ 2 }{ 1.1 } + \frac{ 2 }{ 1. { 1 }^{ 3 } } + \frac{ 2 }{ 1.1 } + \frac{ 2 }{ 1.1 } + \frac{ 0.5 }{ 1.1 } -4$$

Evaluate

$$\frac{53}{11}\approx 4.818181818$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{1}{1.1}+\frac{2}{1.1}+\frac{2}{1^{4}}+\frac{2}{1.1}+\frac{2}{1.1}+\frac{0.5}{1.1}-4$$

Expand \frac{1}{1.1} by multiplying both numerator and the denominator by 10.

$$\frac{10}{11}+\frac{2}{1.1}+\frac{2}{1^{4}}+\frac{2}{1.1}+\frac{2}{1.1}+\frac{0.5}{1.1}-4$$

Expand \frac{2}{1.1} by multiplying both numerator and the denominator by 10.

$$\frac{10}{11}+\frac{20}{11}+\frac{2}{1^{4}}+\frac{2}{1.1}+\frac{2}{1.1}+\frac{0.5}{1.1}-4$$

Since \frac{10}{11} and \frac{20}{11} have the same denominator, add them by adding their numerators.

$$\frac{10+20}{11}+\frac{2}{1^{4}}+\frac{2}{1.1}+\frac{2}{1.1}+\frac{0.5}{1.1}-4$$

Add 10 and 20 to get 30.

$$\frac{30}{11}+\frac{2}{1^{4}}+\frac{2}{1.1}+\frac{2}{1.1}+\frac{0.5}{1.1}-4$$

Calculate 1 to the power of 4 and get 1.

$$\frac{30}{11}+\frac{2}{1}+\frac{2}{1.1}+\frac{2}{1.1}+\frac{0.5}{1.1}-4$$

Anything divided by one gives itself.

$$\frac{30}{11}+2+\frac{2}{1.1}+\frac{2}{1.1}+\frac{0.5}{1.1}-4$$

Convert 2 to fraction \frac{22}{11}.

$$\frac{30}{11}+\frac{22}{11}+\frac{2}{1.1}+\frac{2}{1.1}+\frac{0.5}{1.1}-4$$

Since \frac{30}{11} and \frac{22}{11} have the same denominator, add them by adding their numerators.

$$\frac{30+22}{11}+\frac{2}{1.1}+\frac{2}{1.1}+\frac{0.5}{1.1}-4$$

Add 30 and 22 to get 52.

$$\frac{52}{11}+\frac{2}{1.1}+\frac{2}{1.1}+\frac{0.5}{1.1}-4$$

Expand \frac{2}{1.1} by multiplying both numerator and the denominator by 10.

$$\frac{52}{11}+\frac{20}{11}+\frac{2}{1.1}+\frac{0.5}{1.1}-4$$

Since \frac{52}{11} and \frac{20}{11} have the same denominator, add them by adding their numerators.

$$\frac{52+20}{11}+\frac{2}{1.1}+\frac{0.5}{1.1}-4$$

Add 52 and 20 to get 72.

$$\frac{72}{11}+\frac{2}{1.1}+\frac{0.5}{1.1}-4$$

Expand \frac{2}{1.1} by multiplying both numerator and the denominator by 10.

$$\frac{72}{11}+\frac{20}{11}+\frac{0.5}{1.1}-4$$

Since \frac{72}{11} and \frac{20}{11} have the same denominator, add them by adding their numerators.

$$\frac{72+20}{11}+\frac{0.5}{1.1}-4$$

Add 72 and 20 to get 92.

$$\frac{92}{11}+\frac{0.5}{1.1}-4$$

Expand \frac{0.5}{1.1} by multiplying both numerator and the denominator by 10.

$$\frac{92}{11}+\frac{5}{11}-4$$

Since \frac{92}{11} and \frac{5}{11} have the same denominator, add them by adding their numerators.

$$\frac{92+5}{11}-4$$

Add 92 and 5 to get 97.

$$\frac{97}{11}-4$$

Convert 4 to fraction \frac{44}{11}.

$$\frac{97}{11}-\frac{44}{11}$$

Since \frac{97}{11} and \frac{44}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{97-44}{11}$$

Subtract 44 from 97 to get 53.

$$\frac{53}{11}$$

Factor

$$\frac{53}{11} = 4\frac{9}{11} = 4.818181818181818$$