Basic Math Examples

$\frac{r}{12} = 1 \frac{9}{10}$

Step 1

Simplify the right side.

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Step 1.1

Convert $1 \frac{9}{10}$ to an improper fraction.

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Step 1.1.1

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

$\frac{r}{12} = 1 + \frac{9}{10}$

Step 1.1.2

Add $1$ and $\frac{9}{10}$ .

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Step 1.1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{r}{12} = \frac{10}{10} + \frac{9}{10}$

Step 1.1.2.2

Combine the numerators over the common denominator.

$\frac{r}{12} = \frac{10 + 9}{10}$

Step 1.1.2.3

Add $10$ and $9$ .

$\frac{r}{12} = \frac{19}{10}$

Step 2

Multiply both sides of the equation by $12$ .

$12 \frac{r}{12} = 12 (\frac{19}{10})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $12$ .

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Step 3.1.1.1

Cancel the common factor.

$12 \frac{r}{12} = 12 (\frac{19}{10})$

Step 3.1.1.2

Rewrite the expression.

$r = 12 (\frac{19}{10})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $12 (\frac{19}{10})$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Factor $2$ out of $12$ .

$r = 2 (6) \frac{19}{10}$

Step 3.2.1.1.2

Factor $2$ out of $10$ .

$r = 2 \cdot 6 \frac{19}{2 \cdot 5}$

Step 3.2.1.1.3

Cancel the common factor.

$r = 2 \cdot 6 \frac{19}{2 \cdot 5}$

Step 3.2.1.1.4

Rewrite the expression.

$r = 6 (\frac{19}{5})$

Step 3.2.1.2

Combine $6$ and $\frac{19}{5}$ .

$r = \frac{6 \cdot 19}{5}$

Step 3.2.1.3

Multiply $6$ by $19$ .

$r = \frac{114}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$r = \frac{114}{5}$

Decimal Form:

$r = 22.8$

Mixed Number Form:

$r = 22 \frac{4}{5}$