Basic Math Examples

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

Step 1

Simplify $\frac{1}{3} \cdot (y + 2)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{3} \cdot (y + 2) = \frac{1}{4} \cdot (y - 2)$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Combine $\frac{1}{3}$ and $y$ .

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

Step 1.5

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

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

Step 2

Simplify $\frac{1}{4} \cdot (y - 2)$ .

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Step 2.1

Apply the distributive property.

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

Step 2.2

Combine $\frac{1}{4}$ and $y$ .

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

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $4$ .

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

Step 2.3.2

Factor $2$ out of $- 2$ .

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

Step 2.3.3

Cancel the common factor.

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

Step 2.3.4

Rewrite the expression.

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

Step 2.4

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

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

Step 2.5

Move the negative in front of the fraction.

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

Step 3

Move all terms containing $y$ to the left side of the equation.

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Step 3.1

Subtract $\frac{y}{4}$ from both sides of the equation.

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

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Step 3.4.1

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

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

Step 3.4.2

Multiply $3$ by $4$ .

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

Step 3.4.3

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

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

Step 3.4.4

Multiply $4$ by $3$ .

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

Step 3.5

Combine the numerators over the common denominator.

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

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

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

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Step 3.6.1.1.1

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

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

Step 3.6.1.1.2

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

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

Step 3.6.1.1.3

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

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

Step 3.6.1.2

Multiply $- 1$ by $3$ .

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

Step 3.6.1.3

Subtract $3$ from $4$ .

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

Step 3.6.2

Multiply $y$ by $1$ .

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

Step 4

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

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Step 4.1

Subtract $\frac{2}{3}$ from both sides of the equation.

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

Step 4.2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 4.3

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.4.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

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

Step 4.4.2

Multiply $2$ by $3$ .

$\frac{y}{12} = - \frac{3}{6} - \frac{2}{3} \cdot \frac{2}{2}$

Step 4.4.3

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$\frac{y}{12} = - \frac{3}{6} - \frac{2 \cdot 2}{3 \cdot 2}$

Step 4.4.4

Multiply $3$ by $2$ .

$\frac{y}{12} = - \frac{3}{6} - \frac{2 \cdot 2}{6}$

Step 4.5

Combine the numerators over the common denominator.

$\frac{y}{12} = \frac{- 3 - 2 \cdot 2}{6}$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Multiply $- 2$ by $2$ .

$\frac{y}{12} = \frac{- 3 - 4}{6}$

Step 4.6.2

Subtract $4$ from $- 3$ .

$\frac{y}{12} = \frac{- 7}{6}$

Step 4.7

Move the negative in front of the fraction.

$\frac{y}{12} = - \frac{7}{6}$

Step 5

Multiply both sides of the equation by $12$ .

$12 \frac{y}{12} = 12 (- \frac{7}{6})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $12$ .

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Step 6.1.1.1

Cancel the common factor.

$12 \frac{y}{12} = 12 (- \frac{7}{6})$

Step 6.1.1.2

Rewrite the expression.

$y = 12 (- \frac{7}{6})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $12 (- \frac{7}{6})$ .

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Step 6.2.1.1

Cancel the common factor of $6$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{7}{6}$ into the numerator.

$y = 12 (\frac{- 7}{6})$

Step 6.2.1.1.2

Factor $6$ out of $12$ .

$y = 6 (2) \frac{- 7}{6}$

Step 6.2.1.1.3

Cancel the common factor.

$y = 6 \cdot 2 \frac{- 7}{6}$

Step 6.2.1.1.4

Rewrite the expression.

$y = 2 \cdot - 7$

Step 6.2.1.2

Multiply $2$ by $- 7$ .

$y = - 14$