Basic Math Examples

$\frac{\frac{12 - 1}{9} - \frac{12}{9}}{\frac{2}{9} + \frac{22 - 2}{9}}$

Step 1

Cancel the common factor of $12$ and $9$ .

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Step 1.1

Factor $3$ out of $12$ .

$\frac{\frac{12 - 1}{9} - \frac{3 (4)}{9}}{\frac{2}{9} + \frac{22 - 2}{9}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $9$ .

$\frac{\frac{12 - 1}{9} - \frac{3 \cdot 4}{3 \cdot 3}}{\frac{2}{9} + \frac{22 - 2}{9}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{12 - 1}{9} - \frac{3 \cdot 4}{3 \cdot 3}}{\frac{2}{9} + \frac{22 - 2}{9}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{12 - 1}{9} - \frac{4}{3}}{\frac{2}{9} + \frac{22 - 2}{9}}$

Step 2

Multiply the numerator and denominator of the fraction by $9$ .

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Step 2.1

Multiply $\frac{\frac{12 - 1}{9} - \frac{4}{3}}{\frac{2}{9} + \frac{22 - 2}{9}}$ by $\frac{9}{9}$ .

$\frac{9}{9} \cdot \frac{\frac{12 - 1}{9} - \frac{4}{3}}{\frac{2}{9} + \frac{22 - 2}{9}}$

Step 2.2

Combine.

$\frac{9 (\frac{12 - 1}{9} - \frac{4}{3})}{9 (\frac{2}{9} + \frac{22 - 2}{9})}$

Step 3

Apply the distributive property.

$\frac{9 \frac{12 - 1}{9} + 9 (- \frac{4}{3})}{9 (\frac{2}{9}) + 9 \frac{22 - 2}{9}}$

Step 4

Simplify by cancelling.

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Step 4.1

Cancel the common factor of $9$ .

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Step 4.1.1

Cancel the common factor.

$\frac{9 \frac{12 - 1}{9} + 9 (- \frac{4}{3})}{9 (\frac{2}{9}) + 9 \frac{22 - 2}{9}}$

Step 4.1.2

Rewrite the expression.

$\frac{12 - 1 + 9 (- \frac{4}{3})}{9 (\frac{2}{9}) + 9 \frac{22 - 2}{9}}$

Step 4.2

Cancel the common factor of $3$ .

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Step 4.2.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{12 - 1 + 9 (\frac{- 4}{3})}{9 (\frac{2}{9}) + 9 \frac{22 - 2}{9}}$

Step 4.2.2

Factor $3$ out of $9$ .

$\frac{12 - 1 + 3 (3) \frac{- 4}{3}}{9 (\frac{2}{9}) + 9 \frac{22 - 2}{9}}$

Step 4.2.3

Cancel the common factor.

$\frac{12 - 1 + 3 \cdot 3 \frac{- 4}{3}}{9 (\frac{2}{9}) + 9 \frac{22 - 2}{9}}$

Step 4.2.4

Rewrite the expression.

$\frac{12 - 1 + 3 \cdot - 4}{9 (\frac{2}{9}) + 9 \frac{22 - 2}{9}}$

Step 4.3

Multiply $3$ by $- 4$ .

$\frac{12 - 1 - 12}{9 (\frac{2}{9}) + 9 \frac{22 - 2}{9}}$

Step 4.4

Cancel the common factor of $9$ .

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Step 4.4.1

Cancel the common factor.

$\frac{12 - 1 - 12}{9 (\frac{2}{9}) + 9 \frac{22 - 2}{9}}$

Step 4.4.2

Rewrite the expression.

$\frac{12 - 1 - 12}{2 + 9 \frac{22 - 2}{9}}$

Step 4.5

Cancel the common factor of $9$ .

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Step 4.5.1

Cancel the common factor.

$\frac{12 - 1 - 12}{2 + 9 \frac{22 - 2}{9}}$

Step 4.5.2

Rewrite the expression.

$\frac{12 - 1 - 12}{2 + 22 - 2}$

Step 5

Simplify the numerator.

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Step 5.1

Subtract $1$ from $12$ .

$\frac{11 - 12}{2 + 22 - 2}$

Step 5.2

Subtract $12$ from $11$ .

$\frac{- 1}{2 + 22 - 2}$

Step 6

Simplify the denominator.

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Step 6.1

Add $2$ and $22$ .

$\frac{- 1}{24 - 2}$

Step 6.2

Subtract $2$ from $24$ .

$\frac{- 1}{22}$

Step 7

Move the negative in front of the fraction.

$- \frac{1}{22}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{22}$

Decimal Form:

$- 0.0\overline{45}$