Basic Math Examples

$(\frac{1}{2}) y + (\frac{1}{4}) = (\frac{1}{3}) y - (\frac{1}{6})$

Step 1

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

$\frac{y}{2} + \frac{1}{4} = \frac{1}{3} y - \frac{1}{6}$

Step 2

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

$\frac{y}{2} + \frac{1}{4} = \frac{y}{3} - \frac{1}{6}$

Step 3

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

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Step 3.1

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

$\frac{y}{2} + \frac{1}{4} - \frac{y}{3} = - \frac{1}{6}$

Step 3.2

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

$\frac{y}{2} \cdot \frac{3}{3} - \frac{y}{3} + \frac{1}{4} = - \frac{1}{6}$

Step 3.3

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

$\frac{y}{2} \cdot \frac{3}{3} - \frac{y}{3} \cdot \frac{2}{2} + \frac{1}{4} = - \frac{1}{6}$

Step 3.4

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

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Step 3.4.1

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

$\frac{y \cdot 3}{2 \cdot 3} - \frac{y}{3} \cdot \frac{2}{2} + \frac{1}{4} = - \frac{1}{6}$

Step 3.4.2

Multiply $2$ by $3$ .

$\frac{y \cdot 3}{6} - \frac{y}{3} \cdot \frac{2}{2} + \frac{1}{4} = - \frac{1}{6}$

Step 3.4.3

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

$\frac{y \cdot 3}{6} - \frac{y \cdot 2}{3 \cdot 2} + \frac{1}{4} = - \frac{1}{6}$

Step 3.4.4

Multiply $3$ by $2$ .

$\frac{y \cdot 3}{6} - \frac{y \cdot 2}{6} + \frac{1}{4} = - \frac{1}{6}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{y \cdot 3 - y \cdot 2}{6} + \frac{1}{4} = - \frac{1}{6}$

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 $y \cdot 3 - y \cdot 2$ .

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Step 3.6.1.1.1

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

$\frac{y (3) - y \cdot 2}{6} + \frac{1}{4} = - \frac{1}{6}$

Step 3.6.1.1.2

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

$\frac{y (3) + y (- 1 \cdot 2)}{6} + \frac{1}{4} = - \frac{1}{6}$

Step 3.6.1.1.3

Factor $y$ out of $y (3) + y (- 1 \cdot 2)$ .

$\frac{y (3 - 1 \cdot 2)}{6} + \frac{1}{4} = - \frac{1}{6}$

Step 3.6.1.2

Multiply $- 1$ by $2$ .

$\frac{y (3 - 2)}{6} + \frac{1}{4} = - \frac{1}{6}$

Step 3.6.1.3

Subtract $2$ from $3$ .

$\frac{y \cdot 1}{6} + \frac{1}{4} = - \frac{1}{6}$

Step 3.6.2

Multiply $y$ by $1$ .

$\frac{y}{6} + \frac{1}{4} = - \frac{1}{6}$

Step 4

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

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Step 4.1

Subtract $\frac{1}{4}$ from both sides of the equation.

$\frac{y}{6} = - \frac{1}{6} - \frac{1}{4}$

Step 4.2

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y}{6} = - \frac{1}{6} \cdot \frac{2}{2} - \frac{1}{4}$

Step 4.3

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{y}{6} = - \frac{1}{6} \cdot \frac{2}{2} - \frac{1}{4} \cdot \frac{3}{3}$

Step 4.4

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

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Step 4.4.1

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$\frac{y}{6} = - \frac{2}{6 \cdot 2} - \frac{1}{4} \cdot \frac{3}{3}$

Step 4.4.2

Multiply $6$ by $2$ .

$\frac{y}{6} = - \frac{2}{12} - \frac{1}{4} \cdot \frac{3}{3}$

Step 4.4.3

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{y}{6} = - \frac{2}{12} - \frac{3}{4 \cdot 3}$

Step 4.4.4

Multiply $4$ by $3$ .

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

Step 4.5

Combine the numerators over the common denominator.

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

Step 4.6

Subtract $3$ from $- 2$ .

$\frac{y}{6} = \frac{- 5}{12}$

Step 4.7

Move the negative in front of the fraction.

$\frac{y}{6} = - \frac{5}{12}$

Step 5

Multiply both sides of the equation by $6$ .

$6 \frac{y}{6} = 6 (- \frac{5}{12})$

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 $6$ .

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Step 6.1.1.1

Cancel the common factor.

$6 \frac{y}{6} = 6 (- \frac{5}{12})$

Step 6.1.1.2

Rewrite the expression.

$y = 6 (- \frac{5}{12})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $6 (- \frac{5}{12})$ .

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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 $- \frac{5}{12}$ into the numerator.

$y = 6 (\frac{- 5}{12})$

Step 6.2.1.1.2

Factor $6$ out of $12$ .

$y = 6 \frac{- 5}{6 (2)}$

Step 6.2.1.1.3

Cancel the common factor.

$y = 6 \frac{- 5}{6 \cdot 2}$

Step 6.2.1.1.4

Rewrite the expression.

$y = \frac{- 5}{2}$

Step 6.2.1.2

Move the negative in front of the fraction.

$y = - \frac{5}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{5}{2}$

Decimal Form:

$y = - 2.5$

Mixed Number Form:

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