Algebra Examples

$18 - 12 + 2 \cdot 3^{2} - 12 \div (1 + 1)$

Step 1

Find the common denominator.

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Step 1.1

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

$\frac{18}{1} - 12 + 2 \cdot 3^{2} - 12 \div (1 + 1)$

Step 1.2

Multiply $\frac{18}{1}$ by $\frac{1 + 1}{1 + 1}$ .

$\frac{18}{1} \cdot \frac{1 + 1}{1 + 1} - 12 + 2 \cdot 3^{2} - 12 \div (1 + 1)$

Step 1.3

Multiply $\frac{18}{1}$ by $\frac{1 + 1}{1 + 1}$ .

$\frac{18 (1 + 1)}{1 + 1} - 12 + 2 \cdot 3^{2} - 12 \div (1 + 1)$

Step 1.4

Write $- 12$ as a fraction with denominator $1$ .

$\frac{18 (1 + 1)}{1 + 1} + \frac{- 12}{1} + 2 \cdot 3^{2} - 12 \div (1 + 1)$

Step 1.5

Multiply $\frac{- 12}{1}$ by $\frac{1 + 1}{1 + 1}$ .

$\frac{18 (1 + 1)}{1 + 1} + \frac{- 12}{1} \cdot \frac{1 + 1}{1 + 1} + 2 \cdot 3^{2} - 12 \div (1 + 1)$

Step 1.6

Multiply $\frac{- 12}{1}$ by $\frac{1 + 1}{1 + 1}$ .

$\frac{18 (1 + 1)}{1 + 1} + \frac{- 12 (1 + 1)}{1 + 1} + 2 \cdot 3^{2} - 12 \div (1 + 1)$

Step 1.7

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

$\frac{18 (1 + 1)}{1 + 1} + \frac{- 12 (1 + 1)}{1 + 1} + \frac{2 \cdot 3^{2}}{1} - 12 \div (1 + 1)$

Step 1.8

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

$\frac{18 (1 + 1)}{1 + 1} + \frac{- 12 (1 + 1)}{1 + 1} + \frac{2 \cdot 3^{2}}{1} \cdot \frac{1 + 1}{1 + 1} - 12 \div (1 + 1)$

Step 1.9

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

$\frac{18 (1 + 1)}{1 + 1} + \frac{- 12 (1 + 1)}{1 + 1} + \frac{2 \cdot 3^{2} (1 + 1)}{1 + 1} - 12 \div (1 + 1)$

Step 2

Combine the numerators over the common denominator.

$\frac{18 (1 + 1) - 12 (1 + 1) + 2 \cdot 3^{2} (1 + 1) - 12}{1 + 1}$

Step 3

Simplify each term.

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Step 3.1

Add $1$ and $1$ .

$\frac{18 \cdot 2 - 12 (1 + 1) + 2 \cdot 3^{2} (1 + 1) - 12}{1 + 1}$

Step 3.2

Multiply $18$ by $2$ .

$\frac{36 - 12 (1 + 1) + 2 \cdot 3^{2} (1 + 1) - 12}{1 + 1}$

Step 3.3

Add $1$ and $1$ .

$\frac{36 - 12 \cdot 2 + 2 \cdot 3^{2} (1 + 1) - 12}{1 + 1}$

Step 3.4

Multiply $- 12$ by $2$ .

$\frac{36 - 24 + 2 \cdot 3^{2} (1 + 1) - 12}{1 + 1}$

Step 3.5

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

$\frac{36 - 24 + 2 \cdot 9 (1 + 1) - 12}{1 + 1}$

Step 3.6

Multiply $2$ by $9$ .

$\frac{36 - 24 + 18 (1 + 1) - 12}{1 + 1}$

Step 3.7

Add $1$ and $1$ .

$\frac{36 - 24 + 18 \cdot 2 - 12}{1 + 1}$

Step 3.8

Multiply $18$ by $2$ .

$\frac{36 - 24 + 36 - 12}{1 + 1}$

Step 4

Simplify the expression.

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Step 4.1

Subtract $24$ from $36$ .

$\frac{12 + 36 - 12}{1 + 1}$

Step 4.2

Add $12$ and $36$ .

$\frac{48 - 12}{1 + 1}$

Step 4.3

Subtract $12$ from $48$ .

$\frac{36}{1 + 1}$

Step 4.4

Add $1$ and $1$ .

$\frac{36}{2}$

Step 4.5

Divide $36$ by $2$ .

$18$