Solve 2-[-4/5-(4-7)+1/9-(10/9-6)]+2-1

$$2 - [ - \frac { 4 } { 5 } - ( 4 - 7 ) + \frac { 1 } { 9 } - ( \frac { 10 } { 9 } - 6 ) ] + 2 - 1$$

Evaluate

$$-\frac{21}{5}=-4.2$$

Solution Steps

Subtract 7 from 4 to get -3.

$$2-\left(-\frac{4}{5}-\left(-3\right)+\frac{1}{9}-\left(\frac{10}{9}-6\right)\right)+2-1$$

The opposite of -3 is 3.

$$2-\left(-\frac{4}{5}+3+\frac{1}{9}-\left(\frac{10}{9}-6\right)\right)+2-1$$

Convert 3 to fraction \frac{15}{5}.

$$2-\left(-\frac{4}{5}+\frac{15}{5}+\frac{1}{9}-\left(\frac{10}{9}-6\right)\right)+2-1$$

Since -\frac{4}{5} and \frac{15}{5} have the same denominator, add them by adding their numerators.

$$2-\left(\frac{-4+15}{5}+\frac{1}{9}-\left(\frac{10}{9}-6\right)\right)+2-1$$

Add -4 and 15 to get 11.

$$2-\left(\frac{11}{5}+\frac{1}{9}-\left(\frac{10}{9}-6\right)\right)+2-1$$

Least common multiple of 5 and 9 is 45. Convert \frac{11}{5} and \frac{1}{9} to fractions with denominator 45.

$$2-\left(\frac{99}{45}+\frac{5}{45}-\left(\frac{10}{9}-6\right)\right)+2-1$$

Since \frac{99}{45} and \frac{5}{45} have the same denominator, add them by adding their numerators.

$$2-\left(\frac{99+5}{45}-\left(\frac{10}{9}-6\right)\right)+2-1$$

Add 99 and 5 to get 104.

$$2-\left(\frac{104}{45}-\left(\frac{10}{9}-6\right)\right)+2-1$$

Convert 6 to fraction \frac{54}{9}.

$$2-\left(\frac{104}{45}-\left(\frac{10}{9}-\frac{54}{9}\right)\right)+2-1$$

Since \frac{10}{9} and \frac{54}{9} have the same denominator, subtract them by subtracting their numerators.

$$2-\left(\frac{104}{45}-\frac{10-54}{9}\right)+2-1$$

Subtract 54 from 10 to get -44.

$$2-\left(\frac{104}{45}-\left(-\frac{44}{9}\right)\right)+2-1$$

The opposite of -\frac{44}{9} is \frac{44}{9}.

$$2-\left(\frac{104}{45}+\frac{44}{9}\right)+2-1$$

Least common multiple of 45 and 9 is 45. Convert \frac{104}{45} and \frac{44}{9} to fractions with denominator 45.

$$2-\left(\frac{104}{45}+\frac{220}{45}\right)+2-1$$

Since \frac{104}{45} and \frac{220}{45} have the same denominator, add them by adding their numerators.

$$2-\frac{104+220}{45}+2-1$$

Add 104 and 220 to get 324.

$$2-\frac{324}{45}+2-1$$

Reduce the fraction \frac{324}{45} to lowest terms by extracting and canceling out 9.

$$2-\frac{36}{5}+2-1$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{10}{5}-\frac{36}{5}+2-1$$

Since \frac{10}{5} and \frac{36}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-36}{5}+2-1$$

Subtract 36 from 10 to get -26.

$$-\frac{26}{5}+2-1$$

Convert 2 to fraction \frac{10}{5}.

$$-\frac{26}{5}+\frac{10}{5}-1$$

Since -\frac{26}{5} and \frac{10}{5} have the same denominator, add them by adding their numerators.

$$\frac{-26+10}{5}-1$$

Add -26 and 10 to get -16.

$$-\frac{16}{5}-1$$

Convert 1 to fraction \frac{5}{5}.

$$-\frac{16}{5}-\frac{5}{5}$$

Since -\frac{16}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-16-5}{5}$$

Subtract 5 from -16 to get -21.

$$-\frac{21}{5}$$

Factor

$$-\frac{21}{5} = -4\frac{1}{5} = -4.2$$