Basic Math Examples

1. ¯ ¯¯ ¯ 72

$1.\overline{72}$

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. ¯ ¯¯ ¯ 72

$0.\overline{72}$ .

x = 0. ¯ ¯¯ ¯ 72

$x = 0.\overline{72}$

Step 3

Multiply both sides of

x = 0. ¯ ¯¯ ¯ 72

$x = 0.\overline{72}$ by

100

$100$ to create the second equation.

100 x = 72. ¯ ¯¯ ¯ 72

$100 x = 72.\overline{72}$

Step 4

Subtract

x = 0. ¯ ¯¯ ¯ 72

$x = 0.\overline{72}$ from

100 x = 72. ¯ ¯¯ ¯ 72

$100 x = 72.\overline{72}$ to remove the repeating part.

99 x = 72

$99 x = 72$

Step 5

Divide each term in

99 x = 72

$99 x = 72$ by

99

$99$ and simplify.

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Step 5.1

Divide each term in

99 x = 72

$99 x = 72$ by

99

$99$ .

\frac{99 x}{99} = \frac{72}{99}

$\frac{99 x}{99} = \frac{72}{99}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of

99

$99$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{99 x}{99} = \frac{72}{99}$

Step 5.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{72}{99}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of

$72$ and

$99$ .

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Step 5.3.1.1

Factor

$9$ out of

$72$ .

$x = \frac{9 (8)}{99}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor

$9$ out of

$99$ .

$x = \frac{9 \cdot 8}{9 \cdot 11}$

Step 5.3.1.2.2

Cancel the common factor.

$x = \frac{9 \cdot 8}{9 \cdot 11}$

Step 5.3.1.2.3

Rewrite the expression.

$x = \frac{8}{11}$

Step 6

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

$1 \frac{8}{11}$

Step 7

Convert

$1 \frac{8}{11}$ to an improper fraction.

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Step 7.1

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

$1 + \frac{8}{11}$

Step 7.2

Add

$1$ and

$\frac{8}{11}$ .

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Step 7.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{11}{11} + \frac{8}{11}$

Step 7.2.2

Combine the numerators over the common denominator.

$\frac{11 + 8}{11}$

Step 7.2.3

Add

$11$ and

$8$ .

$\frac{19}{11}$