Basic Math Examples

$3.2\overline{5}$

Step 1

Set up an equation with

$0.2\overline{5}$ .

$x = 0.2\overline{5}$

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

$x = 0.2\overline{5}$ by

$10$ to create the first equation.

$10 x = 2.\overline{5}$

Step 4

Multiply both sides of

$x = 0.2\overline{5}$ by

$100$ to create the second equation.

$100 x = 25.\overline{5}$

Step 5

Subtract

$10 x = 2.\overline{5}$ from

$100 x = 25.\overline{5}$ to remove the repeating part.

$90 x = 23$

Step 6

Divide each term in

$90 x = 23$ by

$90$ and simplify.

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Step 6.1

Divide each term in

$90 x = 23$ by

$90$ .

$\frac{90 x}{90} = \frac{23}{90}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of

$90$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{90 x}{90} = \frac{23}{90}$

Step 6.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{23}{90}$

Step 7

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

$3 \frac{23}{90}$

Step 8

Convert

$3 \frac{23}{90}$ to an improper fraction.

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Step 8.1

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

$3 + \frac{23}{90}$

Step 8.2

Add

$3$ and

$\frac{23}{90}$ .

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Step 8.2.1

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{90}{90}$ .

$3 \cdot \frac{90}{90} + \frac{23}{90}$

Step 8.2.2

Combine

$3$ and

$\frac{90}{90}$ .

$\frac{3 \cdot 90}{90} + \frac{23}{90}$

Step 8.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 90 + 23}{90}$

Step 8.2.4

Simplify the numerator.

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Step 8.2.4.1

Multiply

$3$ by

$90$ .

$\frac{270 + 23}{90}$

Step 8.2.4.2

Add

$270$ and

$23$ .

$\frac{293}{90}$