Algebra Examples

$18 \div 6 + 4 \div 2 - 15 \div (- 3) + 4 + (- 2) \div (- 1)$

Step 1

Find the common denominator.

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Step 1.1

Multiply $4 \div 2$ by $\frac{3}{3}$ .

$18 \div 6 + 4 \div 2 \cdot \frac{3}{3} - 15 \div (- 3) + 4 + (- 2) \div (- 1)$

Step 1.2

Multiply $4 \div 2$ by $\frac{3}{3}$ .

$18 \div 6 + \frac{4 \cdot 3}{2 \cdot 3} - 15 \div (- 3) + 4 + (- 2) \div (- 1)$

Step 1.3

Multiply $15 \div (- 3)$ by $\frac{- 2}{- 2}$ .

$18 \div 6 + \frac{4 \cdot 3}{2 \cdot 3} - (15 \div (- 3) \cdot \frac{- 2}{- 2}) + 4 + (- 2) \div (- 1)$

Step 1.4

Multiply $15 \div (- 3)$ by $\frac{- 2}{- 2}$ .

$18 \div 6 + \frac{4 \cdot 3}{2 \cdot 3} - \frac{15 \cdot - 2}{- 3 \cdot - 2} + 4 + (- 2) \div (- 1)$

Step 1.5

Write $4$ as a fraction with denominator $1$ .

$18 \div 6 + \frac{4 \cdot 3}{2 \cdot 3} - \frac{15 \cdot - 2}{- 3 \cdot - 2} + \frac{4}{1} + (- 2) \div (- 1)$

Step 1.6

Multiply $\frac{4}{1}$ by $\frac{6}{6}$ .

$18 \div 6 + \frac{4 \cdot 3}{2 \cdot 3} - \frac{15 \cdot - 2}{- 3 \cdot - 2} + \frac{4}{1} \cdot \frac{6}{6} + (- 2) \div (- 1)$

Step 1.7

Multiply $\frac{4}{1}$ by $\frac{6}{6}$ .

$18 \div 6 + \frac{4 \cdot 3}{2 \cdot 3} - \frac{15 \cdot - 2}{- 3 \cdot - 2} + \frac{4 \cdot 6}{6} + (- 2) \div (- 1)$

Step 1.8

Multiply $(- 2) \div (- 1)$ by $\frac{- 6}{- 6}$ .

$18 \div 6 + \frac{4 \cdot 3}{2 \cdot 3} - \frac{15 \cdot - 2}{- 3 \cdot - 2} + \frac{4 \cdot 6}{6} + (- 2) \div (- 1) \cdot \frac{- 6}{- 6}$

Step 1.9

Multiply $(- 2) \div (- 1)$ by $\frac{- 6}{- 6}$ .

$18 \div 6 + \frac{4 \cdot 3}{2 \cdot 3} - \frac{15 \cdot - 2}{- 3 \cdot - 2} + \frac{4 \cdot 6}{6} + \frac{- 2 \cdot - 6}{- - 6}$

Step 1.10

Multiply $2$ by $3$ .

$18 \div 6 + \frac{4 \cdot 3}{6} - \frac{15 \cdot - 2}{- 3 \cdot - 2} + \frac{4 \cdot 6}{6} + \frac{- 2 \cdot - 6}{- - 6}$

Step 1.11

Multiply $- 3$ by $- 2$ .

$18 \div 6 + \frac{4 \cdot 3}{6} - \frac{15 \cdot - 2}{6} + \frac{4 \cdot 6}{6} + \frac{- 2 \cdot - 6}{- - 6}$

Step 1.12

Reorder the factors of $- - 6$ .

$18 \div 6 + \frac{4 \cdot 3}{6} - \frac{15 \cdot - 2}{6} + \frac{4 \cdot 6}{6} + \frac{- 2 \cdot - 6}{- 6 \cdot - 1}$

Step 1.13

Multiply $- 6$ by $- 1$ .

$18 \div 6 + \frac{4 \cdot 3}{6} - \frac{15 \cdot - 2}{6} + \frac{4 \cdot 6}{6} + \frac{- 2 \cdot - 6}{6}$

Step 2

Combine the numerators over the common denominator.

$\frac{18 + 4 \cdot 3 - 15 \cdot - 2 + 4 \cdot 6 - 2 \cdot - 6}{6}$

Step 3

Simplify each term.

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Step 3.1

Multiply $4$ by $3$ .

$\frac{18 + 12 - 15 \cdot - 2 + 4 \cdot 6 - 2 \cdot - 6}{6}$

Step 3.2

Multiply $- 15$ by $- 2$ .

$\frac{18 + 12 + 30 + 4 \cdot 6 - 2 \cdot - 6}{6}$

Step 3.3

Multiply $4$ by $6$ .

$\frac{18 + 12 + 30 + 24 - 2 \cdot - 6}{6}$

Step 3.4

Multiply $- 2$ by $- 6$ .

$\frac{18 + 12 + 30 + 24 + 12}{6}$

Step 4

Simplify the expression.

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Step 4.1

Add $18$ and $12$ .

$\frac{30 + 30 + 24 + 12}{6}$

Step 4.2

Add $30$ and $30$ .

$\frac{60 + 24 + 12}{6}$

Step 4.3

Add $60$ and $24$ .

$\frac{84 + 12}{6}$

Step 4.4

Add $84$ and $12$ .

$\frac{96}{6}$

Step 4.5

Divide $96$ by $6$ .

$16$