Basic Math Examples

$\frac{\frac{2}{5}}{y} = \frac{\frac{1}{5}}{11}$

Step 1

Simplify both sides.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{5} \cdot \frac{1}{y} = \frac{\frac{1}{5}}{11}$

Step 1.2

Multiply $\frac{2}{5}$ by $\frac{1}{y}$ .

$\frac{2}{5 y} = \frac{\frac{1}{5}}{11}$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{5 y} = \frac{1}{5} \cdot \frac{1}{11}$

Step 1.4

Multiply $\frac{1}{5} \cdot \frac{1}{11}$ .

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Step 1.4.1

Multiply $\frac{1}{5}$ by $\frac{1}{11}$ .

$\frac{2}{5 y} = \frac{1}{5 \cdot 11}$

Step 1.4.2

Multiply $5$ by $11$ .

$\frac{2}{5 y} = \frac{1}{55}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$2 \cdot 55 = 5 y \cdot 1$

Step 3

Solve the equation for $y$ .

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Step 3.1

Rewrite the equation as $5 y \cdot 1 = 2 \cdot 55$ .

$5 y \cdot 1 = 2 \cdot 55$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $5$ by $1$ .

$5 y = 2 \cdot 55$

Step 3.2.2

Multiply $2$ by $55$ .

$5 y = 110$

Step 3.3

Divide each term in $5 y = 110$ by $5$ and simplify.

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Step 3.3.1

Divide each term in $5 y = 110$ by $5$ .

$\frac{5 y}{5} = \frac{110}{5}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $5$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{110}{5}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{110}{5}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $110$ by $5$ .

$y = 22$