Solve 1/2-[3/5-(0,5-2/5)]-(11/4-frac{4}{5}+frac{1}{2})

$$\frac { 1 } { 2 } - [ \frac { 3 } { 5 } - ( 0,5 - \frac { 2 } { 5 } ) ] - ( 1 \frac { 1 } { 4 } - \frac { 4 } { 5 } + \frac { 1 } { 2 } )$$

Evaluate

$$-0,95$$

Solution Steps

Convert decimal number 0,5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

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

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{2}{5} to fractions with denominator 10.

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

Since \frac{5}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 5 to get 1.

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

Least common multiple of 5 and 10 is 10. Convert \frac{3}{5} and \frac{1}{10} to fractions with denominator 10.

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

Since \frac{6}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 6 to get 5.

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

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

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

Subtract \frac{1}{2} from \frac{1}{2} to get 0.

$$0-\left(\frac{1\times 4+1}{4}-\frac{4}{5}+\frac{1}{2}\right)$$

Multiply 1 and 4 to get 4.

$$0-\left(\frac{4+1}{4}-\frac{4}{5}+\frac{1}{2}\right)$$

Add 4 and 1 to get 5.

$$0-\left(\frac{5}{4}-\frac{4}{5}+\frac{1}{2}\right)$$

Least common multiple of 4 and 5 is 20. Convert \frac{5}{4} and \frac{4}{5} to fractions with denominator 20.

$$0-\left(\frac{25}{20}-\frac{16}{20}+\frac{1}{2}\right)$$

Since \frac{25}{20} and \frac{16}{20} have the same denominator, subtract them by subtracting their numerators.

$$0-\left(\frac{25-16}{20}+\frac{1}{2}\right)$$

Subtract 16 from 25 to get 9.

$$0-\left(\frac{9}{20}+\frac{1}{2}\right)$$

Least common multiple of 20 and 2 is 20. Convert \frac{9}{20} and \frac{1}{2} to fractions with denominator 20.

$$0-\left(\frac{9}{20}+\frac{10}{20}\right)$$

Since \frac{9}{20} and \frac{10}{20} have the same denominator, add them by adding their numerators.

$$0-\frac{9+10}{20}$$

Add 9 and 10 to get 19.

$$0-\frac{19}{20}$$

Subtract \frac{19}{20} from 0 to get -\frac{19}{20}.

$$-\frac{19}{20}$$

Factor

$$-0,95$$