Evaluate ((3^2)/2-(1+4))÷0.5

$(\frac{3^{2}}{2} - (1 + 4)) \div 0.5$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{3^{2}}{2} - (1 + 4)}{0.5}$

Step 2

Raise $3$ to the power of $2$ .

$\frac{\frac{9}{2} - (1 + 4)}{0.5}$

Step 3

Simplify the numerator.

Add $1$ and $4$ .

$\frac{\frac{9}{2} - 1 \cdot 5}{0.5}$

Multiply $- 1$ by $5$ .

$\frac{\frac{9}{2} - 5}{0.5}$

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{9}{2} - 5 \cdot \frac{2}{2}}{0.5}$

Combine $- 5$ and $\frac{2}{2}$ .

$\frac{\frac{9}{2} + \frac{- 5 \cdot 2}{2}}{0.5}$

Combine the numerators over the common denominator.

$\frac{\frac{9 - 5 \cdot 2}{2}}{0.5}$

Simplify the numerator.

Multiply $- 5$ by $2$ .

$\frac{\frac{9 - 10}{2}}{0.5}$

Subtract $10$ from $9$ .

$\frac{\frac{- 1}{2}}{0.5}$

Move the negative in front of the fraction.

$\frac{- \frac{1}{2}}{0.5}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$- \frac{1}{2} \cdot \frac{1}{0.5}$

Step 5

Cancel the common factor of $0.5$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} \cdot \frac{1}{0.5}$

Factor $0.5$ out of $- 1$ .

$\frac{0.5 (- 2)}{2} \cdot \frac{1}{0.5}$

Cancel the common factor.

$\frac{0.5 \cdot - 2}{2} \cdot \frac{1}{0.5}$

Rewrite the expression.

$\frac{- 2}{2}$

Step 6

Divide $- 2$ by $2$ .

$- 1$