Find the Exact Value (1/2+1/6)/(1/4+1/3)

$\frac{\frac{1}{2} + \frac{1}{6}}{\frac{1}{4} + \frac{1}{3}}$

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

Multiply $\frac{\frac{1}{2} + \frac{1}{6}}{\frac{1}{4} + \frac{1}{3}}$ by $\frac{12}{12}$ .

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $2$ .

Factor $2$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify by adding numbers.

Add $6$ and $2$ .

$\frac{8}{3 + 4}$

Add $3$ and $4$ .

$\frac{8}{7}$

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{7}$

Decimal Form:

$1.\overline{142857}$

Mixed Number Form:

$1 \frac{1}{7}$

Find the Exact Value (1/2+1/6)/(1/4+1/3)

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