Evaluate (2*13/20+3)/(5+(13/20+1)/4)

$\frac{2 \cdot \frac{13}{20} + 3}{5 + \frac{\frac{13}{20} + 1}{4}}$

Multiply the numerator and denominator of the complex fraction by $4$ .

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Multiply $\frac{2 \cdot \frac{13}{20} + 3}{5 + \frac{\frac{13}{20} + 1}{4}}$ by $\frac{4}{4}$ .

$\frac{4}{4} \cdot \frac{2 \cdot \frac{13}{20} + 3}{5 + \frac{\frac{13}{20} + 1}{4}}$

Combine.

$\frac{4 (2 \cdot \frac{13}{20} + 3)}{4 (5 + \frac{\frac{13}{20} + 1}{4})}$

Apply the distributive property.

$\frac{4 (2 \cdot \frac{13}{20}) + 4 \cdot 3}{4 \cdot 5 + 4 \frac{\frac{13}{20} + 1}{4}}$

Cancel the common factor of $4$ .

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Cancel the common factor.

$\frac{4 (2 \cdot \frac{13}{20}) + 4 \cdot 3}{4 \cdot 5 + 4 \frac{\frac{13}{20} + 1}{4}}$

Rewrite the expression.

$\frac{4 (2 \cdot \frac{13}{20}) + 4 \cdot 3}{4 \cdot 5 + \frac{13}{20} + 1}$

Multiply the numerator and denominator of the complex fraction by $20$ .

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Multiply $\frac{4 (2 \cdot \frac{13}{20}) + 4 \cdot 3}{4 \cdot 5 + \frac{13}{20} + 1}$ by $\frac{20}{20}$ .

$\frac{20}{20} \cdot \frac{4 (2 \cdot \frac{13}{20}) + 4 \cdot 3}{4 \cdot 5 + \frac{13}{20} + 1}$

Combine.

$\frac{20 (4 (2 \cdot \frac{13}{20}) + 4 \cdot 3)}{20 (4 \cdot 5 + \frac{13}{20} + 1)}$

Apply the distributive property.

$\frac{20 (4 (2 \cdot \frac{13}{20})) + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 20 (\frac{13}{20}) + 20 \cdot 1}$

Cancel the common factor of $20$ .

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Cancel the common factor.

$\frac{20 (4 (2 \cdot \frac{13}{20})) + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 20 (\frac{13}{20}) + 20 \cdot 1}$

Rewrite the expression.

$\frac{20 (4 (2 \cdot \frac{13}{20})) + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Simplify the numerator.

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Cancel the common factor of $2$ .

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Factor $2$ out of $20$ .

$\frac{20 (4 (2 \cdot \frac{13}{2 (10)})) + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Cancel the common factor.

$\frac{20 (4 (2 \cdot \frac{13}{2 \cdot 10})) + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Rewrite the expression.

$\frac{20 (4 (\frac{13}{10})) + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Cancel the common factor of $2$ .

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Factor $2$ out of $4$ .

$\frac{20 (2 (2) \frac{13}{10}) + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Factor $2$ out of $10$ .

$\frac{20 (2 \cdot 2 \frac{13}{2 \cdot 5}) + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Cancel the common factor.

$\frac{20 (2 \cdot 2 \frac{13}{2 \cdot 5}) + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Rewrite the expression.

$\frac{20 (2 (\frac{13}{5})) + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Combine $2$ and $\frac{13}{5}$ .

$\frac{20 \frac{2 \cdot 13}{5} + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Multiply $2$ by $13$ .

$\frac{20 (\frac{26}{5}) + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Cancel the common factor of $5$ .

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Factor $5$ out of $20$ .

$\frac{5 (4) \frac{26}{5} + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Cancel the common factor.

$\frac{5 \cdot 4 \frac{26}{5} + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Rewrite the expression.

$\frac{4 \cdot 26 + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Multiply $4$ by $26$ .

$\frac{104 + 20 (4 \cdot 3)}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Multiply $4$ by $3$ .

$\frac{104 + 20 \cdot 12}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Multiply $20$ by $12$ .

$\frac{104 + 240}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Add $104$ and $240$ .

$\frac{344}{20 (4 \cdot 5) + 13 + 20 \cdot 1}$

Simplify the denominator.

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Multiply $4$ by $5$ .

$\frac{344}{20 \cdot 20 + 13 + 20 \cdot 1}$

Multiply $20$ by $20$ .

$\frac{344}{400 + 13 + 20 \cdot 1}$

Multiply $20$ by $1$ .

$\frac{344}{400 + 13 + 20}$

Add $400$ and $13$ .

$\frac{344}{413 + 20}$

Add $413$ and $20$ .

$\frac{344}{433}$

The result can be shown in multiple forms.

Exact Form:

$\frac{344}{433}$

Decimal Form:

$0.79445727 \dots$

Evaluate (2*13/20+3)/(5+(13/20+1)/4)

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