Pre-Algebra Examples

$\frac{9}{10} n = - 1 \frac{1}{10}$

Step 1

Simplify the left side.

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Step 1.1

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

$\frac{9 n}{10} = - 1 \frac{1}{10}$

Step 2

Simplify the right side.

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Step 2.1

Convert $1 \frac{1}{10}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{9 n}{10} = - (1 + \frac{1}{10})$

Step 2.1.2

Add $1$ and $\frac{1}{10}$ .

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Step 2.1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{9 n}{10} = - (\frac{10}{10} + \frac{1}{10})$

Step 2.1.2.2

Combine the numerators over the common denominator.

$\frac{9 n}{10} = - \frac{10 + 1}{10}$

Step 2.1.2.3

Add $10$ and $1$ .

$\frac{9 n}{10} = - \frac{11}{10}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$9 n = - 11$

Step 4

Divide each term in $9 n = - 11$ by $9$ and simplify.

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Step 4.1

Divide each term in $9 n = - 11$ by $9$ .

$\frac{9 n}{9} = \frac{- 11}{9}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $9$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{9 n}{9} = \frac{- 11}{9}$

Step 4.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 11}{9}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$n = - \frac{11}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{11}{9}$

Decimal Form:

$n = - 1.\overline{2}$

Mixed Number Form:

$n = - 1 \frac{2}{9}$