Basic Math Examples

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

Step 1

Multiply the numerator and denominator of the fraction by $12$ .

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Step 1.1

Multiply $\frac{\frac{1}{4} + \frac{1}{2}}{\frac{1}{4} + \frac{1}{6}}$ by $\frac{12}{12}$ .

$\frac{12}{12} \cdot \frac{\frac{1}{4} + \frac{1}{2}}{\frac{1}{4} + \frac{1}{6}}$

Step 1.2

Combine.

$\frac{12 (\frac{1}{4} + \frac{1}{2})}{12 (\frac{1}{4} + \frac{1}{6})}$

Step 2

Apply the distributive property.

$\frac{12 (\frac{1}{4}) + 12 (\frac{1}{2})}{12 (\frac{1}{4}) + 12 (\frac{1}{6})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $4$ .

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Step 3.1.1

Factor $4$ out of $12$ .

$\frac{4 (3) \frac{1}{4} + 12 (\frac{1}{2})}{12 (\frac{1}{4}) + 12 (\frac{1}{6})}$

Step 3.1.2

Cancel the common factor.

$\frac{4 \cdot 3 \frac{1}{4} + 12 (\frac{1}{2})}{12 (\frac{1}{4}) + 12 (\frac{1}{6})}$

Step 3.1.3

Rewrite the expression.

$\frac{3 + 12 (\frac{1}{2})}{12 (\frac{1}{4}) + 12 (\frac{1}{6})}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $12$ .

$\frac{3 + 2 (6) \frac{1}{2}}{12 (\frac{1}{4}) + 12 (\frac{1}{6})}$

Step 3.2.2

Cancel the common factor.

$\frac{3 + 2 \cdot 6 \frac{1}{2}}{12 (\frac{1}{4}) + 12 (\frac{1}{6})}$

Step 3.2.3

Rewrite the expression.

$\frac{3 + 6}{12 (\frac{1}{4}) + 12 (\frac{1}{6})}$

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Factor $4$ out of $12$ .

$\frac{3 + 6}{4 (3) \frac{1}{4} + 12 (\frac{1}{6})}$

Step 3.3.2

Cancel the common factor.

$\frac{3 + 6}{4 \cdot 3 \frac{1}{4} + 12 (\frac{1}{6})}$

Step 3.3.3

Rewrite the expression.

$\frac{3 + 6}{3 + 12 (\frac{1}{6})}$

Step 3.4

Cancel the common factor of $6$ .

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Step 3.4.1

Factor $6$ out of $12$ .

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

Step 3.4.2

Cancel the common factor.

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

Step 3.4.3

Rewrite the expression.

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

Step 4

Simplify by adding numbers.

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Step 4.1

Add $3$ and $6$ .

$\frac{9}{3 + 2}$

Step 4.2

Add $3$ and $2$ .

$\frac{9}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{5}$

Decimal Form:

$1.8$

Mixed Number Form:

$1 \frac{4}{5}$