Basic Math Examples

$\frac{4}{5} \cdot (n - 10) = - \frac{8}{9}$

Step 1

Multiply both sides of the equation by $\frac{5}{4}$ .

$\frac{5}{4} (\frac{4}{5} \cdot (n - 10)) = \frac{5}{4} (- \frac{8}{9})$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{5}{4} (\frac{4}{5} \cdot (n - 10))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{5}{4} (\frac{4}{5} n + \frac{4}{5} \cdot - 10) = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.2

Combine $\frac{4}{5}$ and $n$ .

$\frac{5}{4} (\frac{4 n}{5} + \frac{4}{5} \cdot - 10) = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.3

Cancel the common factor of $5$ .

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Step 2.1.1.3.1

Factor $5$ out of $- 10$ .

$\frac{5}{4} (\frac{4 n}{5} + \frac{4}{5} \cdot (5 (- 2))) = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{5}{4} (\frac{4 n}{5} + \frac{4}{5} \cdot (5 \cdot - 2)) = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.3.3

Rewrite the expression.

$\frac{5}{4} (\frac{4 n}{5} + 4 \cdot - 2) = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.4

Multiply $4$ by $- 2$ .

$\frac{5}{4} (\frac{4 n}{5} - 8) = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.5

Apply the distributive property.

$\frac{5}{4} \cdot \frac{4 n}{5} + \frac{5}{4} \cdot - 8 = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.6

Cancel the common factor of $5$ .

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Step 2.1.1.6.1

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 n}{5} + \frac{5}{4} \cdot - 8 = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.6.2

Rewrite the expression.

$\frac{1}{4} (4 n) + \frac{5}{4} \cdot - 8 = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.7

Cancel the common factor of $4$ .

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Step 2.1.1.7.1

Factor $4$ out of $4 n$ .

$\frac{1}{4} (4 (n)) + \frac{5}{4} \cdot - 8 = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.7.2

Cancel the common factor.

$\frac{1}{4} (4 n) + \frac{5}{4} \cdot - 8 = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.7.3

Rewrite the expression.

$n + \frac{5}{4} \cdot - 8 = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.8

Cancel the common factor of $4$ .

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Step 2.1.1.8.1

Factor $4$ out of $- 8$ .

$n + \frac{5}{4} \cdot (4 (- 2)) = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.8.2

Cancel the common factor.

$n + \frac{5}{4} \cdot (4 \cdot - 2) = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.8.3

Rewrite the expression.

$n + 5 \cdot - 2 = \frac{5}{4} (- \frac{8}{9})$

Step 2.1.1.9

Multiply $5$ by $- 2$ .

$n - 10 = \frac{5}{4} (- \frac{8}{9})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{5}{4} (- \frac{8}{9})$ .

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Step 2.2.1.1

Cancel the common factor of $4$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{8}{9}$ into the numerator.

$n - 10 = \frac{5}{4} \cdot \frac{- 8}{9}$

Step 2.2.1.1.2

Factor $4$ out of $- 8$ .

$n - 10 = \frac{5}{4} \cdot \frac{4 (- 2)}{9}$

Step 2.2.1.1.3

Cancel the common factor.

$n - 10 = \frac{5}{4} \cdot \frac{4 \cdot - 2}{9}$

Step 2.2.1.1.4

Rewrite the expression.

$n - 10 = 5 (\frac{- 2}{9})$

Step 2.2.1.2

Combine $5$ and $\frac{- 2}{9}$ .

$n - 10 = \frac{5 \cdot - 2}{9}$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Multiply $5$ by $- 2$ .

$n - 10 = \frac{- 10}{9}$

Step 2.2.1.3.2

Move the negative in front of the fraction.

$n - 10 = - \frac{10}{9}$

Step 3

Move all terms not containing $n$ to the right side of the equation.

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Step 3.1

Add $10$ to both sides of the equation.

$n = - \frac{10}{9} + 10$

Step 3.2

To write $10$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$n = - \frac{10}{9} + 10 \cdot \frac{9}{9}$

Step 3.3

Combine $10$ and $\frac{9}{9}$ .

$n = - \frac{10}{9} + \frac{10 \cdot 9}{9}$

Step 3.4

Combine the numerators over the common denominator.

$n = \frac{- 10 + 10 \cdot 9}{9}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $10$ by $9$ .

$n = \frac{- 10 + 90}{9}$

Step 3.5.2

Add $- 10$ and $90$ .

$n = \frac{80}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$n = \frac{80}{9}$

Decimal Form:

$n = 8.\overline{8}$

Mixed Number Form:

$n = 8 \frac{8}{9}$