Solve {-1/100-[-3/10-9/50-9/20+(frac{7}{10}-frac{1}{20})-(frac{3}{20}+frac{2}{25})+frac{1}{50}]-frac{12}{25}}+frac{11}{50}

$$\{ - \frac { 1 } { 100 } - [ \frac { - 3 } { 10 } - \frac { 9 } { 50 } - \frac { 9 } { 20 } + ( \frac { 7 } { 10 } - \frac { 1 } { 20 } ) - ( \frac { 3 } { 20 } + \frac { 2 } { 25 } ) + \frac { 1 } { 50 } ] - \frac { 12 } { 25 } \} + \frac { 11 } { 50 }$$

Evaluate

$$\frac{11}{50}=0.22$$

Solution Steps

Fraction \frac{-3}{10} can be rewritten as -\frac{3}{10} by extracting the negative sign.

$$-\frac{1}{100}-\left(-\frac{3}{10}-\frac{9}{50}-\frac{9}{20}+\frac{7}{10}-\frac{1}{20}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Least common multiple of 10 and 50 is 50. Convert -\frac{3}{10} and \frac{9}{50} to fractions with denominator 50.

$$-\frac{1}{100}-\left(-\frac{15}{50}-\frac{9}{50}-\frac{9}{20}+\frac{7}{10}-\frac{1}{20}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Since -\frac{15}{50} and \frac{9}{50} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{100}-\left(\frac{-15-9}{50}-\frac{9}{20}+\frac{7}{10}-\frac{1}{20}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Subtract 9 from -15 to get -24.

$$-\frac{1}{100}-\left(\frac{-24}{50}-\frac{9}{20}+\frac{7}{10}-\frac{1}{20}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Reduce the fraction \frac{-24}{50} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{100}-\left(-\frac{12}{25}-\frac{9}{20}+\frac{7}{10}-\frac{1}{20}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Least common multiple of 25 and 20 is 100. Convert -\frac{12}{25} and \frac{9}{20} to fractions with denominator 100.

$$-\frac{1}{100}-\left(-\frac{48}{100}-\frac{45}{100}+\frac{7}{10}-\frac{1}{20}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Since -\frac{48}{100} and \frac{45}{100} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{100}-\left(\frac{-48-45}{100}+\frac{7}{10}-\frac{1}{20}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Subtract 45 from -48 to get -93.

$$-\frac{1}{100}-\left(-\frac{93}{100}+\frac{7}{10}-\frac{1}{20}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Least common multiple of 100 and 10 is 100. Convert -\frac{93}{100} and \frac{7}{10} to fractions with denominator 100.

$$-\frac{1}{100}-\left(-\frac{93}{100}+\frac{70}{100}-\frac{1}{20}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Since -\frac{93}{100} and \frac{70}{100} have the same denominator, add them by adding their numerators.

$$-\frac{1}{100}-\left(\frac{-93+70}{100}-\frac{1}{20}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Add -93 and 70 to get -23.

$$-\frac{1}{100}-\left(-\frac{23}{100}-\frac{1}{20}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Least common multiple of 100 and 20 is 100. Convert -\frac{23}{100} and \frac{1}{20} to fractions with denominator 100.

$$-\frac{1}{100}-\left(-\frac{23}{100}-\frac{5}{100}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Since -\frac{23}{100} and \frac{5}{100} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{100}-\left(\frac{-23-5}{100}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Subtract 5 from -23 to get -28.

$$-\frac{1}{100}-\left(\frac{-28}{100}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Reduce the fraction \frac{-28}{100} to lowest terms by extracting and canceling out 4.

$$-\frac{1}{100}-\left(-\frac{7}{25}-\left(\frac{3}{20}+\frac{2}{25}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Least common multiple of 20 and 25 is 100. Convert \frac{3}{20} and \frac{2}{25} to fractions with denominator 100.

$$-\frac{1}{100}-\left(-\frac{7}{25}-\left(\frac{15}{100}+\frac{8}{100}\right)+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Since \frac{15}{100} and \frac{8}{100} have the same denominator, add them by adding their numerators.

$$-\frac{1}{100}-\left(-\frac{7}{25}-\frac{15+8}{100}+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Add 15 and 8 to get 23.

$$-\frac{1}{100}-\left(-\frac{7}{25}-\frac{23}{100}+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Least common multiple of 25 and 100 is 100. Convert -\frac{7}{25} and \frac{23}{100} to fractions with denominator 100.

$$-\frac{1}{100}-\left(-\frac{28}{100}-\frac{23}{100}+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Since -\frac{28}{100} and \frac{23}{100} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{100}-\left(\frac{-28-23}{100}+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Subtract 23 from -28 to get -51.

$$-\frac{1}{100}-\left(-\frac{51}{100}+\frac{1}{50}\right)-\frac{12}{25}+\frac{11}{50}$$

Least common multiple of 100 and 50 is 100. Convert -\frac{51}{100} and \frac{1}{50} to fractions with denominator 100.

$$-\frac{1}{100}-\left(-\frac{51}{100}+\frac{2}{100}\right)-\frac{12}{25}+\frac{11}{50}$$

Since -\frac{51}{100} and \frac{2}{100} have the same denominator, add them by adding their numerators.

$$-\frac{1}{100}-\frac{-51+2}{100}-\frac{12}{25}+\frac{11}{50}$$

Add -51 and 2 to get -49.

$$-\frac{1}{100}-\left(-\frac{49}{100}\right)-\frac{12}{25}+\frac{11}{50}$$

The opposite of -\frac{49}{100} is \frac{49}{100}.

$$-\frac{1}{100}+\frac{49}{100}-\frac{12}{25}+\frac{11}{50}$$

Since -\frac{1}{100} and \frac{49}{100} have the same denominator, add them by adding their numerators.

$$\frac{-1+49}{100}-\frac{12}{25}+\frac{11}{50}$$

Add -1 and 49 to get 48.

$$\frac{48}{100}-\frac{12}{25}+\frac{11}{50}$$

Reduce the fraction \frac{48}{100} to lowest terms by extracting and canceling out 4.

$$\frac{12}{25}-\frac{12}{25}+\frac{11}{50}$$

Subtract \frac{12}{25} from \frac{12}{25} to get 0.

$$\frac{11}{50}$$

Factor

$$\frac{11}{2 \cdot 5 ^ {2}} = 0.22$$