Basic Math Examples

1. ¯ 7

$1.\overline{7}$

Step 1

Create two equations where the only numbers to the right of the decimal place are the repeating part.

Step 2

Set up an equation with

0. ¯ 7

$0.\overline{7}$ .

x = 0. ¯ 7

$x = 0.\overline{7}$

Step 3

Multiply both sides of

x = 0. ¯ 7

$x = 0.\overline{7}$ by

10

$10$ to create the second equation.

10 x = 7. ¯ 7

$10 x = 7.\overline{7}$

Step 4

Subtract

x = 0. ¯ 7

$x = 0.\overline{7}$ from

10 x = 7. ¯ 7

$10 x = 7.\overline{7}$ to remove the repeating part.

9 x = 7

$9 x = 7$

Step 5

Divide each term in

9 x = 7

$9 x = 7$ by

9

$9$ and simplify.

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Step 5.1

Divide each term in

9 x = 7

$9 x = 7$ by

9

$9$ .

\frac{9 x}{9} = \frac{7}{9}

$\frac{9 x}{9} = \frac{7}{9}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of

9

$9$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{7}{9}$

Step 5.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{7}{9}$

Step 6

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

$1 \frac{7}{9}$

Step 7

Convert

$1 \frac{7}{9}$ to an improper fraction.

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Step 7.1

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

$1 + \frac{7}{9}$

Step 7.2

Add

$1$ and

$\frac{7}{9}$ .

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Step 7.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{9}{9} + \frac{7}{9}$

Step 7.2.2

Combine the numerators over the common denominator.

$\frac{9 + 7}{9}$

Step 7.2.3

Add

$9$ and

$7$ .

$\frac{16}{9}$