Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Combine.

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

Step 5

Apply the distributive property.

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

Step 6

Cancel the common factor of $20$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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

Step 7

Simplify the numerator.

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Step 7.1

Multiply $20 \cdot 4 \cdot 2$ .

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Step 7.1.1

Multiply $20$ by $4$ .

$\frac{80 \cdot 2 \cdot \frac{13}{20} + 20 \cdot 4 \cdot 3}{20 \cdot 4 \cdot 5 + 13 + 20 \cdot 1}$

Step 7.1.2

Multiply $80$ by $2$ .

$\frac{160 \cdot \frac{13}{20} + 20 \cdot 4 \cdot 3}{20 \cdot 4 \cdot 5 + 13 + 20 \cdot 1}$

Step 7.2

Cancel the common factor of $20$ .

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Step 7.2.1

Factor $20$ out of $160$ .

$\frac{20 (8) \cdot \frac{13}{20} + 20 \cdot 4 \cdot 3}{20 \cdot 4 \cdot 5 + 13 + 20 \cdot 1}$

Step 7.2.2

Cancel the common factor.

$\frac{20 \cdot 8 \cdot \frac{13}{20} + 20 \cdot 4 \cdot 3}{20 \cdot 4 \cdot 5 + 13 + 20 \cdot 1}$

Step 7.2.3

Rewrite the expression.

$\frac{8 \cdot 13 + 20 \cdot 4 \cdot 3}{20 \cdot 4 \cdot 5 + 13 + 20 \cdot 1}$

Step 7.3

Multiply $8$ by $13$ .

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

Step 7.4

Multiply $20 \cdot 4 \cdot 3$ .

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Step 7.4.1

Multiply $20$ by $4$ .

$\frac{104 + 80 \cdot 3}{20 \cdot 4 \cdot 5 + 13 + 20 \cdot 1}$

Step 7.4.2

Multiply $80$ by $3$ .

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

Step 7.5

Add $104$ and $240$ .

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

Step 8

Simplify the denominator.

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Step 8.1

Multiply $20 \cdot 4 \cdot 5$ .

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Step 8.1.1

Multiply $20$ by $4$ .

$\frac{344}{80 \cdot 5 + 13 + 20 \cdot 1}$

Step 8.1.2

Multiply $80$ by $5$ .

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

Step 8.2

Multiply $20$ by $1$ .

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

Step 8.3

Add $400$ and $13$ .

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

Step 8.4

Add $413$ and $20$ .

$\frac{344}{433}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{344}{433}$

Decimal Form:

$0.79445727 \dots$