Basic Math Examples

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

Step 1

Simplify $\frac{1}{2} \cdot (6 - y)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (6 - y) = y$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $6$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

Step 1.5

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

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

Step 2

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

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Step 2.1

Subtract $y$ from both sides of the equation.

$3 - \frac{y}{2} - y = 0$

Step 2.2

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

$3 - \frac{y}{2} - y \cdot \frac{2}{2} = 0$

Step 2.3

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

$3 - \frac{y}{2} + \frac{- y \cdot 2}{2} = 0$

Step 2.4

Combine the numerators over the common denominator.

$3 + \frac{- y - y \cdot 2}{2} = 0$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $y$ out of $- y - y \cdot 2$ .

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Step 2.5.1.1.1

Factor $y$ out of $- y$ .

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

Step 2.5.1.1.2

Factor $y$ out of $- y \cdot 2$ .

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

Step 2.5.1.1.3

Factor $y$ out of $y \cdot - 1 + y (- 1 \cdot 2)$ .

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

Step 2.5.1.2

Multiply $- 1$ by $2$ .

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

Step 2.5.1.3

Subtract $2$ from $- 1$ .

$3 + \frac{y \cdot - 3}{2} = 0$

Step 2.5.2

Move $- 3$ to the left of $y$ .

$3 + \frac{- 3 \cdot y}{2} = 0$

Step 2.5.3

Move the negative in front of the fraction.

$3 - \frac{3 y}{2} = 0$

Step 3

Subtract $3$ from both sides of the equation.

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

Step 4

Multiply both sides of the equation by $- \frac{2}{3}$ .

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

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

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

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Step 5.1.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Step 5.1.1.1.2

Move the leading negative in $- \frac{3 y}{2}$ into the numerator.

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

Step 5.1.1.1.3

Factor $2$ out of $- 2$ .

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

Step 5.1.1.1.4

Cancel the common factor.

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

Step 5.1.1.1.5

Rewrite the expression.

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

Step 5.1.1.2

Cancel the common factor of $3$ .

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Step 5.1.1.2.1

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

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

Step 5.1.1.2.2

Cancel the common factor.

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

Step 5.1.1.2.3

Rewrite the expression.

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

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 5.1.1.3.2

Multiply $y$ by $1$ .

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

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{2}{3} \cdot - 3$ .

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Step 5.2.1.1

Cancel the common factor of $3$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Step 5.2.1.1.2

Factor $3$ out of $- 3$ .

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

Step 5.2.1.1.3

Cancel the common factor.

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

Step 5.2.1.1.4

Rewrite the expression.

$y = - 2 \cdot - 1$

Step 5.2.1.2

Multiply $- 2$ by $- 1$ .

$y = 2$