Basic Math Examples

$y + 1 = \frac{1}{3} y$

Step 1

Simplify $\frac{1}{3} y$ .

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Step 1.1

Rewrite.

$y + 1 = 0 + 0 + \frac{1}{3} y$

Step 1.2

Simplify by adding zeros.

$y + 1 = \frac{1}{3} y$

Step 1.3

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

$y + 1 = \frac{y}{3}$

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Subtract $y$ from $y \cdot 3$ .

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Step 2.5.1

Reorder $y$ and $3$ .

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

Step 2.5.2

Subtract $y$ from $3 \cdot y$ .

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

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

Step 3

Subtract $1$ from both sides of the equation.

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

Step 4

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

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

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 $\frac{3}{2} \cdot \frac{2 y}{3}$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Cancel the common factor.

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

Step 5.1.1.1.2

Rewrite the expression.

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

Step 5.1.1.2

Cancel the common factor of $2$ .

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Step 5.1.1.2.1

Factor $2$ out of $2 y$ .

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

Step 5.1.1.2.2

Cancel the common factor.

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

Step 5.1.1.2.3

Rewrite the expression.

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

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{3}{2} \cdot - 1$ .

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Step 5.2.1.1

Multiply $\frac{3}{2} \cdot - 1$ .

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Step 5.2.1.1.1

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

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

Step 5.2.1.1.2

Multiply $3$ by $- 1$ .

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

Step 5.2.1.2

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = - 1.5$

Mixed Number Form:

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