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

$$\frac{71}{45}\approx 1.577777778$$

Solution Steps

Subtract 7 from 4 to get -3.

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

The opposite of -3 is 3.

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

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

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

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

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

Add -4 and 15 to get 11.

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

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

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

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

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

Add 99 and 5 to get 104.

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

Least common multiple of 45 and 9 is 45. Convert \frac{104}{45} and \frac{10}{9} to fractions with denominator 45.

$$-2-\left(\frac{104}{45}+\frac{50}{45}-6\right)+2-1$$

Since \frac{104}{45} and \frac{50}{45} have the same denominator, add them by adding their numerators.

$$-2-\left(\frac{104+50}{45}-6\right)+2-1$$

Add 104 and 50 to get 154.

$$-2-\left(\frac{154}{45}-6\right)+2-1$$

Convert 6 to fraction \frac{270}{45}.

$$-2-\left(\frac{154}{45}-\frac{270}{45}\right)+2-1$$

Since \frac{154}{45} and \frac{270}{45} have the same denominator, subtract them by subtracting their numerators.

$$-2-\frac{154-270}{45}+2-1$$

Subtract 270 from 154 to get -116.

$$-2-\left(-\frac{116}{45}\right)+2-1$$

The opposite of -\frac{116}{45} is \frac{116}{45}.

$$-2+\frac{116}{45}+2-1$$

Convert -2 to fraction -\frac{90}{45}.

$$-\frac{90}{45}+\frac{116}{45}+2-1$$

Since -\frac{90}{45} and \frac{116}{45} have the same denominator, add them by adding their numerators.

$$\frac{-90+116}{45}+2-1$$

Add -90 and 116 to get 26.

$$\frac{26}{45}+2-1$$

Convert 2 to fraction \frac{90}{45}.

$$\frac{26}{45}+\frac{90}{45}-1$$

Since \frac{26}{45} and \frac{90}{45} have the same denominator, add them by adding their numerators.

$$\frac{26+90}{45}-1$$

Add 26 and 90 to get 116.

$$\frac{116}{45}-1$$

Convert 1 to fraction \frac{45}{45}.

$$\frac{116}{45}-\frac{45}{45}$$

Since \frac{116}{45} and \frac{45}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{116-45}{45}$$

Subtract 45 from 116 to get 71.

$$\frac{71}{45}$$

Factor

$$\frac{71}{3 ^ {2} \cdot 5} = 1\frac{26}{45} = 1.5777777777777777$$