Solve 1/5+{[4/9-(1/2+2/4-frac{1}{9})]}

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

Evaluate

$$-\frac{11}{45}\approx -0.244444444$$

Solution Steps

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Since \frac{1}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 1 and 1 to get 2.

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

Divide 2 by 2 to get 1.

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

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

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

Since \frac{9}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}+\frac{4}{9}-\frac{9-1}{9}$$

Subtract 1 from 9 to get 8.

$$\frac{1}{5}+\frac{4}{9}-\frac{8}{9}$$

Since \frac{4}{9} and \frac{8}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}+\frac{4-8}{9}$$

Subtract 8 from 4 to get -4.

$$\frac{1}{5}-\frac{4}{9}$$

Least common multiple of 5 and 9 is 45. Convert \frac{1}{5} and \frac{4}{9} to fractions with denominator 45.

$$\frac{9}{45}-\frac{20}{45}$$

Since \frac{9}{45} and \frac{20}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-20}{45}$$

Subtract 20 from 9 to get -11.

$$-\frac{11}{45}$$

Factor

$$-\frac{11}{45} = -0.24444444444444444$$