Algebra Examples

0.8\overline{3}

$0.8\overline{3}$

Step 1

Set up an equation with

0.8\overline{3}

$0.8\overline{3}$ .

x = 0.8\overline{3}

$x = 0.8\overline{3}$

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 = 0.8\overline{3}

$x = 0.8\overline{3}$ by

10

$10$ to create the first equation.

10 x = 8.\overline{3}

$10 x = 8.\overline{3}$

Step 4

Multiply both sides of

x = 0.8\overline{3}

$x = 0.8\overline{3}$ by

100

$100$ to create the second equation.

100 x = 83.\overline{3}

$100 x = 83.\overline{3}$

Step 5

Subtract

10 x = 8.\overline{3}

$10 x = 8.\overline{3}$ from

100 x = 83.\overline{3}

$100 x = 83.\overline{3}$ to remove the repeating part.

90 x = 75

$90 x = 75$

Step 6

Divide each term in

90 x = 75

$90 x = 75$ by

90

$90$ and simplify.

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Step 6.1

Divide each term in

90 x = 75

$90 x = 75$ by

90

$90$ .

\frac{90 x}{90} = \frac{75}{90}

$\frac{90 x}{90} = \frac{75}{90}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of

90

$90$ .

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Step 6.2.1.1

Cancel the common factor.

\frac{90 x}{90} = \frac{75}{90}

$\frac{90 x}{90} = \frac{75}{90}$

Step 6.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{75}{90}

$x = \frac{75}{90}$

x = \frac{75}{90}

$x = \frac{75}{90}$

x = \frac{75}{90}

$x = \frac{75}{90}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of

75

$75$ and

90

$90$ .

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Step 6.3.1.1

Factor

15

$15$ out of

75

$75$ .

x = \frac{15 (5)}{90}

$x = \frac{15 (5)}{90}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor

15

$15$ out of

90

$90$ .

x = \frac{15 \cdot 5}{15 \cdot 6}

$x = \frac{15 \cdot 5}{15 \cdot 6}$

Step 6.3.1.2.2

Cancel the common factor.

x = \frac{15 \cdot 5}{15 \cdot 6}

$x = \frac{15 \cdot 5}{15 \cdot 6}$

Step 6.3.1.2.3

Rewrite the expression.

x = \frac{5}{6}

$x = \frac{5}{6}$

x = \frac{5}{6}

$x = \frac{5}{6}$

x = \frac{5}{6}

$x = \frac{5}{6}$

x = \frac{5}{6}

$x = \frac{5}{6}$

x = \frac{5}{6}

$x = \frac{5}{6}$

Step 7

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

0 \frac{5}{6}

$0 \frac{5}{6}$

Step 8

Convert

0 \frac{5}{6}

$0 \frac{5}{6}$ 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{5}{6}

$0 + \frac{5}{6}$

Step 8.2

Add

0

$0$ and

\frac{5}{6}

$\frac{5}{6}$ .

\frac{5}{6}

$\frac{5}{6}$

\frac{5}{6}

$\frac{5}{6}$