Algebra Examples

$\frac{6 + 4 \div 2}{4 \div 6 - 1}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $4$ and $2$ .

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Step 1.1.1

Factor $2$ out of $4$ .

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

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $2$ .

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

$\frac{6 + \frac{2}{1}}{4 \div 6 - 1}$

Step 1.1.2.4

Divide $2$ by $1$ .

$\frac{6 + 2}{4 \div 6 - 1}$

Step 1.2

Cancel the common factor of $4$ and $6$ .

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Step 1.2.1

Factor $2$ out of $4$ .

$\frac{6 + 2}{2 (2) \div 6 - 1}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $2$ out of $6$ .

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

$\frac{6 + 2}{\frac{2}{3} - 1}$

Step 2

Multiply the numerator and denominator of the fraction by $3$ .

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Step 2.1

Multiply $\frac{6 + 2}{\frac{2}{3} - 1}$ by $\frac{3}{3}$ .

$\frac{3}{3} \cdot \frac{6 + 2}{\frac{2}{3} - 1}$

Step 2.2

Combine.

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

Step 3

Apply the distributive property.

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

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$\frac{3 \cdot 6 + 3 \cdot 2}{2 + 3 \cdot - 1}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $6$ .

$\frac{18 + 3 \cdot 2}{2 + 3 \cdot - 1}$

Step 5.2

Multiply $3$ by $2$ .

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

Step 5.3

Add $18$ and $6$ .

$\frac{24}{2 + 3 \cdot - 1}$

Step 6

Simplify the denominator.

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Step 6.1

Multiply $3$ by $- 1$ .

$\frac{24}{2 - 3}$

Step 6.2

Subtract $3$ from $2$ .

$\frac{24}{- 1}$

Step 7

Divide $24$ by $- 1$ .

$- 24$