Evaluate -1/6(200)^2+100(200)

$- \frac{1}{6} {(200)}^{2} + 100 (200)$

Step 1

Simplify each term.

Raise $200$ to the power of $2$ .

$- \frac{1}{6} \cdot 40000 + 100 (200)$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$\frac{- 1}{6} \cdot 40000 + 100 (200)$

Factor $2$ out of $6$ .

$\frac{- 1}{2 (3)} \cdot 40000 + 100 (200)$

Factor $2$ out of $40000$ .

$\frac{- 1}{2 \cdot 3} \cdot (2 \cdot 20000) + 100 (200)$

Cancel the common factor.

$\frac{- 1}{2 \cdot 3} \cdot (2 \cdot 20000) + 100 (200)$

Rewrite the expression.

$\frac{- 1}{3} \cdot 20000 + 100 (200)$

Combine $\frac{- 1}{3}$ and $20000$ .

$\frac{- 1 \cdot 20000}{3} + 100 (200)$

Multiply $- 1$ by $20000$ .

$\frac{- 20000}{3} + 100 (200)$

Move the negative in front of the fraction.

$- \frac{20000}{3} + 100 (200)$

Multiply $100$ by $200$ .

$- \frac{20000}{3} + 20000$

Step 2

To write $20000$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{20000}{3} + 20000 \cdot \frac{3}{3}$

Step 3

Combine $20000$ and $\frac{3}{3}$ .

$- \frac{20000}{3} + \frac{20000 \cdot 3}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 20000 + 20000 \cdot 3}{3}$

Step 5

Simplify the numerator.

Multiply $20000$ by $3$ .

$\frac{- 20000 + 60000}{3}$

Add $- 20000$ and $60000$ .

$\frac{40000}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{40000}{3}$

Decimal Form:

$13333.\overline{3}$

Mixed Number Form:

$13333 \frac{1}{3}$

Evaluate -1/6(200)^2+100(200)

Related Questions

Support LCMGCF.com by disabling your adblocker.