Solve 2-3/4-{5/9-[-2+(7/8+1/8)]}

$$2 - \frac { 3 } { 4 } - \{ \frac { 5 } { 9 } - [ - 2 + ( \frac { 7 } { 8 } + \frac { 1 } { 8 } ) ] \}$$

Evaluate

$$-\frac{11}{36}\approx -0.305555556$$

Solution Steps

Convert 2 to fraction \frac{8}{4}.

$$\frac{8}{4}-\frac{3}{4}-\left(\frac{5}{9}-\left(-2+\frac{7}{8}+\frac{1}{8}\right)\right)$$

Since \frac{8}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-3}{4}-\left(\frac{5}{9}-\left(-2+\frac{7}{8}+\frac{1}{8}\right)\right)$$

Subtract 3 from 8 to get 5.

$$\frac{5}{4}-\left(\frac{5}{9}-\left(-2+\frac{7}{8}+\frac{1}{8}\right)\right)$$

Convert -2 to fraction -\frac{16}{8}.

$$\frac{5}{4}-\left(\frac{5}{9}-\left(-\frac{16}{8}+\frac{7}{8}+\frac{1}{8}\right)\right)$$

Since -\frac{16}{8} and \frac{7}{8} have the same denominator, add them by adding their numerators.

$$\frac{5}{4}-\left(\frac{5}{9}-\left(\frac{-16+7}{8}+\frac{1}{8}\right)\right)$$

Add -16 and 7 to get -9.

$$\frac{5}{4}-\left(\frac{5}{9}-\left(-\frac{9}{8}+\frac{1}{8}\right)\right)$$

Since -\frac{9}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{5}{4}-\left(\frac{5}{9}-\frac{-9+1}{8}\right)$$

Add -9 and 1 to get -8.

$$\frac{5}{4}-\left(\frac{5}{9}-\frac{-8}{8}\right)$$

Divide -8 by 8 to get -1.

$$\frac{5}{4}-\left(\frac{5}{9}-\left(-1\right)\right)$$

The opposite of -1 is 1.

$$\frac{5}{4}-\left(\frac{5}{9}+1\right)$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{5}{4}-\left(\frac{5}{9}+\frac{9}{9}\right)$$

Since \frac{5}{9} and \frac{9}{9} have the same denominator, add them by adding their numerators.

$$\frac{5}{4}-\frac{5+9}{9}$$

Add 5 and 9 to get 14.

$$\frac{5}{4}-\frac{14}{9}$$

Least common multiple of 4 and 9 is 36. Convert \frac{5}{4} and \frac{14}{9} to fractions with denominator 36.

$$\frac{45}{36}-\frac{56}{36}$$

Since \frac{45}{36} and \frac{56}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{45-56}{36}$$

Subtract 56 from 45 to get -11.

$$-\frac{11}{36}$$

Factor

$$-\frac{11}{36} = -0.3055555555555556$$