Solve 1-frac{sqrt{2}}{2}+1/2*(-2.648)

$$1- \frac{ \sqrt{ 2 } }{ 2 } + \frac{ 1 }{ 2 } \times (-2.648)$$

Evaluate

$$-\frac{\sqrt{2}}{2}-0.324\approx -1.031106781$$

Short Solution Steps

Convert decimal number -2.648 to fraction -\frac{2648}{1000}. Reduce the fraction -\frac{2648}{1000} to lowest terms by extracting and canceling out 8.

$$1-\frac{\sqrt{2}}{2}+\frac{1}{2}\left(-\frac{331}{125}\right)$$

Multiply \frac{1}{2} times -\frac{331}{125} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{\sqrt{2}}{2}+\frac{1\left(-331\right)}{2\times 125}$$

Do the multiplications in the fraction \frac{1\left(-331\right)}{2\times 125}.

$$1-\frac{\sqrt{2}}{2}+\frac{-331}{250}$$

Fraction \frac{-331}{250} can be rewritten as -\frac{331}{250} by extracting the negative sign.

$$1-\frac{\sqrt{2}}{2}-\frac{331}{250}$$

Convert 1 to fraction \frac{250}{250}.

$$\frac{250}{250}-\frac{\sqrt{2}}{2}-\frac{331}{250}$$

Since \frac{250}{250} and \frac{331}{250} have the same denominator, subtract them by subtracting their numerators.

$$\frac{250-331}{250}-\frac{\sqrt{2}}{2}$$

Subtract 331 from 250 to get -81.

$$-\frac{81}{250}-\frac{\sqrt{2}}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 250 and 2 is 250. Multiply \frac{\sqrt{2}}{2} times \frac{125}{125}.

$$-\frac{81}{250}-\frac{125\sqrt{2}}{250}$$

Since -\frac{81}{250} and \frac{125\sqrt{2}}{250} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-81-125\sqrt{2}}{250}$$

Factor

$$\frac{-125 \sqrt{2} - 81}{250} = -1.0311067811865475$$