Convert to a Simplified Fraction -4.666666666667

$- 4.\overline{6}$

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

$0.\overline{6}$ .

$x = 0.\overline{6}$

Step 3

Multiply both sides of

$x = 0.\overline{6}$ by

$10$ to create the second equation.

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

Step 4

Subtract

$x = 0.\overline{6}$ from

$10 x = 6.\overline{6}$ to remove the repeating part.

$9 x = 6$

Step 5

Divide each term in

$9 x = 6$ by

$9$ and simplify.

Divide each term in

$9 x = 6$ by

$9$ .

$\frac{9 x}{9} = \frac{6}{9}$

Simplify the left side.

Cancel the common factor of

$9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{6}{9}$

Divide

$x$ by

$1$ .

$x = \frac{6}{9}$

Simplify the right side.

Cancel the common factor of

$6$ and

$9$ .

Factor

$3$ out of

$6$ .

$x = \frac{3 (2)}{9}$

Cancel the common factors.

Factor

$3$ out of

$9$ .

$x = \frac{3 \cdot 2}{3 \cdot 3}$

Cancel the common factor.

$x = \frac{3 \cdot 2}{3 \cdot 3}$

Rewrite the expression.

$x = \frac{2}{3}$

Step 6

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

$- 4 \frac{2}{3}$

Step 7

Convert

$4 \frac{2}{3}$ to an improper fraction.

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

$- (4 + \frac{2}{3})$

Add

$4$ and

$\frac{2}{3}$ .

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$- (4 \cdot \frac{3}{3} + \frac{2}{3})$

Combine

$4$ and

$\frac{3}{3}$ .

$- (\frac{4 \cdot 3}{3} + \frac{2}{3})$

Combine the numerators over the common denominator.

$- \frac{4 \cdot 3 + 2}{3}$

Simplify the numerator.

Multiply

$4$ by

$3$ .

$- \frac{12 + 2}{3}$

Add

$12$ and

$2$ .

$- \frac{14}{3}$

Convert to a Simplified Fraction -4.666666666667

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