Basic Math Examples

$\frac{\frac{3}{2} + \frac{3}{4}}{\frac{6}{11} - \frac{4}{22}}$

Step 1

Cancel the common factor of $4$ and $22$ .

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Step 1.1

Factor $2$ out of $4$ .

$\frac{\frac{3}{2} + \frac{3}{4}}{\frac{6}{11} - \frac{2 (2)}{22}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $22$ .

$\frac{\frac{3}{2} + \frac{3}{4}}{\frac{6}{11} - \frac{2 \cdot 2}{2 \cdot 11}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{3}{2} + \frac{3}{4}}{\frac{6}{11} - \frac{2 \cdot 2}{2 \cdot 11}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{3}{2} + \frac{3}{4}}{\frac{6}{11} - \frac{2}{11}}$

Step 2

Multiply the numerator and denominator of the fraction by $44$ .

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Step 2.1

Multiply $\frac{\frac{3}{2} + \frac{3}{4}}{\frac{6}{11} - \frac{2}{11}}$ by $\frac{44}{44}$ .

$\frac{44}{44} \cdot \frac{\frac{3}{2} + \frac{3}{4}}{\frac{6}{11} - \frac{2}{11}}$

Step 2.2

Combine.

$\frac{44 (\frac{3}{2} + \frac{3}{4})}{44 (\frac{6}{11} - \frac{2}{11})}$

Step 3

Apply the distributive property.

$\frac{44 (\frac{3}{2}) + 44 (\frac{3}{4})}{44 (\frac{6}{11}) + 44 (- \frac{2}{11})}$

Step 4

Simplify by cancelling.

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Step 4.1

Cancel the common factor of $2$ .

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Step 4.1.1

Factor $2$ out of $44$ .

$\frac{2 (22) \frac{3}{2} + 44 (\frac{3}{4})}{44 (\frac{6}{11}) + 44 (- \frac{2}{11})}$

Step 4.1.2

Cancel the common factor.

$\frac{2 \cdot 22 \frac{3}{2} + 44 (\frac{3}{4})}{44 (\frac{6}{11}) + 44 (- \frac{2}{11})}$

Step 4.1.3

Rewrite the expression.

$\frac{22 \cdot 3 + 44 (\frac{3}{4})}{44 (\frac{6}{11}) + 44 (- \frac{2}{11})}$

Step 4.2

Multiply $22$ by $3$ .

$\frac{66 + 44 (\frac{3}{4})}{44 (\frac{6}{11}) + 44 (- \frac{2}{11})}$

Step 4.3

Cancel the common factor of $4$ .

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Step 4.3.1

Factor $4$ out of $44$ .

$\frac{66 + 4 (11) \frac{3}{4}}{44 (\frac{6}{11}) + 44 (- \frac{2}{11})}$

Step 4.3.2

Cancel the common factor.

$\frac{66 + 4 \cdot 11 \frac{3}{4}}{44 (\frac{6}{11}) + 44 (- \frac{2}{11})}$

Step 4.3.3

Rewrite the expression.

$\frac{66 + 11 \cdot 3}{44 (\frac{6}{11}) + 44 (- \frac{2}{11})}$

Step 4.4

Multiply $11$ by $3$ .

$\frac{66 + 33}{44 (\frac{6}{11}) + 44 (- \frac{2}{11})}$

Step 4.5

Cancel the common factor of $11$ .

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Step 4.5.1

Factor $11$ out of $44$ .

$\frac{66 + 33}{11 (4) \frac{6}{11} + 44 (- \frac{2}{11})}$

Step 4.5.2

Cancel the common factor.

$\frac{66 + 33}{11 \cdot 4 \frac{6}{11} + 44 (- \frac{2}{11})}$

Step 4.5.3

Rewrite the expression.

$\frac{66 + 33}{4 \cdot 6 + 44 (- \frac{2}{11})}$

Step 4.6

Multiply $4$ by $6$ .

$\frac{66 + 33}{24 + 44 (- \frac{2}{11})}$

Step 4.7

Cancel the common factor of $11$ .

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Step 4.7.1

Move the leading negative in $- \frac{2}{11}$ into the numerator.

$\frac{66 + 33}{24 + 44 (\frac{- 2}{11})}$

Step 4.7.2

Factor $11$ out of $44$ .

$\frac{66 + 33}{24 + 11 (4) \frac{- 2}{11}}$

Step 4.7.3

Cancel the common factor.

$\frac{66 + 33}{24 + 11 \cdot 4 \frac{- 2}{11}}$

Step 4.7.4

Rewrite the expression.

$\frac{66 + 33}{24 + 4 \cdot - 2}$

Step 4.8

Multiply $4$ by $- 2$ .

$\frac{66 + 33}{24 - 8}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $66$ and $33$ .

$\frac{99}{24 - 8}$

Step 5.2

Subtract $8$ from $24$ .

$\frac{99}{16}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{99}{16}$

Decimal Form:

$6.1875$

Mixed Number Form:

$6 \frac{3}{16}$