Solve {12/5+21/10-[1/4+3/5-(3frac{1}{2}+frac{3}{4})-2]}+(-frac{5}{4}+2)=

$$\{ \frac { 12 } { 5 } + 2 \frac { 1 } { 10 } - [ \frac { 1 } { 4 } + \frac { 3 } { 5 } - ( 3 \frac { 1 } { 2 } + \frac { 3 } { 4 } ) - 2 ] \} + ( - \frac { 5 } { 4 } + 2 ) =$$

Evaluate

$$\frac{213}{20}=10.65$$

Solution Steps

Multiply 2 and 10 to get 20.

$$\frac{12}{5}+\frac{20+1}{10}-\left(\frac{1}{4}+\frac{3}{5}-\left(\frac{3\times 2+1}{2}+\frac{3}{4}\right)-2\right)-\frac{5}{4}+2$$

Add 20 and 1 to get 21.

$$\frac{12}{5}+\frac{21}{10}-\left(\frac{1}{4}+\frac{3}{5}-\left(\frac{3\times 2+1}{2}+\frac{3}{4}\right)-2\right)-\frac{5}{4}+2$$

Least common multiple of 5 and 10 is 10. Convert \frac{12}{5} and \frac{21}{10} to fractions with denominator 10.

$$\frac{24}{10}+\frac{21}{10}-\left(\frac{1}{4}+\frac{3}{5}-\left(\frac{3\times 2+1}{2}+\frac{3}{4}\right)-2\right)-\frac{5}{4}+2$$

Since \frac{24}{10} and \frac{21}{10} have the same denominator, add them by adding their numerators.

$$\frac{24+21}{10}-\left(\frac{1}{4}+\frac{3}{5}-\left(\frac{3\times 2+1}{2}+\frac{3}{4}\right)-2\right)-\frac{5}{4}+2$$

Add 24 and 21 to get 45.

$$\frac{45}{10}-\left(\frac{1}{4}+\frac{3}{5}-\left(\frac{3\times 2+1}{2}+\frac{3}{4}\right)-2\right)-\frac{5}{4}+2$$

Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

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

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{3}{5} to fractions with denominator 20.

$$\frac{9}{2}-\left(\frac{5}{20}+\frac{12}{20}-\left(\frac{3\times 2+1}{2}+\frac{3}{4}\right)-2\right)-\frac{5}{4}+2$$

Since \frac{5}{20} and \frac{12}{20} have the same denominator, add them by adding their numerators.

$$\frac{9}{2}-\left(\frac{5+12}{20}-\left(\frac{3\times 2+1}{2}+\frac{3}{4}\right)-2\right)-\frac{5}{4}+2$$

Add 5 and 12 to get 17.

$$\frac{9}{2}-\left(\frac{17}{20}-\left(\frac{3\times 2+1}{2}+\frac{3}{4}\right)-2\right)-\frac{5}{4}+2$$

Multiply 3 and 2 to get 6.

$$\frac{9}{2}-\left(\frac{17}{20}-\left(\frac{6+1}{2}+\frac{3}{4}\right)-2\right)-\frac{5}{4}+2$$

Add 6 and 1 to get 7.

$$\frac{9}{2}-\left(\frac{17}{20}-\left(\frac{7}{2}+\frac{3}{4}\right)-2\right)-\frac{5}{4}+2$$

Least common multiple of 2 and 4 is 4. Convert \frac{7}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{9}{2}-\left(\frac{17}{20}-\left(\frac{14}{4}+\frac{3}{4}\right)-2\right)-\frac{5}{4}+2$$

Since \frac{14}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{9}{2}-\left(\frac{17}{20}-\frac{14+3}{4}-2\right)-\frac{5}{4}+2$$

Add 14 and 3 to get 17.

$$\frac{9}{2}-\left(\frac{17}{20}-\frac{17}{4}-2\right)-\frac{5}{4}+2$$

Least common multiple of 20 and 4 is 20. Convert \frac{17}{20} and \frac{17}{4} to fractions with denominator 20.

$$\frac{9}{2}-\left(\frac{17}{20}-\frac{85}{20}-2\right)-\frac{5}{4}+2$$

Since \frac{17}{20} and \frac{85}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{2}-\left(\frac{17-85}{20}-2\right)-\frac{5}{4}+2$$

Subtract 85 from 17 to get -68.

$$\frac{9}{2}-\left(\frac{-68}{20}-2\right)-\frac{5}{4}+2$$

Reduce the fraction \frac{-68}{20} to lowest terms by extracting and canceling out 4.

$$\frac{9}{2}-\left(-\frac{17}{5}-2\right)-\frac{5}{4}+2$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{9}{2}-\left(-\frac{17}{5}-\frac{10}{5}\right)-\frac{5}{4}+2$$

Since -\frac{17}{5} and \frac{10}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{2}-\frac{-17-10}{5}-\frac{5}{4}+2$$

Subtract 10 from -17 to get -27.

$$\frac{9}{2}-\left(-\frac{27}{5}\right)-\frac{5}{4}+2$$

The opposite of -\frac{27}{5} is \frac{27}{5}.

$$\frac{9}{2}+\frac{27}{5}-\frac{5}{4}+2$$

Least common multiple of 2 and 5 is 10. Convert \frac{9}{2} and \frac{27}{5} to fractions with denominator 10.

$$\frac{45}{10}+\frac{54}{10}-\frac{5}{4}+2$$

Since \frac{45}{10} and \frac{54}{10} have the same denominator, add them by adding their numerators.

$$\frac{45+54}{10}-\frac{5}{4}+2$$

Add 45 and 54 to get 99.

$$\frac{99}{10}-\frac{5}{4}+2$$

Least common multiple of 10 and 4 is 20. Convert \frac{99}{10} and \frac{5}{4} to fractions with denominator 20.

$$\frac{198}{20}-\frac{25}{20}+2$$

Since \frac{198}{20} and \frac{25}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{198-25}{20}+2$$

Subtract 25 from 198 to get 173.

$$\frac{173}{20}+2$$

Convert 2 to fraction \frac{40}{20}.

$$\frac{173}{20}+\frac{40}{20}$$

Since \frac{173}{20} and \frac{40}{20} have the same denominator, add them by adding their numerators.

$$\frac{173+40}{20}$$

Add 173 and 40 to get 213.

$$\frac{213}{20}$$

Factor

$$\frac{3 \cdot 71}{2 ^ {2} \cdot 5} = 10\frac{13}{20} = 10.65$$