Basic Math Examples

$1.\overline{72}$

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 $0.\overline{72}$ .

$x = 0.\overline{72}$

Step 3

Multiply both sides of $x = 0.\overline{72}$ by $100$ to create the second equation.

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

Step 4

Subtract $x = 0.\overline{72}$ from $100 x = 72.\overline{72}$ to remove the repeating part.

$99 x = 72$

Step 5

Divide each term in $99 x = 72$ by $99$ and simplify.

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Step 5.1

Divide each term in $99 x = 72$ by $99$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $99$ .

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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 $8$ .

$\frac{19}{11}$