Basic Math Examples

$y \cdot \frac{9}{52} = \frac{3}{13}$

Step 1

Simplify $y \cdot \frac{9}{52}$ .

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Step 1.1

Combine $y$ and $\frac{9}{52}$ .

$\frac{y \cdot 9}{52} = \frac{3}{13}$

Step 1.2

Move $9$ to the left of $y$ .

$\frac{9 y}{52} = \frac{3}{13}$

Step 2

Multiply both sides of the equation by $\frac{52}{9}$ .

$\frac{52}{9} \cdot \frac{9 y}{52} = \frac{52}{9} \cdot \frac{3}{13}$

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

Simplify $\frac{52}{9} \cdot \frac{9 y}{52}$ .

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Step 3.1.1.1

Cancel the common factor of $52$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{52}{9} \cdot \frac{9 y}{52} = \frac{52}{9} \cdot \frac{3}{13}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 y) = \frac{52}{9} \cdot \frac{3}{13}$

Step 3.1.1.2

Cancel the common factor of $9$ .

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Step 3.1.1.2.1

Factor $9$ out of $9 y$ .

$\frac{1}{9} (9 (y)) = \frac{52}{9} \cdot \frac{3}{13}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 y) = \frac{52}{9} \cdot \frac{3}{13}$

Step 3.1.1.2.3

Rewrite the expression.

$y = \frac{52}{9} \cdot \frac{3}{13}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{52}{9} \cdot \frac{3}{13}$ .

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Step 3.2.1.1

Cancel the common factor of $13$ .

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Step 3.2.1.1.1

Factor $13$ out of $52$ .

$y = \frac{13 (4)}{9} \cdot \frac{3}{13}$

Step 3.2.1.1.2

Cancel the common factor.

$y = \frac{13 \cdot 4}{9} \cdot \frac{3}{13}$

Step 3.2.1.1.3

Rewrite the expression.

$y = \frac{4}{9} \cdot 3$

Step 3.2.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.2.1

Factor $3$ out of $9$ .

$y = \frac{4}{3 (3)} \cdot 3$

Step 3.2.1.2.2

Cancel the common factor.

$y = \frac{4}{3 \cdot 3} \cdot 3$

Step 3.2.1.2.3

Rewrite the expression.

$y = \frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{4}{3}$

Decimal Form:

$y = 1.\overline{3}$

Mixed Number Form:

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