Solve 1/0.1+1-1/0.1

$$\frac{ \frac{ 1 }{ 0.1+1 } -1 }{ 0.1 }$$

Evaluate

$$-\frac{10}{11}\approx -0.909090909$$

Solution Steps

Add 0.1 and 1 to get 1.1.

$$\frac{\frac{1}{1.1}-1}{0.1}$$

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

$$\frac{\frac{10}{11}-1}{0.1}$$

Convert 1 to fraction \frac{11}{11}.

$$\frac{\frac{10}{11}-\frac{11}{11}}{0.1}$$

Since \frac{10}{11} and \frac{11}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-11}{11}}{0.1}$$

Subtract 11 from 10 to get -1.

$$\frac{-\frac{1}{11}}{0.1}$$

Express \frac{-\frac{1}{11}}{0.1} as a single fraction.

$$\frac{-1}{11\times 0.1}$$

Multiply 11 and 0.1 to get 1.1.

$$\frac{-1}{1.1}$$

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

$$\frac{-10}{11}$$

Fraction \frac{-10}{11} can be rewritten as -\frac{10}{11} by extracting the negative sign.

$$-\frac{10}{11}$$

Factor

$$-\frac{10}{11} = -0.9090909090909091$$