Basic Math Examples

$\frac{1}{3} \cdot {(3)}^{3} + \frac{5}{2} \cdot {(3)}^{2} - 6 \cdot 3 + 8$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $3$ .

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Step 1.1.1

Factor $3$ out of ${(3)}^{3}$ .

$\frac{1}{3} \cdot (3 \cdot 3^{2}) + \frac{5}{2} \cdot {(3)}^{2} - 6 \cdot 3 + 8$

Step 1.1.2

Cancel the common factor.

$\frac{1}{3} \cdot (3 \cdot 3^{2}) + \frac{5}{2} \cdot {(3)}^{2} - 6 \cdot 3 + 8$

Step 1.1.3

Rewrite the expression.

$3^{2} + \frac{5}{2} \cdot {(3)}^{2} - 6 \cdot 3 + 8$

Step 1.2

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

$9 + \frac{5}{2} \cdot {(3)}^{2} - 6 \cdot 3 + 8$

Step 1.3

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

$9 + \frac{5}{2} \cdot 9 - 6 \cdot 3 + 8$

Step 1.4

Multiply $\frac{5}{2} \cdot 9$ .

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Step 1.4.1

Combine $\frac{5}{2}$ and $9$ .

$9 + \frac{5 \cdot 9}{2} - 6 \cdot 3 + 8$

Step 1.4.2

Multiply $5$ by $9$ .

$9 + \frac{45}{2} - 6 \cdot 3 + 8$

Step 1.5

Multiply $- 6$ by $3$ .

$9 + \frac{45}{2} - 18 + 8$

Step 2

Find the common denominator.

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Step 2.1

Write $9$ as a fraction with denominator $1$ .

$\frac{9}{1} + \frac{45}{2} - 18 + 8$

Step 2.2

Multiply $\frac{9}{1}$ by $\frac{2}{2}$ .

$\frac{9}{1} \cdot \frac{2}{2} + \frac{45}{2} - 18 + 8$

Step 2.3

Multiply $\frac{9}{1}$ by $\frac{2}{2}$ .

$\frac{9 \cdot 2}{2} + \frac{45}{2} - 18 + 8$

Step 2.4

Write $- 18$ as a fraction with denominator $1$ .

$\frac{9 \cdot 2}{2} + \frac{45}{2} + \frac{- 18}{1} + 8$

Step 2.5

Multiply $\frac{- 18}{1}$ by $\frac{2}{2}$ .

$\frac{9 \cdot 2}{2} + \frac{45}{2} + \frac{- 18}{1} \cdot \frac{2}{2} + 8$

Step 2.6

Multiply $\frac{- 18}{1}$ by $\frac{2}{2}$ .

$\frac{9 \cdot 2}{2} + \frac{45}{2} + \frac{- 18 \cdot 2}{2} + 8$

Step 2.7

Write $8$ as a fraction with denominator $1$ .

$\frac{9 \cdot 2}{2} + \frac{45}{2} + \frac{- 18 \cdot 2}{2} + \frac{8}{1}$

Step 2.8

Multiply $\frac{8}{1}$ by $\frac{2}{2}$ .

$\frac{9 \cdot 2}{2} + \frac{45}{2} + \frac{- 18 \cdot 2}{2} + \frac{8}{1} \cdot \frac{2}{2}$

Step 2.9

Multiply $\frac{8}{1}$ by $\frac{2}{2}$ .

$\frac{9 \cdot 2}{2} + \frac{45}{2} + \frac{- 18 \cdot 2}{2} + \frac{8 \cdot 2}{2}$

Step 3

Combine the numerators over the common denominator.

$\frac{9 \cdot 2 + 45 - 18 \cdot 2 + 8 \cdot 2}{2}$

Step 4

Simplify each term.

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Step 4.1

Multiply $9$ by $2$ .

$\frac{18 + 45 - 18 \cdot 2 + 8 \cdot 2}{2}$

Step 4.2

Multiply $- 18$ by $2$ .

$\frac{18 + 45 - 36 + 8 \cdot 2}{2}$

Step 4.3

Multiply $8$ by $2$ .

$\frac{18 + 45 - 36 + 16}{2}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $18$ and $45$ .

$\frac{63 - 36 + 16}{2}$

Step 5.2

Subtract $36$ from $63$ .

$\frac{27 + 16}{2}$

Step 5.3

Add $27$ and $16$ .

$\frac{43}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{43}{2}$

Decimal Form:

$21.5$

Mixed Number Form:

$21 \frac{1}{2}$