Solve 1-2.7-(-1-1/2.7)

$$1-2.7-(-1- \frac{ 1 }{ 2.7 } )$$

Evaluate

$$-\frac{89}{270}\approx -0.32962963$$

Solution Steps

Subtract 2.7 from 1 to get -1.7.

$$-1.7-\left(-1-\frac{1}{2.7}\right)$$

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

$$-1.7-\left(-1-\frac{10}{27}\right)$$

Convert -1 to fraction -\frac{27}{27}.

$$-1.7-\left(-\frac{27}{27}-\frac{10}{27}\right)$$

Since -\frac{27}{27} and \frac{10}{27} have the same denominator, subtract them by subtracting their numerators.

$$-1.7-\frac{-27-10}{27}$$

Subtract 10 from -27 to get -37.

$$-1.7-\left(-\frac{37}{27}\right)$$

The opposite of -\frac{37}{27} is \frac{37}{27}.

$$-1.7+\frac{37}{27}$$

Convert decimal number -1.7 to fraction -\frac{17}{10}.

$$-\frac{17}{10}+\frac{37}{27}$$

Least common multiple of 10 and 27 is 270. Convert -\frac{17}{10} and \frac{37}{27} to fractions with denominator 270.

$$-\frac{459}{270}+\frac{370}{270}$$

Since -\frac{459}{270} and \frac{370}{270} have the same denominator, add them by adding their numerators.

$$\frac{-459+370}{270}$$

Add -459 and 370 to get -89.

$$-\frac{89}{270}$$

Factor

$$-\frac{89}{270} = -0.3296296296296296$$