Basic Math Examples

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

Step 1

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

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

Step 2

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

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

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.

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

Step 3.2

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

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

Step 3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

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

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

Step 3.3.2

Multiply $2$ by $2$ .

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Combine the numerators over the common denominator.

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

Step 3.6

Move $2$ to the left of $y$ .

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

Step 3.7

Subtract $y$ from $2 y$ .

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

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$y + 1 = - 1$

Step 5

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

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Step 5.1

Subtract $1$ from both sides of the equation.

$y = - 1 - 1$

Step 5.2

Subtract $1$ from $- 1$ .

$y = - 2$