Basic Math Examples

$- 2.\overline{481}$

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 $0.\overline{481}$ .

$x = 0.\overline{481}$

Step 3

Multiply both sides of $x = 0.\overline{481}$ by $1000$ to create the second equation.

$1000 x = 481.\overline{481}$

Step 4

Subtract $x = 0.\overline{481}$ from $1000 x = 481.\overline{481}$ to remove the repeating part.

$999 x = 481$

Step 5

Divide each term in $999 x = 481$ by $999$ and simplify.

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Step 5.1

Divide each term in $999 x = 481$ by $999$ .

$\frac{999 x}{999} = \frac{481}{999}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $999$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{999 x}{999} = \frac{481}{999}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{481}{999}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $481$ and $999$ .

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Step 5.3.1.1

Factor $37$ out of $481$ .

$x = \frac{37 (13)}{999}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $37$ out of $999$ .

$x = \frac{37 \cdot 13}{37 \cdot 27}$

Step 5.3.1.2.2

Cancel the common factor.

$x = \frac{37 \cdot 13}{37 \cdot 27}$

Step 5.3.1.2.3

Rewrite the expression.

$x = \frac{13}{27}$

Step 6

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

$- 2 \frac{13}{27}$

Step 7

Convert $2 \frac{13}{27}$ to an improper fraction.

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Step 7.1

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

$- (2 + \frac{13}{27})$

Step 7.2

Add $2$ and $\frac{13}{27}$ .

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Step 7.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$- (2 \cdot \frac{27}{27} + \frac{13}{27})$

Step 7.2.2

Combine $2$ and $\frac{27}{27}$ .

$- (\frac{2 \cdot 27}{27} + \frac{13}{27})$

Step 7.2.3

Combine the numerators over the common denominator.

$- \frac{2 \cdot 27 + 13}{27}$

Step 7.2.4

Simplify the numerator.

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Step 7.2.4.1

Multiply $2$ by $27$ .

$- \frac{54 + 13}{27}$

Step 7.2.4.2

Add $54$ and $13$ .

$- \frac{67}{27}$