Solve (5/12-1/5+3/4-2)-(-7/2+frac{7}{15}-frac{1}{4})

$$( \frac { 5 } { 12 } - \frac { 1 } { 5 } + \frac { 3 } { 4 } - 2 ) - ( - \frac { 7 } { 2 } + \frac { 7 } { 15 } - \frac { 1 } { 4 } )$$

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

Least common multiple of 12 and 5 is 60. Convert \frac{5}{12} and \frac{1}{5} to fractions with denominator 60.

$$\frac{25}{60}-\frac{12}{60}+\frac{3}{4}-2-\left(-\frac{7}{2}+\frac{7}{15}-\frac{1}{4}\right)$$

Since \frac{25}{60} and \frac{12}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-12}{60}+\frac{3}{4}-2-\left(-\frac{7}{2}+\frac{7}{15}-\frac{1}{4}\right)$$

Subtract 12 from 25 to get 13.

$$\frac{13}{60}+\frac{3}{4}-2-\left(-\frac{7}{2}+\frac{7}{15}-\frac{1}{4}\right)$$

Least common multiple of 60 and 4 is 60. Convert \frac{13}{60} and \frac{3}{4} to fractions with denominator 60.

$$\frac{13}{60}+\frac{45}{60}-2-\left(-\frac{7}{2}+\frac{7}{15}-\frac{1}{4}\right)$$

Since \frac{13}{60} and \frac{45}{60} have the same denominator, add them by adding their numerators.

$$\frac{13+45}{60}-2-\left(-\frac{7}{2}+\frac{7}{15}-\frac{1}{4}\right)$$

Add 13 and 45 to get 58.

$$\frac{58}{60}-2-\left(-\frac{7}{2}+\frac{7}{15}-\frac{1}{4}\right)$$

Reduce the fraction \frac{58}{60} to lowest terms by extracting and canceling out 2.

$$\frac{29}{30}-2-\left(-\frac{7}{2}+\frac{7}{15}-\frac{1}{4}\right)$$

Convert 2 to fraction \frac{60}{30}.

$$\frac{29}{30}-\frac{60}{30}-\left(-\frac{7}{2}+\frac{7}{15}-\frac{1}{4}\right)$$

Since \frac{29}{30} and \frac{60}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{29-60}{30}-\left(-\frac{7}{2}+\frac{7}{15}-\frac{1}{4}\right)$$

Subtract 60 from 29 to get -31.

$$-\frac{31}{30}-\left(-\frac{7}{2}+\frac{7}{15}-\frac{1}{4}\right)$$

Least common multiple of 2 and 15 is 30. Convert -\frac{7}{2} and \frac{7}{15} to fractions with denominator 30.

$$-\frac{31}{30}-\left(-\frac{105}{30}+\frac{14}{30}-\frac{1}{4}\right)$$

Since -\frac{105}{30} and \frac{14}{30} have the same denominator, add them by adding their numerators.

$$-\frac{31}{30}-\left(\frac{-105+14}{30}-\frac{1}{4}\right)$$

Add -105 and 14 to get -91.

$$-\frac{31}{30}-\left(-\frac{91}{30}-\frac{1}{4}\right)$$

Least common multiple of 30 and 4 is 60. Convert -\frac{91}{30} and \frac{1}{4} to fractions with denominator 60.

$$-\frac{31}{30}-\left(-\frac{182}{60}-\frac{15}{60}\right)$$

Since -\frac{182}{60} and \frac{15}{60} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{31}{30}-\frac{-182-15}{60}$$

Subtract 15 from -182 to get -197.

$$-\frac{31}{30}-\left(-\frac{197}{60}\right)$$

The opposite of -\frac{197}{60} is \frac{197}{60}.

$$-\frac{31}{30}+\frac{197}{60}$$

Least common multiple of 30 and 60 is 60. Convert -\frac{31}{30} and \frac{197}{60} to fractions with denominator 60.

$$-\frac{62}{60}+\frac{197}{60}$$

Since -\frac{62}{60} and \frac{197}{60} have the same denominator, add them by adding their numerators.

$$\frac{-62+197}{60}$$

Add -62 and 197 to get 135.

$$\frac{135}{60}$$

Reduce the fraction \frac{135}{60} to lowest terms by extracting and canceling out 15.

$$\frac{9}{4}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25$$