Basic Math Examples

$\frac{\frac{12 - 1}{9} - \frac{12 - 1}{90}}{\frac{2}{9} + \frac{22 - 2}{9}}$

Step 1

Multiply the numerator and denominator of the fraction by $90$ .

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Step 1.1

Multiply $\frac{\frac{12 - 1}{9} - \frac{12 - 1}{90}}{\frac{2}{9} + \frac{22 - 2}{9}}$ by $\frac{90}{90}$ .

$\frac{90}{90} \cdot \frac{\frac{12 - 1}{9} - \frac{12 - 1}{90}}{\frac{2}{9} + \frac{22 - 2}{9}}$

Step 1.2

Combine.

$\frac{90 (\frac{12 - 1}{9} - \frac{12 - 1}{90})}{90 (\frac{2}{9} + \frac{22 - 2}{9})}$

Step 2

Apply the distributive property.

$\frac{90 \frac{12 - 1}{9} + 90 (- \frac{12 - 1}{90})}{90 (\frac{2}{9}) + 90 \frac{22 - 2}{9}}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $9$ .

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Step 3.1.1

Factor $9$ out of $90$ .

$\frac{9 (10) \frac{12 - 1}{9} + 90 (- \frac{12 - 1}{90})}{90 (\frac{2}{9}) + 90 \frac{22 - 2}{9}}$

Step 3.1.2

Cancel the common factor.

$\frac{9 \cdot 10 \frac{12 - 1}{9} + 90 (- \frac{12 - 1}{90})}{90 (\frac{2}{9}) + 90 \frac{22 - 2}{9}}$

Step 3.1.3

Rewrite the expression.

$\frac{10 (12 - 1) + 90 (- \frac{12 - 1}{90})}{90 (\frac{2}{9}) + 90 \frac{22 - 2}{9}}$

Step 3.2

Cancel the common factor of $90$ .

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Step 3.2.1

Move the leading negative in $- \frac{12 - 1}{90}$ into the numerator.

$\frac{10 (12 - 1) + 90 \frac{- (12 - 1)}{90}}{90 (\frac{2}{9}) + 90 \frac{22 - 2}{9}}$

Step 3.2.2

Cancel the common factor.

$\frac{10 (12 - 1) + 90 \frac{- (12 - 1)}{90}}{90 (\frac{2}{9}) + 90 \frac{22 - 2}{9}}$

Step 3.2.3

Rewrite the expression.

$\frac{10 (12 - 1) - (12 - 1)}{90 (\frac{2}{9}) + 90 \frac{22 - 2}{9}}$

Step 3.3

Cancel the common factor of $9$ .

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Step 3.3.1

Factor $9$ out of $90$ .

$\frac{10 (12 - 1) - (12 - 1)}{9 (10) \frac{2}{9} + 90 \frac{22 - 2}{9}}$

Step 3.3.2

Cancel the common factor.

$\frac{10 (12 - 1) - (12 - 1)}{9 \cdot 10 \frac{2}{9} + 90 \frac{22 - 2}{9}}$

Step 3.3.3

Rewrite the expression.

$\frac{10 (12 - 1) - (12 - 1)}{10 \cdot 2 + 90 \frac{22 - 2}{9}}$

Step 3.4

Multiply $10$ by $2$ .

$\frac{10 (12 - 1) - (12 - 1)}{20 + 90 \frac{22 - 2}{9}}$

Step 3.5

Cancel the common factor of $9$ .

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Step 3.5.1

Factor $9$ out of $90$ .

$\frac{10 (12 - 1) - (12 - 1)}{20 + 9 (10) \frac{22 - 2}{9}}$

Step 3.5.2

Cancel the common factor.

$\frac{10 (12 - 1) - (12 - 1)}{20 + 9 \cdot 10 \frac{22 - 2}{9}}$

Step 3.5.3

Rewrite the expression.

$\frac{10 (12 - 1) - (12 - 1)}{20 + 10 (22 - 2)}$

Step 4

Simplify the numerator.

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Step 4.1

Subtract $1$ from $12$ .

$\frac{10 \cdot 11 - (12 - 1)}{20 + 10 (22 - 2)}$

Step 4.2

Multiply $10$ by $11$ .

$\frac{110 - (12 - 1)}{20 + 10 (22 - 2)}$

Step 4.3

Subtract $1$ from $12$ .

$\frac{110 - 1 \cdot 11}{20 + 10 (22 - 2)}$

Step 4.4

Multiply $- 1$ by $11$ .

$\frac{110 - 11}{20 + 10 (22 - 2)}$

Step 4.5

Subtract $11$ from $110$ .

$\frac{99}{20 + 10 (22 - 2)}$

Step 5

Simplify the denominator.

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Step 5.1

Subtract $2$ from $22$ .

$\frac{99}{20 + 10 \cdot 20}$

Step 5.2

Multiply $10$ by $20$ .

$\frac{99}{20 + 200}$

Step 5.3

Add $20$ and $200$ .

$\frac{99}{220}$

Step 6

Cancel the common factor of $99$ and $220$ .

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Step 6.1

Factor $11$ out of $99$ .

$\frac{11 (9)}{220}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $11$ out of $220$ .

$\frac{11 \cdot 9}{11 \cdot 20}$

Step 6.2.2

Cancel the common factor.

$\frac{11 \cdot 9}{11 \cdot 20}$

Step 6.2.3

Rewrite the expression.

$\frac{9}{20}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{20}$

Decimal Form:

$0.45$