Basic Math Examples

$\frac{5}{6} - \frac{1}{3} n = p (5 - 2 n)$

Step 1

Rewrite the equation as $p (5 - 2 n) = \frac{5}{6} - \frac{1}{3} n$ .

$p (5 - 2 n) = \frac{5}{6} - \frac{1}{3} n$

Step 2

Divide each term in $p (5 - 2 n) = \frac{5}{6} - \frac{1}{3} n$ by $5 - 2 n$ and simplify.

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Step 2.1

Divide each term in $p (5 - 2 n) = \frac{5}{6} - \frac{1}{3} n$ by $5 - 2 n$ .

$\frac{p (5 - 2 n)}{5 - 2 n} = \frac{\frac{5}{6}}{5 - 2 n} + \frac{- \frac{1}{3} n}{5 - 2 n}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5 - 2 n$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{p (5 - 2 n)}{5 - 2 n} = \frac{\frac{5}{6}}{5 - 2 n} + \frac{- \frac{1}{3} n}{5 - 2 n}$

Step 2.2.1.2

Divide $p$ by $1$ .

$p = \frac{\frac{5}{6}}{5 - 2 n} + \frac{- \frac{1}{3} n}{5 - 2 n}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify terms.

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Step 2.3.1.1

Combine the numerators over the common denominator.

$p = \frac{\frac{5}{6} - \frac{1}{3} n}{5 - 2 n}$

Step 2.3.1.2

Combine $n$ and $\frac{1}{3}$ .

$p = \frac{\frac{5}{6} - \frac{n}{3}}{5 - 2 n}$

Step 2.3.2

Multiply the numerator and denominator of the fraction by $6$ .

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Step 2.3.2.1

Multiply $\frac{\frac{5}{6} - \frac{n}{3}}{5 - 2 n}$ by $\frac{6}{6}$ .

$p = \frac{6}{6} \cdot \frac{\frac{5}{6} - \frac{n}{3}}{5 - 2 n}$

Step 2.3.2.2

Combine.

$p = \frac{6 (\frac{5}{6} - \frac{n}{3})}{6 (5 - 2 n)}$

Step 2.3.3

Apply the distributive property.

$p = \frac{6 (\frac{5}{6}) + 6 (- \frac{n}{3})}{6 \cdot 5 + 6 (- 2 n)}$

Step 2.3.4

Simplify by cancelling.

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Step 2.3.4.1

Cancel the common factor of $6$ .

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Step 2.3.4.1.1

Cancel the common factor.

$p = \frac{6 (\frac{5}{6}) + 6 (- \frac{n}{3})}{6 \cdot 5 + 6 (- 2 n)}$

Step 2.3.4.1.2

Rewrite the expression.

$p = \frac{5 + 6 (- \frac{n}{3})}{6 \cdot 5 + 6 (- 2 n)}$

Step 2.3.4.2

Cancel the common factor of $3$ .

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Step 2.3.4.2.1

Move the leading negative in $- \frac{n}{3}$ into the numerator.

$p = \frac{5 + 6 \frac{- n}{3}}{6 \cdot 5 + 6 (- 2 n)}$

Step 2.3.4.2.2

Factor $3$ out of $6$ .

$p = \frac{5 + 3 (2) \frac{- n}{3}}{6 \cdot 5 + 6 (- 2 n)}$

Step 2.3.4.2.3

Cancel the common factor.

$p = \frac{5 + 3 \cdot 2 \frac{- n}{3}}{6 \cdot 5 + 6 (- 2 n)}$

Step 2.3.4.2.4

Rewrite the expression.

$p = \frac{5 + 2 (- n)}{6 \cdot 5 + 6 (- 2 n)}$

Step 2.3.4.3

Multiply $- 1$ by $2$ .

$p = \frac{5 - 2 n}{6 \cdot 5 + 6 (- 2 n)}$

Step 2.3.5

Simplify terms.

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Step 2.3.5.1

Factor $6$ out of $6 \cdot 5 + 6 (- 2 n)$ .

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Step 2.3.5.1.1

Factor $6$ out of $6 \cdot 5$ .

$p = \frac{5 - 2 n}{6 (5) + 6 (- 2 n)}$

Step 2.3.5.1.2

Factor $6$ out of $6 (5) + 6 (- 2 n)$ .

$p = \frac{5 - 2 n}{6 (5 - 2 n)}$

Step 2.3.5.2

Cancel the common factor of $5 - 2 n$ .

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Step 2.3.5.2.1

Cancel the common factor.

$p = \frac{5 - 2 n}{6 (5 - 2 n)}$

Step 2.3.5.2.2

Rewrite the expression.

$p = \frac{1}{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$p = \frac{1}{6}$

Decimal Form:

$p = 0.1\overline{6}$