Algebra Examples

$y = \frac{a b}{2 c}$

Step 1

Rewrite the equation as $\frac{a b}{2 c} = y$ .

$\frac{a b}{2 c} = y$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$2 c, 1$

Step 2.2

The LCM of one and any expression is the expression.

$2 c$

Step 3

Multiply each term in $\frac{a b}{2 c} = y$ by $2 c$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{a b}{2 c} = y$ by $2 c$ .

$\frac{a b}{2 c} (2 c) = y (2 c)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

$2 \frac{a b}{2 c} c = y (2 c)$

Step 3.2.2

Cancel the common factor of $2$ .

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Step 3.2.2.1

Factor $2$ out of $2 c$ .

$2 \frac{a b}{2 (c)} c = y (2 c)$

Step 3.2.2.2

Cancel the common factor.

$2 \frac{a b}{2 c} c = y (2 c)$

Step 3.2.2.3

Rewrite the expression.

$\frac{a b}{c} c = y (2 c)$

Step 3.2.3

Cancel the common factor of $c$ .

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Step 3.2.3.1

Cancel the common factor.

$\frac{a b}{c} c = y (2 c)$

Step 3.2.3.2

Rewrite the expression.

$a b = y (2 c)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Rewrite using the commutative property of multiplication.

$a b = 2 y c$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $2 y c = a b$ .

$2 y c = a b$

Step 4.2

Divide each term in $2 y c = a b$ by $2 y$ and simplify.

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Step 4.2.1

Divide each term in $2 y c = a b$ by $2 y$ .

$\frac{2 y c}{2 y} = \frac{a b}{2 y}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 y c}{2 y} = \frac{a b}{2 y}$

Step 4.2.2.1.2

Rewrite the expression.

$\frac{y c}{y} = \frac{a b}{2 y}$

Step 4.2.2.2

Cancel the common factor of $y$ .

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Step 4.2.2.2.1

Cancel the common factor.

$\frac{y c}{y} = \frac{a b}{2 y}$

Step 4.2.2.2.2

Divide $c$ by $1$ .

$c = \frac{a b}{2 y}$