Basic Math Examples

$3.\overline{1}$

Step 1

Create two equations where the only numbers to the right of the decimal place are the repeating part.

Step 2

Set up an equation with $0.\overline{1}$ .

$x = 0.\overline{1}$

Step 3

Multiply both sides of $x = 0.\overline{1}$ by $10$ to create the second equation.

$10 x = 1.\overline{1}$

Step 4

Subtract $x = 0.\overline{1}$ from $10 x = 1.\overline{1}$ to remove the repeating part.

$9 x = 1$

Step 5

Divide each term in $9 x = 1$ by $9$ and simplify.

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Step 5.1

Divide each term in $9 x = 1$ by $9$ .

$\frac{9 x}{9} = \frac{1}{9}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $9$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{1}{9}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{9}$

Step 6

Write as a mixed number by taking the whole number part along with the solution to the equation.

$3 \frac{1}{9}$

Step 7

Convert $3 \frac{1}{9}$ to an improper fraction.

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Step 7.1

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

$3 + \frac{1}{9}$

Step 7.2

Add $3$ and $\frac{1}{9}$ .

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Step 7.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$3 \cdot \frac{9}{9} + \frac{1}{9}$

Step 7.2.2

Combine $3$ and $\frac{9}{9}$ .

$\frac{3 \cdot 9}{9} + \frac{1}{9}$

Step 7.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 9 + 1}{9}$

Step 7.2.4

Simplify the numerator.

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Step 7.2.4.1

Multiply $3$ by $9$ .

$\frac{27 + 1}{9}$

Step 7.2.4.2

Add $27$ and $1$ .

$\frac{28}{9}$