Evaluate (1/4+1/2)/(1/4+1/6)

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

Step 1

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

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

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

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.

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify by adding numbers.

Add $3$ and $6$ .

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

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:

$1 \frac{4}{5}$

Evaluate (1/4+1/2)/(1/4+1/6)

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