Basic Math Examples

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

Step 1

Find the common denominator.

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Step 1.1

Write $3^{2}$ as a fraction with denominator $1$ .

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

Step 1.2

Multiply $\frac{3^{2}}{1}$ by $\frac{3}{3}$ .

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

Step 1.3

Multiply $\frac{3^{2}}{1}$ by $\frac{3}{3}$ .

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

Step 1.4

Write $3 \cdot 3$ as a fraction with denominator $1$ .

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

Step 1.5

Multiply $\frac{3 \cdot 3}{1}$ by $\frac{3}{3}$ .

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

Step 1.6

Multiply $\frac{3 \cdot 3}{1}$ by $\frac{3}{3}$ .

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

Step 1.7

Write $- (\frac{1^{3}}{3} - 1 + 3 \cdot (- 1))$ as a fraction with denominator $1$ .

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

Step 1.8

Multiply $\frac{- (\frac{1^{3}}{3} - 1 + 3 \cdot (- 1))}{1}$ by $\frac{3}{3}$ .

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

Step 1.9

Multiply $\frac{- (\frac{1^{3}}{3} - 1 + 3 \cdot (- 1))}{1}$ by $\frac{3}{3}$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

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Step 3.1

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

$\frac{- 1 \cdot 9 + 3^{2} \cdot 3 + 3 \cdot 3 \cdot 3 - (\frac{1^{3}}{3} - 1 + 3 \cdot (- 1)) \cdot 3}{3}$

Step 3.2

Multiply $- 1$ by $9$ .

$\frac{- 9 + 3^{2} \cdot 3 + 3 \cdot 3 \cdot 3 - (\frac{1^{3}}{3} - 1 + 3 \cdot (- 1)) \cdot 3}{3}$

Step 3.3

Multiply $3^{2}$ by $3$ by adding the exponents.

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Step 3.3.1

Multiply $3^{2}$ by $3$ .

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Step 3.3.1.1

Raise $3$ to the power of $1$ .

$\frac{- 9 + 3^{2} \cdot 3^{1} + 3 \cdot 3 \cdot 3 - (\frac{1^{3}}{3} - 1 + 3 \cdot (- 1)) \cdot 3}{3}$

Step 3.3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 9 + 3^{2 + 1} + 3 \cdot 3 \cdot 3 - (\frac{1^{3}}{3} - 1 + 3 \cdot (- 1)) \cdot 3}{3}$

Step 3.3.2

Add $2$ and $1$ .

$\frac{- 9 + 3^{3} + 3 \cdot 3 \cdot 3 - (\frac{1^{3}}{3} - 1 + 3 \cdot (- 1)) \cdot 3}{3}$

Step 3.4

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

$\frac{- 9 + 27 + 3 \cdot 3 \cdot 3 - (\frac{1^{3}}{3} - 1 + 3 \cdot (- 1)) \cdot 3}{3}$

Step 3.5

Multiply $3 \cdot 3 \cdot 3$ .

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Step 3.5.1

Multiply $3$ by $3$ .

$\frac{- 9 + 27 + 9 \cdot 3 - (\frac{1^{3}}{3} - 1 + 3 \cdot (- 1)) \cdot 3}{3}$

Step 3.5.2

Multiply $9$ by $3$ .

$\frac{- 9 + 27 + 27 - (\frac{1^{3}}{3} - 1 + 3 \cdot (- 1)) \cdot 3}{3}$

Step 3.6

Simplify each term.

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Step 3.6.1

One to any power is one.

$\frac{- 9 + 27 + 27 - (\frac{1}{3} - 1 + 3 \cdot (- 1)) \cdot 3}{3}$

Step 3.6.2

Multiply $3$ by $- 1$ .

$\frac{- 9 + 27 + 27 - (\frac{1}{3} - 1 - 3) \cdot 3}{3}$

Step 3.7

Find the common denominator.

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Step 3.7.1

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

$\frac{- 9 + 27 + 27 - (\frac{1}{3} + \frac{- 1}{1} - 3) \cdot 3}{3}$

Step 3.7.2

Multiply $\frac{- 1}{1}$ by $\frac{3}{3}$ .

$\frac{- 9 + 27 + 27 - (\frac{1}{3} + \frac{- 1}{1} \cdot \frac{3}{3} - 3) \cdot 3}{3}$

Step 3.7.3

Multiply $\frac{- 1}{1}$ by $\frac{3}{3}$ .

$\frac{- 9 + 27 + 27 - (\frac{1}{3} + \frac{- 1 \cdot 3}{3} - 3) \cdot 3}{3}$

Step 3.7.4

Write $- 3$ as a fraction with denominator $1$ .

$\frac{- 9 + 27 + 27 - (\frac{1}{3} + \frac{- 1 \cdot 3}{3} + \frac{- 3}{1}) \cdot 3}{3}$

Step 3.7.5

Multiply $\frac{- 3}{1}$ by $\frac{3}{3}$ .

$\frac{- 9 + 27 + 27 - (\frac{1}{3} + \frac{- 1 \cdot 3}{3} + \frac{- 3}{1} \cdot \frac{3}{3}) \cdot 3}{3}$

Step 3.7.6

Multiply $\frac{- 3}{1}$ by $\frac{3}{3}$ .

$\frac{- 9 + 27 + 27 - (\frac{1}{3} + \frac{- 1 \cdot 3}{3} + \frac{- 3 \cdot 3}{3}) \cdot 3}{3}$

Step 3.8

Combine the numerators over the common denominator.

$\frac{- 9 + 27 + 27 - \frac{1 - 1 \cdot 3 - 3 \cdot 3}{3} \cdot 3}{3}$

Step 3.9

Simplify each term.

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Step 3.9.1

Multiply $- 1$ by $3$ .

$\frac{- 9 + 27 + 27 - \frac{1 - 3 - 3 \cdot 3}{3} \cdot 3}{3}$

Step 3.9.2

Multiply $- 3$ by $3$ .

$\frac{- 9 + 27 + 27 - \frac{1 - 3 - 9}{3} \cdot 3}{3}$

Step 3.10

Subtract $3$ from $1$ .

$\frac{- 9 + 27 + 27 - \frac{- 2 - 9}{3} \cdot 3}{3}$

Step 3.11

Subtract $9$ from $- 2$ .

$\frac{- 9 + 27 + 27 - \frac{- 11}{3} \cdot 3}{3}$

Step 3.12

Cancel the common factor of $3$ .

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Step 3.12.1

Move the leading negative in $- \frac{- 11}{3}$ into the numerator.

$\frac{- 9 + 27 + 27 + \frac{11}{3} \cdot 3}{3}$

Step 3.12.2

Cancel the common factor.

$\frac{- 9 + 27 + 27 + \frac{11}{3} \cdot 3}{3}$

Step 3.12.3

Rewrite the expression.

$\frac{- 9 + 27 + 27 + 11}{3}$

Step 4

Simplify by adding numbers.

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Step 4.1

Add $- 9$ and $27$ .

$\frac{18 + 27 + 11}{3}$

Step 4.2

Add $18$ and $27$ .

$\frac{45 + 11}{3}$

Step 4.3

Add $45$ and $11$ .

$\frac{56}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{56}{3}$

Decimal Form:

$18.\overline{6}$

Mixed Number Form:

$18 \frac{2}{3}$