Solve 7/4(-11/4)+(-5/4)^2

$$\frac { 7 } { 4 } ( - \frac { 11 } { 4 } ) + ( - \frac { 5 } { 4 } ) ^ { 2 }$$

Evaluate

$$-\frac{13}{4}=-3.25$$

Solution Steps

Multiply \frac{7}{4} times -\frac{11}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(-11\right)}{4\times 4}+\left(-\frac{5}{4}\right)^{2}$$

Do the multiplications in the fraction \frac{7\left(-11\right)}{4\times 4}.

$$\frac{-77}{16}+\left(-\frac{5}{4}\right)^{2}$$

Fraction \frac{-77}{16} can be rewritten as -\frac{77}{16} by extracting the negative sign.

$$-\frac{77}{16}+\left(-\frac{5}{4}\right)^{2}$$

Calculate -\frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$-\frac{77}{16}+\frac{25}{16}$$

Since -\frac{77}{16} and \frac{25}{16} have the same denominator, add them by adding their numerators.

$$\frac{-77+25}{16}$$

Add -77 and 25 to get -52.

$$\frac{-52}{16}$$

Reduce the fraction \frac{-52}{16} to lowest terms by extracting and canceling out 4.

$$-\frac{13}{4}$$

Factor

$$-\frac{13}{4} = -3\frac{1}{4} = -3.25$$