Solve {l}{3/4-(-1/2)5/2}{-(-1/4)2}

$$\left. \begin{array} { l } { \frac { 3 } { 4 } - ( - \frac { 1 } { 2 } ) \frac { 5 } { 2 } } \\ { - ( - \frac { 1 } { 4 } ) 2 } \end{array} \right.$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Multiply -\frac{1}{2} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-5}{2\times 2}.

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

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

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

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

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

Since \frac{3}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

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

Add 3 and 5 to get 8.

$$\frac{8}{4}-\left(-\frac{1}{4}\times 2\right)$$

Divide 8 by 4 to get 2.

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

Express -\frac{1}{4}\times 2 as a single fraction.

$$2-\frac{-2}{4}$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

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

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$2+\frac{1}{2}$$

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

$$\frac{4}{2}+\frac{1}{2}$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{4+1}{2}$$

Add 4 and 1 to get 5.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$