Finite Math Examples

$\frac{y}{4} - \frac{y}{3} = \frac{1}{2}$

Step 1

Simplify $\frac{y}{4} - \frac{y}{3}$ .

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Step 1.1

To write $\frac{y}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{y}{4} \cdot \frac{3}{3} - \frac{y}{3} = \frac{1}{2}$

Step 1.2

To write $- \frac{y}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{y}{4} \cdot \frac{3}{3} - \frac{y}{3} \cdot \frac{4}{4} = \frac{1}{2}$

Step 1.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{y}{4}$ by $\frac{3}{3}$ .

$\frac{y \cdot 3}{4 \cdot 3} - \frac{y}{3} \cdot \frac{4}{4} = \frac{1}{2}$

Step 1.3.2

Multiply $4$ by $3$ .

$\frac{y \cdot 3}{12} - \frac{y}{3} \cdot \frac{4}{4} = \frac{1}{2}$

Step 1.3.3

Multiply $\frac{y}{3}$ by $\frac{4}{4}$ .

$\frac{y \cdot 3}{12} - \frac{y \cdot 4}{3 \cdot 4} = \frac{1}{2}$

Step 1.3.4

Multiply $3$ by $4$ .

$\frac{y \cdot 3}{12} - \frac{y \cdot 4}{12} = \frac{1}{2}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{y \cdot 3 - y \cdot 4}{12} = \frac{1}{2}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $y$ out of $y \cdot 3 - y \cdot 4$ .

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Step 1.5.1.1

Factor $y$ out of $y \cdot 3$ .

$\frac{y (3) - y \cdot 4}{12} = \frac{1}{2}$

Step 1.5.1.2

Factor $y$ out of $- y \cdot 4$ .

$\frac{y (3) + y (- 1 \cdot 4)}{12} = \frac{1}{2}$

Step 1.5.1.3

Factor $y$ out of $y (3) + y (- 1 \cdot 4)$ .

$\frac{y (3 - 1 \cdot 4)}{12} = \frac{1}{2}$

Step 1.5.2

Multiply $- 1$ by $4$ .

$\frac{y (3 - 4)}{12} = \frac{1}{2}$

Step 1.5.3

Subtract $4$ from $3$ .

$\frac{y \cdot - 1}{12} = \frac{1}{2}$

Step 1.6

Simplify the expression.

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Step 1.6.1

Move $- 1$ to the left of $y$ .

$\frac{- 1 \cdot y}{12} = \frac{1}{2}$

Step 1.6.2

Move the negative in front of the fraction.

$- \frac{y}{12} = \frac{1}{2}$

Step 2

Multiply both sides of the equation by $- 12$ .

$- 12 (- \frac{y}{12}) = - 12 (\frac{1}{2})$

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 $- 12 (- \frac{y}{12})$ .

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Step 3.1.1.1

Cancel the common factor of $12$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{y}{12}$ into the numerator.

$- 12 \frac{- y}{12} = - 12 (\frac{1}{2})$

Step 3.1.1.1.2

Factor $12$ out of $- 12$ .

$12 (- 1) \frac{- y}{12} = - 12 (\frac{1}{2})$

Step 3.1.1.1.3

Cancel the common factor.

$12 \cdot - 1 \frac{- y}{12} = - 12 (\frac{1}{2})$

Step 3.1.1.1.4

Rewrite the expression.

$- - y = - 12 (\frac{1}{2})$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 12 (\frac{1}{2})$

Step 3.1.1.2.2

Multiply $y$ by $1$ .

$y = - 12 (\frac{1}{2})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Factor $2$ out of $- 12$ .

$y = 2 (- 6) \frac{1}{2}$

Step 3.2.1.2

Cancel the common factor.

$y = 2 \cdot - 6 \frac{1}{2}$

Step 3.2.1.3

Rewrite the expression.

$y = - 6$