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

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

Evaluate

$$3$$

Solution Steps

The opposite of -\frac{3}{4} is \frac{3}{4}.

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

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

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

Since \frac{6}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

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

Add 6 and 3 to get 9.

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

Least common multiple of 4 and 2 is 4. Convert \frac{9}{4} and \frac{1}{2} to fractions with denominator 4.

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

Since \frac{9}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 9 to get 7.

$$\frac{7}{4}-\left(-\frac{5}{4}\right)$$

The opposite of -\frac{5}{4} is \frac{5}{4}.

$$\frac{7}{4}+\frac{5}{4}$$

Since \frac{7}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{7+5}{4}$$

Add 7 and 5 to get 12.

$$\frac{12}{4}$$

Divide 12 by 4 to get 3.

$$3$$

Factor

$$3$$