Solve 2-(5/2+3/4)-(1-4/5)-3/4

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

Evaluate

$$-\frac{11}{5}=-2.2$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{5}{2} and \frac{3}{4} to fractions with denominator 4.

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

Since \frac{10}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

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

Add 10 and 3 to get 13.

$$2-\frac{13}{4}-\left(1-\frac{4}{5}\right)-\frac{3}{4}$$

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

$$\frac{8}{4}-\frac{13}{4}-\left(1-\frac{4}{5}\right)-\frac{3}{4}$$

Since \frac{8}{4} and \frac{13}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-13}{4}-\left(1-\frac{4}{5}\right)-\frac{3}{4}$$

Subtract 13 from 8 to get -5.

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

Convert 1 to fraction \frac{5}{5}.

$$-\frac{5}{4}-\left(\frac{5}{5}-\frac{4}{5}\right)-\frac{3}{4}$$

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

$$-\frac{5}{4}-\frac{5-4}{5}-\frac{3}{4}$$

Subtract 4 from 5 to get 1.

$$-\frac{5}{4}-\frac{1}{5}-\frac{3}{4}$$

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

$$-\frac{25}{20}-\frac{4}{20}-\frac{3}{4}$$

Since -\frac{25}{20} and \frac{4}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-25-4}{20}-\frac{3}{4}$$

Subtract 4 from -25 to get -29.

$$-\frac{29}{20}-\frac{3}{4}$$

Least common multiple of 20 and 4 is 20. Convert -\frac{29}{20} and \frac{3}{4} to fractions with denominator 20.

$$-\frac{29}{20}-\frac{15}{20}$$

Since -\frac{29}{20} and \frac{15}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-29-15}{20}$$

Subtract 15 from -29 to get -44.

$$\frac{-44}{20}$$

Reduce the fraction \frac{-44}{20} to lowest terms by extracting and canceling out 4.

$$-\frac{11}{5}$$

Factor

$$-\frac{11}{5} = -2\frac{1}{5} = -2.2$$