Basic Math Examples

$| - 18 | - (2) (- 3) \div (- 3) - 2 - (- 4)$

Step 1

Find the common denominator.

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Step 1.1

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

$\frac{| - 18 |}{1} - (2) (- 3) \div (- 3) - 2 - (- 4)$

Step 1.2

Multiply $\frac{| - 18 |}{1}$ by $\frac{3}{3}$ .

$\frac{| - 18 |}{1} \cdot \frac{3}{3} - (2) (- 3) \div (- 3) - 2 - (- 4)$

Step 1.3

Multiply $\frac{| - 18 |}{1}$ by $\frac{3}{3}$ .

$\frac{| - 18 | \cdot 3}{3} - (2) (- 3) \div (- 3) - 2 - (- 4)$

Step 1.4

Multiply $(2) (- 3) \div (- 3)$ by $\frac{- 1}{- 1}$ .

$\frac{| - 18 | \cdot 3}{3} - ((2) (- 3) \div (- 3) \cdot \frac{- 1}{- 1}) - 2 - (- 4)$

Step 1.5

Multiply $(2) (- 3) \div (- 3)$ by $\frac{- 1}{- 1}$ .

$\frac{| - 18 | \cdot 3}{3} - \frac{(2) (- 3) \cdot - 1}{- 3 \cdot - 1} - 2 - (- 4)$

Step 1.6

Write $- 2$ as a fraction with denominator $1$ .

$\frac{| - 18 | \cdot 3}{3} - \frac{(2) (- 3) \cdot - 1}{- 3 \cdot - 1} + \frac{- 2}{1} - (- 4)$

Step 1.7

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

$\frac{| - 18 | \cdot 3}{3} - \frac{(2) (- 3) \cdot - 1}{- 3 \cdot - 1} + \frac{- 2}{1} \cdot \frac{3}{3} - (- 4)$

Step 1.8

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

$\frac{| - 18 | \cdot 3}{3} - \frac{(2) (- 3) \cdot - 1}{- 3 \cdot - 1} + \frac{- 2 \cdot 3}{3} - (- 4)$

Step 1.9

Write $- (- 4)$ as a fraction with denominator $1$ .

$\frac{| - 18 | \cdot 3}{3} - \frac{(2) (- 3) \cdot - 1}{- 3 \cdot - 1} + \frac{- 2 \cdot 3}{3} + \frac{- (- 4)}{1}$

Step 1.10

Multiply $\frac{- (- 4)}{1}$ by $\frac{3}{3}$ .

$\frac{| - 18 | \cdot 3}{3} - \frac{(2) (- 3) \cdot - 1}{- 3 \cdot - 1} + \frac{- 2 \cdot 3}{3} + \frac{- (- 4)}{1} \cdot \frac{3}{3}$

Step 1.11

Multiply $\frac{- (- 4)}{1}$ by $\frac{3}{3}$ .

$\frac{| - 18 | \cdot 3}{3} - \frac{(2) (- 3) \cdot - 1}{- 3 \cdot - 1} + \frac{- 2 \cdot 3}{3} + \frac{- (- 4) \cdot 3}{3}$

Step 1.12

Multiply $- 3$ by $- 1$ .

$\frac{| - 18 | \cdot 3}{3} - \frac{(2) (- 3) \cdot - 1}{3} + \frac{- 2 \cdot 3}{3} + \frac{- (- 4) \cdot 3}{3}$

Step 2

Combine the numerators over the common denominator.

$\frac{| - 18 | \cdot 3 - 2 \cdot - 3 \cdot - 1 - 2 \cdot 3 - (- 4) \cdot 3}{3}$

Step 3

Simplify each term.

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Step 3.1

The absolute value is the distance between a number and zero. The distance between $- 18$ and $0$ is $18$ .

$\frac{18 \cdot 3 - 2 \cdot - 3 \cdot - 1 - 2 \cdot 3 - (- 4) \cdot 3}{3}$

Step 3.2

Multiply $18$ by $3$ .

$\frac{54 - 2 \cdot - 3 \cdot - 1 - 2 \cdot 3 - (- 4) \cdot 3}{3}$

Step 3.3

Multiply $- 2 \cdot - 3 \cdot - 1$ .

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Step 3.3.1

Multiply $- 2$ by $- 3$ .

$\frac{54 + 6 \cdot - 1 - 2 \cdot 3 - (- 4) \cdot 3}{3}$

Step 3.3.2

Multiply $6$ by $- 1$ .

$\frac{54 - 6 - 2 \cdot 3 - (- 4) \cdot 3}{3}$

Step 3.4

Multiply $- 2$ by $3$ .

$\frac{54 - 6 - 6 - (- 4) \cdot 3}{3}$

Step 3.5

Multiply $- (- 4) \cdot 3$ .

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Step 3.5.1

Multiply $- 1$ by $- 4$ .

$\frac{54 - 6 - 6 + 4 \cdot 3}{3}$

Step 3.5.2

Multiply $4$ by $3$ .

$\frac{54 - 6 - 6 + 12}{3}$

Step 4

Simplify the expression.

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Step 4.1

Subtract $6$ from $54$ .

$\frac{48 - 6 + 12}{3}$

Step 4.2

Subtract $6$ from $48$ .

$\frac{42 + 12}{3}$

Step 4.3

Add $42$ and $12$ .

$\frac{54}{3}$

Step 4.4

Divide $54$ by $3$ .

$18$