Basic Math Examples

$\frac{1}{2} = \frac{y - 5}{n - 3}$

Step 1

Rewrite the equation as $\frac{y - 5}{n - 3} = \frac{1}{2}$ .

$\frac{y - 5}{n - 3} = \frac{1}{2}$

Step 2

Multiply both sides by $n - 3$ .

$\frac{y - 5}{n - 3} (n - 3) = \frac{1}{2} (n - 3)$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $n - 3$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{y - 5}{n - 3} (n - 3) = \frac{1}{2} (n - 3)$

Step 3.1.1.2

Rewrite the expression.

$y - 5 = \frac{1}{2} (n - 3)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{1}{2} (n - 3)$ .

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Step 3.2.1.1

Apply the distributive property.

$y - 5 = \frac{1}{2} n + \frac{1}{2} \cdot - 3$

Step 3.2.1.2

Combine $\frac{1}{2}$ and $n$ .

$y - 5 = \frac{n}{2} + \frac{1}{2} \cdot - 3$

Step 3.2.1.3

Combine $\frac{1}{2}$ and $- 3$ .

$y - 5 = \frac{n}{2} + \frac{- 3}{2}$

Step 3.2.1.4

Move the negative in front of the fraction.

$y - 5 = \frac{n}{2} - \frac{3}{2}$

Step 4

Move all terms not containing $y$ to the right side of the equation.

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Step 4.1

Add $5$ to both sides of the equation.

$y = \frac{n}{2} - \frac{3}{2} + 5$

Step 4.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{n}{2} - \frac{3}{2} + 5 \cdot \frac{2}{2}$

Step 4.3

Combine $5$ and $\frac{2}{2}$ .

$y = \frac{n}{2} - \frac{3}{2} + \frac{5 \cdot 2}{2}$

Step 4.4

Combine the numerators over the common denominator.

$y = \frac{n}{2} + \frac{- 3 + 5 \cdot 2}{2}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $5$ by $2$ .

$y = \frac{n}{2} + \frac{- 3 + 10}{2}$

Step 4.5.2

Add $- 3$ and $10$ .

$y = \frac{n}{2} + \frac{7}{2}$