Basic Math Examples

$f + \frac{2}{9} = 9 \frac{1}{9}$

Step 1

Simplify the right side.

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Step 1.1

Convert $9 \frac{1}{9}$ to an improper fraction.

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Step 1.1.1

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

$f + \frac{2}{9} = 9 + \frac{1}{9}$

Step 1.1.2

Add $9$ and $\frac{1}{9}$ .

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Step 1.1.2.1

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

$f + \frac{2}{9} = 9 \cdot \frac{9}{9} + \frac{1}{9}$

Step 1.1.2.2

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

$f + \frac{2}{9} = \frac{9 \cdot 9}{9} + \frac{1}{9}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$f + \frac{2}{9} = \frac{9 \cdot 9 + 1}{9}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $9$ by $9$ .

$f + \frac{2}{9} = \frac{81 + 1}{9}$

Step 1.1.2.4.2

Add $81$ and $1$ .

$f + \frac{2}{9} = \frac{82}{9}$

Step 2

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

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Step 2.1

Subtract $\frac{2}{9}$ from both sides of the equation.

$f = \frac{82}{9} - \frac{2}{9}$

Step 2.2

Combine the numerators over the common denominator.

$f = \frac{82 - 2}{9}$

Step 2.3

Subtract $2$ from $82$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$f = 8.\overline{8}$

Mixed Number Form:

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