Basic Math Examples

1.0 ¯ ¯¯ ¯ 35

$1.0\overline{35}$

Step 1

Set up an equation with

0.0 ¯ ¯¯ ¯ 35

$0.0\overline{35}$ .

x = 0.0 ¯ ¯¯ ¯ 35

$x = 0.0\overline{35}$

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 = 0.0 ¯ ¯¯ ¯ 35

$x = 0.0\overline{35}$ by

10

$10$ to create the first equation.

10 x = 0. ¯ ¯¯ ¯ 35

$10 x = 0.\overline{35}$

Step 4

Multiply both sides of

x = 0.0 ¯ ¯¯ ¯ 35

$x = 0.0\overline{35}$ by

1000

$1000$ to create the second equation.

1000 x = 35. ¯ ¯¯ ¯ 35

$1000 x = 35.\overline{35}$

Step 5

Subtract

10 x = 0. ¯ ¯¯ ¯ 35

$10 x = 0.\overline{35}$ from

1000 x = 35. ¯ ¯¯ ¯ 35

$1000 x = 35.\overline{35}$ to remove the repeating part.

990 x = 35

$990 x = 35$

Step 6

Divide each term in

990 x = 35

$990 x = 35$ by

990

$990$ and simplify.

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Step 6.1

Divide each term in

990 x = 35

$990 x = 35$ by

990

$990$ .

\frac{990 x}{990} = \frac{35}{990}

$\frac{990 x}{990} = \frac{35}{990}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of

990

$990$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{990 x}{990} = \frac{35}{990}$

Step 6.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{35}{990}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of

$35$ and

$990$ .

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Step 6.3.1.1

Factor

$5$ out of

$35$ .

$x = \frac{5 (7)}{990}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor

$5$ out of

$990$ .

$x = \frac{5 \cdot 7}{5 \cdot 198}$

Step 6.3.1.2.2

Cancel the common factor.

$x = \frac{5 \cdot 7}{5 \cdot 198}$

Step 6.3.1.2.3

Rewrite the expression.

$x = \frac{7}{198}$

Step 7

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

$1 \frac{7}{198}$

Step 8

Convert

$1 \frac{7}{198}$ to an improper fraction.

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Step 8.1

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

$1 + \frac{7}{198}$

Step 8.2

Add

$1$ and

$\frac{7}{198}$ .

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Step 8.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{198}{198} + \frac{7}{198}$

Step 8.2.2

Combine the numerators over the common denominator.

$\frac{198 + 7}{198}$

Step 8.2.3

Add

$198$ and

$7$ .

$\frac{205}{198}$