Basic Math Examples

$\frac{0.5}{9} = \frac{y}{30}$

Step 1

Rewrite the equation as $\frac{y}{30} = \frac{0.5}{9}$ .

$\frac{y}{30} = \frac{0.5}{9}$

Step 2

Multiply both sides of the equation by $30$ .

$30 \frac{y}{30} = 30 (\frac{0.5}{9})$

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 $30$ .

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Step 3.1.1.1

Cancel the common factor.

$30 \frac{y}{30} = 30 (\frac{0.5}{9})$

Step 3.1.1.2

Rewrite the expression.

$y = 30 (\frac{0.5}{9})$

$y = 30 (\frac{0.5}{9})$

$y = 30 (\frac{0.5}{9})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $30 (\frac{0.5}{9})$ .

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Step 3.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Factor $3$ out of $30$ .

$y = 3 (10) \frac{0.5}{9}$

Step 3.2.1.1.2

Factor $3$ out of $9$ .

$y = 3 \cdot 10 \frac{0.5}{3 \cdot 3}$

Step 3.2.1.1.3

Cancel the common factor.

$y = 3 \cdot 10 \frac{0.5}{3 \cdot 3}$

Step 3.2.1.1.4

Rewrite the expression.

$y = 10 (\frac{0.5}{3})$

$y = 10 (\frac{0.5}{3})$

Step 3.2.1.2

Combine $10$ and $\frac{0.5}{3}$ .

$y = \frac{10 \cdot 0.5}{3}$

Step 3.2.1.3

Multiply $10$ by $0.5$ .

$y = \frac{5}{3}$

Step 3.2.1.4

Cancel the common factor of $5$ and $3$ .

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Step 3.2.1.4.1

Rewrite $5$ as $1 (5)$ .

$y = \frac{1 (5)}{3}$

Step 3.2.1.4.2

Cancel the common factors.

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Step 3.2.1.4.2.1

Rewrite $3$ as $1 (3)$ .

$y = \frac{1 \cdot 5}{1 \cdot 3}$

Step 3.2.1.4.2.2

Cancel the common factor.

$y = \frac{1 \cdot 5}{1 \cdot 3}$

Step 3.2.1.4.2.3

Rewrite the expression.

$y = \frac{5}{3}$

$y = \frac{5}{3}$

$y = \frac{5}{3}$

$y = \frac{5}{3}$

$y = \frac{5}{3}$

$y = \frac{5}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{5}{3}$

Decimal Form:

$y = 1.\overline{6}$

Mixed Number Form:

$y = 1 \frac{2}{3}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$