Solve 100+1/2(-9.8)*5^2

$$100 + \frac { 1 } { 2 } ( - 9.8 ) \cdot 5 ^ { 2 }$$

Evaluate

$$-22.5$$

Solution Steps

Convert decimal number -9.8 to fraction -\frac{98}{10}. Reduce the fraction -\frac{98}{10} to lowest terms by extracting and canceling out 2.

$$100+\frac{1}{2}\left(-\frac{49}{5}\right)\times 5^{2}$$

Multiply \frac{1}{2} times -\frac{49}{5} by multiplying numerator times numerator and denominator times denominator.

$$100+\frac{1\left(-49\right)}{2\times 5}\times 5^{2}$$

Do the multiplications in the fraction \frac{1\left(-49\right)}{2\times 5}.

$$100+\frac{-49}{10}\times 5^{2}$$

Fraction \frac{-49}{10} can be rewritten as -\frac{49}{10} by extracting the negative sign.

$$100-\frac{49}{10}\times 5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$100-\frac{49}{10}\times 25$$

Express -\frac{49}{10}\times 25 as a single fraction.

$$100+\frac{-49\times 25}{10}$$

Multiply -49 and 25 to get -1225.

$$100+\frac{-1225}{10}$$

Reduce the fraction \frac{-1225}{10} to lowest terms by extracting and canceling out 5.

$$100-\frac{245}{2}$$

Convert 100 to fraction \frac{200}{2}.

$$\frac{200}{2}-\frac{245}{2}$$

Since \frac{200}{2} and \frac{245}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{200-245}{2}$$

Subtract 245 from 200 to get -45.

$$-\frac{45}{2}$$

Factor

$$-22.5$$