Basic Math Examples

117.8 ¯ 3

$117.8\overline{3}$

Step 1

Set up an equation with

0.8 ¯ 3

$0.8\overline{3}$ .

x = 0.8 ¯ 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 ¯ 3

$x = 0.8\overline{3}$ by

10

$10$ to create the first equation.

10 x = 8. ¯ 3

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

Step 4

Multiply both sides of

x = 0.8 ¯ 3

$x = 0.8\overline{3}$ by

100

$100$ to create the second equation.

100 x = 83. ¯ 3

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

Step 5

Subtract

10 x = 8. ¯ 3

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

100 x = 83. ¯ 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.

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

Step 6.2.1.2

Divide

$x$ by

$1$ .

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

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of

$75$ and

$90$ .

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Step 6.3.1.1

Factor

$15$ out of

$75$ .

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

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor

$15$ out of

$90$ .

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

Step 6.3.1.2.2

Cancel the common factor.

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

Step 6.3.1.2.3

Rewrite the expression.

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

Step 7

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

$117 \frac{5}{6}$

Step 8

Convert

$117 \frac{5}{6}$ to an improper fraction.

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Step 8.1

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

$117 + \frac{5}{6}$

Step 8.2

Add

$117$ and

$\frac{5}{6}$ .

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Step 8.2.1

To write

$117$ as a fraction with a common denominator, multiply by

$\frac{6}{6}$ .

$117 \cdot \frac{6}{6} + \frac{5}{6}$

Step 8.2.2

Combine

$117$ and

$\frac{6}{6}$ .

$\frac{117 \cdot 6}{6} + \frac{5}{6}$

Step 8.2.3

Combine the numerators over the common denominator.

$\frac{117 \cdot 6 + 5}{6}$

Step 8.2.4

Simplify the numerator.

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Step 8.2.4.1

Multiply

$117$ by

$6$ .

$\frac{702 + 5}{6}$

Step 8.2.4.2

Add

$702$ and

$5$ .

$\frac{707}{6}$