Algebra Examples

$\frac{1.5}{9}$

Step 1

Set up an equation with $0.1\overline{6}$ .

$x = 0.1\overline{6}$

Step 2

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

Step 3

Multiply both sides of $x = 0.1\overline{6}$ by $10$ to create the first equation.

$10 x = 1.\overline{6}$

Step 4

Multiply both sides of $x = 0.1\overline{6}$ by $100$ to create the second equation.

$100 x = 16.\overline{6}$

Step 5

Subtract $10 x = 1.\overline{6}$ from $100 x = 16.\overline{6}$ to remove the repeating part.

$90 x = 15$

Step 6

Divide each term in $90 x = 15$ by $90$ and simplify.

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Step 6.1

Divide each term in $90 x = 15$ by $90$ .

$\frac{90 x}{90} = \frac{15}{90}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $90$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{90 x}{90} = \frac{15}{90}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{90}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of $15$ and $90$ .

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Step 6.3.1.1

Factor $15$ out of $15$ .

$x = \frac{15 (1)}{90}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor $15$ out of $90$ .

$x = \frac{15 \cdot 1}{15 \cdot 6}$

Step 6.3.1.2.2

Cancel the common factor.

$x = \frac{15 \cdot 1}{15 \cdot 6}$

Step 6.3.1.2.3

Rewrite the expression.

$x = \frac{1}{6}$

Step 7

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

$0 \frac{1}{6}$

Step 8

Convert $0 \frac{1}{6}$ to an improper fraction.

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Step 8.1

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

$0 + \frac{1}{6}$

Step 8.2

Add $0$ and $\frac{1}{6}$ .

$\frac{1}{6}$