Basic Math Examples

$0.41\overline{6}$

Step 1

Set up an equation with

$0.41\overline{6}$ .

$x = 0.41\overline{6}$

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

$x = 0.41\overline{6}$ by

$100$ to create the first equation.

$100 x = 41.\overline{6}$

Step 4

Multiply both sides of

$x = 0.41\overline{6}$ by

$1000$ to create the second equation.

$1000 x = 416.\overline{6}$

Step 5

Subtract

$100 x = 41.\overline{6}$ from

$1000 x = 416.\overline{6}$ to remove the repeating part.

$900 x = 375$

Step 6

Divide each term in

$900 x = 375$ by

$900$ and simplify.

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Step 6.1

Divide each term in

$900 x = 375$ by

$900$ .

$\frac{900 x}{900} = \frac{375}{900}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of

$900$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{900 x}{900} = \frac{375}{900}$

Step 6.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{375}{900}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of

$375$ and

$900$ .

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Step 6.3.1.1

Factor

$75$ out of

$375$ .

$x = \frac{75 (5)}{900}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor

$75$ out of

$900$ .

$x = \frac{75 \cdot 5}{75 \cdot 12}$

Step 6.3.1.2.2

Cancel the common factor.

$x = \frac{75 \cdot 5}{75 \cdot 12}$

Step 6.3.1.2.3

Rewrite the expression.

$x = \frac{5}{12}$

Step 7

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

$0 \frac{5}{12}$

Step 8

Convert

$0 \frac{5}{12}$ to an improper fraction.

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Step 8.1

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

$0 + \frac{5}{12}$

Step 8.2

Add

$0$ and

$\frac{5}{12}$ .

$\frac{5}{12}$