Calculus Examples

$\frac{3}{2} \cdot {(5)}^{2} + 10 (5) - \frac{1}{3} \cdot {(5)}^{3}$

Step 1

Simplify each term.

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Step 1.1

Raise $5$ to the power of $2$ .

$\frac{3}{2} \cdot 25 + 10 (5) - \frac{1}{3} \cdot {(5)}^{3}$

Step 1.2

Multiply $\frac{3}{2} \cdot 25$ .

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Step 1.2.1

Combine $\frac{3}{2}$ and $25$ .

$\frac{3 \cdot 25}{2} + 10 (5) - \frac{1}{3} \cdot {(5)}^{3}$

Step 1.2.2

Multiply $3$ by $25$ .

$\frac{75}{2} + 10 (5) - \frac{1}{3} \cdot {(5)}^{3}$

Step 1.3

Multiply $10$ by $5$ .

$\frac{75}{2} + 50 - \frac{1}{3} \cdot {(5)}^{3}$

Step 1.4

Raise $5$ to the power of $3$ .

$\frac{75}{2} + 50 - \frac{1}{3} \cdot 125$

Step 1.5

Multiply $- \frac{1}{3} \cdot 125$ .

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Step 1.5.1

Multiply $125$ by $- 1$ .

$\frac{75}{2} + 50 - 125 (\frac{1}{3})$

Step 1.5.2

Combine $- 125$ and $\frac{1}{3}$ .

$\frac{75}{2} + 50 + \frac{- 125}{3}$

Step 1.6

Move the negative in front of the fraction.

$\frac{75}{2} + 50 - \frac{125}{3}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{75}{2}$ by $\frac{3}{3}$ .

$\frac{75}{2} \cdot \frac{3}{3} + 50 - \frac{125}{3}$

Step 2.2

Multiply $\frac{75}{2}$ by $\frac{3}{3}$ .

$\frac{75 \cdot 3}{2 \cdot 3} + 50 - \frac{125}{3}$

Step 2.3

Write $50$ as a fraction with denominator $1$ .

$\frac{75 \cdot 3}{2 \cdot 3} + \frac{50}{1} - \frac{125}{3}$

Step 2.4

Multiply $\frac{50}{1}$ by $\frac{6}{6}$ .

$\frac{75 \cdot 3}{2 \cdot 3} + \frac{50}{1} \cdot \frac{6}{6} - \frac{125}{3}$

Step 2.5

Multiply $\frac{50}{1}$ by $\frac{6}{6}$ .

$\frac{75 \cdot 3}{2 \cdot 3} + \frac{50 \cdot 6}{6} - \frac{125}{3}$

Step 2.6

Multiply $\frac{125}{3}$ by $\frac{2}{2}$ .

$\frac{75 \cdot 3}{2 \cdot 3} + \frac{50 \cdot 6}{6} - (\frac{125}{3} \cdot \frac{2}{2})$

Step 2.7

Multiply $\frac{125}{3}$ by $\frac{2}{2}$ .

$\frac{75 \cdot 3}{2 \cdot 3} + \frac{50 \cdot 6}{6} - \frac{125 \cdot 2}{3 \cdot 2}$

Step 2.8

Multiply $2$ by $3$ .

$\frac{75 \cdot 3}{6} + \frac{50 \cdot 6}{6} - \frac{125 \cdot 2}{3 \cdot 2}$

Step 2.9

Reorder the factors of $3 \cdot 2$ .

$\frac{75 \cdot 3}{6} + \frac{50 \cdot 6}{6} - \frac{125 \cdot 2}{2 \cdot 3}$

Step 2.10

Multiply $2$ by $3$ .

$\frac{75 \cdot 3}{6} + \frac{50 \cdot 6}{6} - \frac{125 \cdot 2}{6}$

Step 3

Combine the numerators over the common denominator.

$\frac{75 \cdot 3 + 50 \cdot 6 - 125 \cdot 2}{6}$

Step 4

Simplify each term.

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Step 4.1

Multiply $75$ by $3$ .

$\frac{225 + 50 \cdot 6 - 125 \cdot 2}{6}$

Step 4.2

Multiply $50$ by $6$ .

$\frac{225 + 300 - 125 \cdot 2}{6}$

Step 4.3

Multiply $- 125$ by $2$ .

$\frac{225 + 300 - 250}{6}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $225$ and $300$ .

$\frac{525 - 250}{6}$

Step 5.2

Subtract $250$ from $525$ .

$\frac{275}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{275}{6}$

Decimal Form:

$45.8\overline{3}$

Mixed Number Form:

$45 \frac{5}{6}$