Algebra Examples

$12 \cdot 12 \cdot 12 + 12 \cdot 12 + 12 \cdot 12 + 12 \div 12 \div 12 + 12 \div 12$

Step 1

Combine the numerators over the common denominator.

$12 \cdot 12 \cdot 12 + 12 \cdot 12 + 12 \cdot 12 + \frac{12 \div 12 + 12}{12}$

Step 2

Simplify the expression.

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Step 2.1

Divide $12$ by $12$ .

$12 \cdot 12 \cdot 12 + 12 \cdot 12 + 12 \cdot 12 + \frac{1 + 12}{12}$

Step 2.2

Add $1$ and $12$ .

$12 \cdot 12 \cdot 12 + 12 \cdot 12 + 12 \cdot 12 + \frac{13}{12}$

Step 3

Find the common denominator.

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Step 3.1

Write $12 \cdot 12 \cdot 12$ as a fraction with denominator $1$ .

$\frac{12 \cdot 12 \cdot 12}{1} + 12 \cdot 12 + 12 \cdot 12 + \frac{13}{12}$

Step 3.2

Multiply $\frac{12 \cdot 12 \cdot 12}{1}$ by $\frac{12}{12}$ .

$\frac{12 \cdot 12 \cdot 12}{1} \cdot \frac{12}{12} + 12 \cdot 12 + 12 \cdot 12 + \frac{13}{12}$

Step 3.3

Multiply $\frac{12 \cdot 12 \cdot 12}{1}$ by $\frac{12}{12}$ .

$\frac{12 \cdot 12 \cdot 12 \cdot 12}{12} + 12 \cdot 12 + 12 \cdot 12 + \frac{13}{12}$

Step 3.4

Write $12 \cdot 12$ as a fraction with denominator $1$ .

$\frac{12 \cdot 12 \cdot 12 \cdot 12}{12} + \frac{12 \cdot 12}{1} + 12 \cdot 12 + \frac{13}{12}$

Step 3.5

Multiply $\frac{12 \cdot 12}{1}$ by $\frac{12}{12}$ .

$\frac{12 \cdot 12 \cdot 12 \cdot 12}{12} + \frac{12 \cdot 12}{1} \cdot \frac{12}{12} + 12 \cdot 12 + \frac{13}{12}$

Step 3.6

Multiply $\frac{12 \cdot 12}{1}$ by $\frac{12}{12}$ .

$\frac{12 \cdot 12 \cdot 12 \cdot 12}{12} + \frac{12 \cdot 12 \cdot 12}{12} + 12 \cdot 12 + \frac{13}{12}$

Step 3.7

Write $12 \cdot 12$ as a fraction with denominator $1$ .

$\frac{12 \cdot 12 \cdot 12 \cdot 12}{12} + \frac{12 \cdot 12 \cdot 12}{12} + \frac{12 \cdot 12}{1} + \frac{13}{12}$

Step 3.8

Multiply $\frac{12 \cdot 12}{1}$ by $\frac{12}{12}$ .

$\frac{12 \cdot 12 \cdot 12 \cdot 12}{12} + \frac{12 \cdot 12 \cdot 12}{12} + \frac{12 \cdot 12}{1} \cdot \frac{12}{12} + \frac{13}{12}$

Step 3.9

Multiply $\frac{12 \cdot 12}{1}$ by $\frac{12}{12}$ .

$\frac{12 \cdot 12 \cdot 12 \cdot 12}{12} + \frac{12 \cdot 12 \cdot 12}{12} + \frac{12 \cdot 12 \cdot 12}{12} + \frac{13}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{12 \cdot 12 \cdot 12 \cdot 12 + 12 \cdot 12 \cdot 12 + 12 \cdot 12 \cdot 12 + 13}{12}$

Step 5

Simplify each term.

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Step 5.1

Multiply $12 \cdot 12 \cdot 12 \cdot 12$ .

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Step 5.1.1

Multiply $12$ by $12$ .

$\frac{144 \cdot 12 \cdot 12 + 12 \cdot 12 \cdot 12 + 12 \cdot 12 \cdot 12 + 13}{12}$

Step 5.1.2

Multiply $144$ by $12$ .

$\frac{1728 \cdot 12 + 12 \cdot 12 \cdot 12 + 12 \cdot 12 \cdot 12 + 13}{12}$

Step 5.1.3

Multiply $1728$ by $12$ .

$\frac{20736 + 12 \cdot 12 \cdot 12 + 12 \cdot 12 \cdot 12 + 13}{12}$

Step 5.2

Multiply $12 \cdot 12 \cdot 12$ .

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Step 5.2.1

Multiply $12$ by $12$ .

$\frac{20736 + 144 \cdot 12 + 12 \cdot 12 \cdot 12 + 13}{12}$

Step 5.2.2

Multiply $144$ by $12$ .

$\frac{20736 + 1728 + 12 \cdot 12 \cdot 12 + 13}{12}$

Step 5.3

Multiply $12 \cdot 12 \cdot 12$ .

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Step 5.3.1

Multiply $12$ by $12$ .

$\frac{20736 + 1728 + 144 \cdot 12 + 13}{12}$

Step 5.3.2

Multiply $144$ by $12$ .

$\frac{20736 + 1728 + 1728 + 13}{12}$

Step 6

Simplify by adding numbers.

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Step 6.1

Add $20736$ and $1728$ .

$\frac{22464 + 1728 + 13}{12}$

Step 6.2

Add $22464$ and $1728$ .

$\frac{24192 + 13}{12}$

Step 6.3

Add $24192$ and $13$ .

$\frac{24205}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{24205}{12}$

Decimal Form:

$2017.08\overline{3}$

Mixed Number Form:

$2017 \frac{1}{12}$