Basic Math Examples

$\frac{13}{78} = \frac{n}{15}$

Step 1

Rewrite the equation as $\frac{n}{15} = \frac{13}{78}$ .

$\frac{n}{15} = \frac{13}{78}$

Step 2

Multiply both sides of the equation by $15$ .

$15 \frac{n}{15} = 15 (\frac{13}{78})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $15$ .

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Step 3.1.1.1

Cancel the common factor.

$15 \frac{n}{15} = 15 (\frac{13}{78})$

Step 3.1.1.2

Rewrite the expression.

$n = 15 (\frac{13}{78})$

$n = 15 (\frac{13}{78})$

$n = 15 (\frac{13}{78})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $15 (\frac{13}{78})$ .

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Step 3.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Factor $3$ out of $15$ .

$n = 3 (5) \frac{13}{78}$

Step 3.2.1.1.2

Factor $3$ out of $78$ .

$n = 3 \cdot 5 \frac{13}{3 \cdot 26}$

Step 3.2.1.1.3

Cancel the common factor.

$n = 3 \cdot 5 \frac{13}{3 \cdot 26}$

Step 3.2.1.1.4

Rewrite the expression.

$n = 5 (\frac{13}{26})$

$n = 5 (\frac{13}{26})$

Step 3.2.1.2

Combine $5$ and $\frac{13}{26}$ .

$n = \frac{5 \cdot 13}{26}$

Step 3.2.1.3

Multiply $5$ by $13$ .

$n = \frac{65}{26}$

Step 3.2.1.4

Cancel the common factor of $65$ and $26$ .

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Step 3.2.1.4.1

Factor $13$ out of $65$ .

$n = \frac{13 (5)}{26}$

Step 3.2.1.4.2

Cancel the common factors.

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Step 3.2.1.4.2.1

Factor $13$ out of $26$ .

$n = \frac{13 \cdot 5}{13 \cdot 2}$

Step 3.2.1.4.2.2

Cancel the common factor.

$n = \frac{13 \cdot 5}{13 \cdot 2}$

Step 3.2.1.4.2.3

Rewrite the expression.

$n = \frac{5}{2}$

$n = \frac{5}{2}$

$n = \frac{5}{2}$

$n = \frac{5}{2}$

$n = \frac{5}{2}$

$n = \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$n = \frac{5}{2}$

Decimal Form:

$n = 2.5$

Mixed Number Form:

$n = 2 \frac{1}{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$