Basic Math Examples

1.1 ¯ 6

$1.1\overline{6}$

Step 1

Set up an equation with

0.1 ¯ 6

$0.1\overline{6}$ .

x = 0.1 ¯ 6

$x = 0.1\overline{6}$

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 = 0.1 ¯ 6

$x = 0.1\overline{6}$ by

10

$10$ to create the first equation.

10 x = 1. ¯ 6

$10 x = 1.\overline{6}$

Step 4

Multiply both sides of

x = 0.1 ¯ 6

$x = 0.1\overline{6}$ by

100

$100$ to create the second equation.

100 x = 16. ¯ 6

$100 x = 16.\overline{6}$

Step 5

Subtract

10 x = 1. ¯ 6

$10 x = 1.\overline{6}$ from

100 x = 16. ¯ 6

$100 x = 16.\overline{6}$ to remove the repeating part.

90 x = 15

$90 x = 15$

Step 6

Divide each term in

90 x = 15

$90 x = 15$ by

90

$90$ and simplify.

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Step 6.1

Divide each term in

90 x = 15

$90 x = 15$ by

90

$90$ .

\frac{90 x}{90} = \frac{15}{90}

$\frac{90 x}{90} = \frac{15}{90}$

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.

$\frac{90 x}{90} = \frac{15}{90}$

Step 6.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{15}{90}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of

$15$ and

$90$ .

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Step 6.3.1.1

Factor

$15$ out of

$15$ .

$x = \frac{15 (1)}{90}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor

$15$ out of

$90$ .

$x = \frac{15 \cdot 1}{15 \cdot 6}$

Step 6.3.1.2.2

Cancel the common factor.

$x = \frac{15 \cdot 1}{15 \cdot 6}$

Step 6.3.1.2.3

Rewrite the expression.

$x = \frac{1}{6}$

Step 7

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

$1 \frac{1}{6}$

Step 8

Convert

$1 \frac{1}{6}$ to an improper fraction.

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Step 8.1

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

$1 + \frac{1}{6}$

Step 8.2

Add

$1$ and

$\frac{1}{6}$ .

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Step 8.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{6}{6} + \frac{1}{6}$

Step 8.2.2

Combine the numerators over the common denominator.

$\frac{6 + 1}{6}$

Step 8.2.3

Add

$6$ and

$1$ .

$\frac{7}{6}$