Basic Math Examples

$9 \frac{5}{9} - n = 8 \frac{2}{9}$

Step 1

Simplify the left side.

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Step 1.1

Convert $9 \frac{5}{9}$ to an improper fraction.

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Step 1.1.1

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

$9 + \frac{5}{9} - n = 8 \frac{2}{9}$

Step 1.1.2

Add $9$ and $\frac{5}{9}$ .

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Step 1.1.2.1

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

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

Step 1.1.2.2

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

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

Step 1.1.2.3

Combine the numerators over the common denominator.

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

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $9$ by $9$ .

$\frac{81 + 5}{9} - n = 8 \frac{2}{9}$

Step 1.1.2.4.2

Add $81$ and $5$ .

$\frac{86}{9} - n = 8 \frac{2}{9}$

Step 2

Simplify the right side.

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Step 2.1

Convert $8 \frac{2}{9}$ to an improper fraction.

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Step 2.1.1

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

$\frac{86}{9} - n = 8 + \frac{2}{9}$

Step 2.1.2

Add $8$ and $\frac{2}{9}$ .

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Step 2.1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{86}{9} - n = 8 \cdot \frac{9}{9} + \frac{2}{9}$

Step 2.1.2.2

Combine $8$ and $\frac{9}{9}$ .

$\frac{86}{9} - n = \frac{8 \cdot 9}{9} + \frac{2}{9}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{86}{9} - n = \frac{8 \cdot 9 + 2}{9}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $8$ by $9$ .

$\frac{86}{9} - n = \frac{72 + 2}{9}$

Step 2.1.2.4.2

Add $72$ and $2$ .

$\frac{86}{9} - n = \frac{74}{9}$

Step 3

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

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Step 3.1

Subtract $\frac{86}{9}$ from both sides of the equation.

$- n = \frac{74}{9} - \frac{86}{9}$

Step 3.2

Combine the numerators over the common denominator.

$- n = \frac{74 - 86}{9}$

Step 3.3

Subtract $86$ from $74$ .

$- n = \frac{- 12}{9}$

Step 3.4

Cancel the common factor of $- 12$ and $9$ .

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Step 3.4.1

Factor $3$ out of $- 12$ .

$- n = \frac{3 (- 4)}{9}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $3$ out of $9$ .

$- n = \frac{3 \cdot - 4}{3 \cdot 3}$

Step 3.4.2.2

Cancel the common factor.

$- n = \frac{3 \cdot - 4}{3 \cdot 3}$

Step 3.4.2.3

Rewrite the expression.

$- n = \frac{- 4}{3}$

Step 3.5

Move the negative in front of the fraction.

$- n = - \frac{4}{3}$

Step 4

Divide each term in $- n = - \frac{4}{3}$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- n = - \frac{4}{3}$ by $- 1$ .

$\frac{- n}{- 1} = \frac{- \frac{4}{3}}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{n}{1} = \frac{- \frac{4}{3}}{- 1}$

Step 4.2.2

Divide $n$ by $1$ .

$n = \frac{- \frac{4}{3}}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Dividing two negative values results in a positive value.

$n = \frac{\frac{4}{3}}{1}$

Step 4.3.2

Divide $\frac{4}{3}$ by $1$ .

$n = \frac{4}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = \frac{4}{3}$

Decimal Form:

$n = 1.\overline{3}$

Mixed Number Form:

$n = 1 \frac{1}{3}$