Basic Math Examples

$\frac{\frac{9}{130}}{\frac{9}{130} + \frac{25}{65} \cdot \frac{1}{4}}$

Step 1

Cancel the common factor of $25$ and $65$ .

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Step 1.1

Factor $5$ out of $25$ .

$\frac{\frac{9}{130}}{\frac{9}{130} + \frac{5 (5)}{65} \cdot \frac{1}{4}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5$ out of $65$ .

$\frac{\frac{9}{130}}{\frac{9}{130} + \frac{5 \cdot 5}{5 \cdot 13} \cdot \frac{1}{4}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{9}{130}}{\frac{9}{130} + \frac{5 \cdot 5}{5 \cdot 13} \cdot \frac{1}{4}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{9}{130}}{\frac{9}{130} + \frac{5}{13} \cdot \frac{1}{4}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{9}{130} \cdot \frac{1}{\frac{9}{130} + \frac{5}{13} \cdot \frac{1}{4}}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $\frac{5}{13} \cdot \frac{1}{4}$ .

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Step 3.1.1

Multiply $\frac{5}{13}$ by $\frac{1}{4}$ .

$\frac{9}{130} \cdot \frac{1}{\frac{9}{130} + \frac{5}{13 \cdot 4}}$

Step 3.1.2

Multiply $13$ by $4$ .

$\frac{9}{130} \cdot \frac{1}{\frac{9}{130} + \frac{5}{52}}$

Step 3.2

To write $\frac{9}{130}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9}{130} \cdot \frac{1}{\frac{9}{130} \cdot \frac{2}{2} + \frac{5}{52}}$

Step 3.3

To write $\frac{5}{52}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{9}{130} \cdot \frac{1}{\frac{9}{130} \cdot \frac{2}{2} + \frac{5}{52} \cdot \frac{5}{5}}$

Step 3.4

Write each expression with a common denominator of $260$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{9}{130}$ by $\frac{2}{2}$ .

$\frac{9}{130} \cdot \frac{1}{\frac{9 \cdot 2}{130 \cdot 2} + \frac{5}{52} \cdot \frac{5}{5}}$

Step 3.4.2

Multiply $130$ by $2$ .

$\frac{9}{130} \cdot \frac{1}{\frac{9 \cdot 2}{260} + \frac{5}{52} \cdot \frac{5}{5}}$

Step 3.4.3

Multiply $\frac{5}{52}$ by $\frac{5}{5}$ .

$\frac{9}{130} \cdot \frac{1}{\frac{9 \cdot 2}{260} + \frac{5 \cdot 5}{52 \cdot 5}}$

Step 3.4.4

Multiply $52$ by $5$ .

$\frac{9}{130} \cdot \frac{1}{\frac{9 \cdot 2}{260} + \frac{5 \cdot 5}{260}}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{9}{130} \cdot \frac{1}{\frac{9 \cdot 2 + 5 \cdot 5}{260}}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $9$ by $2$ .

$\frac{9}{130} \cdot \frac{1}{\frac{18 + 5 \cdot 5}{260}}$

Step 3.6.2

Multiply $5$ by $5$ .

$\frac{9}{130} \cdot \frac{1}{\frac{18 + 25}{260}}$

Step 3.6.3

Add $18$ and $25$ .

$\frac{9}{130} \cdot \frac{1}{\frac{43}{260}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{9}{130} (1 (\frac{260}{43}))$

Step 5

Multiply $\frac{260}{43}$ by $1$ .

$\frac{9}{130} \cdot \frac{260}{43}$

Step 6

Cancel the common factor of $130$ .

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Step 6.1

Factor $130$ out of $260$ .

$\frac{9}{130} \cdot \frac{130 (2)}{43}$

Step 6.2

Cancel the common factor.

$\frac{9}{130} \cdot \frac{130 \cdot 2}{43}$

Step 6.3

Rewrite the expression.

$9 (\frac{2}{43})$

Step 7

Combine $9$ and $\frac{2}{43}$ .

$\frac{9 \cdot 2}{43}$

Step 8

Multiply $9$ by $2$ .

$\frac{18}{43}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{18}{43}$

Decimal Form:

$0.41860465 \dots$