Evaluate -1/6(250)^2+100(250)

$- \frac{1}{6} {(250)}^{2} + 100 (250)$

Step 1

Simplify each term.

Raise $250$ to the power of $2$ .

$- \frac{1}{6} \cdot 62500 + 100 (250)$

Cancel the common factor of $2$ .

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

$\frac{- 1}{6} \cdot 62500 + 100 (250)$

Factor $2$ out of $6$ .

$\frac{- 1}{2 (3)} \cdot 62500 + 100 (250)$

Factor $2$ out of $62500$ .

$\frac{- 1}{2 \cdot 3} \cdot (2 \cdot 31250) + 100 (250)$

Cancel the common factor.

$\frac{- 1}{2 \cdot 3} \cdot (2 \cdot 31250) + 100 (250)$

Rewrite the expression.

$\frac{- 1}{3} \cdot 31250 + 100 (250)$

Combine $\frac{- 1}{3}$ and $31250$ .

$\frac{- 1 \cdot 31250}{3} + 100 (250)$

Multiply $- 1$ by $31250$ .

$\frac{- 31250}{3} + 100 (250)$

Move the negative in front of the fraction.

$- \frac{31250}{3} + 100 (250)$

Multiply $100$ by $250$ .

$- \frac{31250}{3} + 25000$

Step 2

To write $25000$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{31250}{3} + 25000 \cdot \frac{3}{3}$

Step 3

Combine $25000$ and $\frac{3}{3}$ .

$- \frac{31250}{3} + \frac{25000 \cdot 3}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 31250 + 25000 \cdot 3}{3}$

Step 5

Simplify the numerator.

Multiply $25000$ by $3$ .

$\frac{- 31250 + 75000}{3}$

Add $- 31250$ and $75000$ .

$\frac{43750}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{43750}{3}$

Decimal Form:

$14583.\overline{3}$

Mixed Number Form:

$14583 \frac{1}{3}$

Evaluate -1/6(250)^2+100(250)

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