Basic Math Examples

$\frac{5 y - 1}{12} + \frac{y}{3} = - \frac{1}{4}$

Step 1

Simplify $\frac{5 y - 1}{12} + \frac{y}{3}$ .

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Step 1.1

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

$\frac{5 y - 1}{12} + \frac{y}{3} \cdot \frac{4}{4} = - \frac{1}{4}$

Step 1.2

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

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Step 1.2.1

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

$\frac{5 y - 1}{12} + \frac{y \cdot 4}{3 \cdot 4} = - \frac{1}{4}$

Step 1.2.2

Multiply $3$ by $4$ .

$\frac{5 y - 1}{12} + \frac{y \cdot 4}{12} = - \frac{1}{4}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{5 y - 1 + y \cdot 4}{12} = - \frac{1}{4}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Move $4$ to the left of $y$ .

$\frac{5 y - 1 + 4 \cdot y}{12} = - \frac{1}{4}$

Step 1.4.2

Add $5 y$ and $4 y$ .

$\frac{9 y - 1}{12} = - \frac{1}{4}$

Step 2

Multiply both sides by $12$ .

$\frac{9 y - 1}{12} \cdot 12 = - \frac{1}{4} \cdot 12$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $12$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{9 y - 1}{12} \cdot 12 = - \frac{1}{4} \cdot 12$

Step 3.1.1.2

Rewrite the expression.

$9 y - 1 = - \frac{1}{4} \cdot 12$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{1}{4} \cdot 12$ .

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Step 3.2.1.1

Cancel the common factor of $4$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$9 y - 1 = \frac{- 1}{4} \cdot 12$

Step 3.2.1.1.2

Factor $4$ out of $12$ .

$9 y - 1 = \frac{- 1}{4} \cdot (4 (3))$

Step 3.2.1.1.3

Cancel the common factor.

$9 y - 1 = \frac{- 1}{4} \cdot (4 \cdot 3)$

Step 3.2.1.1.4

Rewrite the expression.

$9 y - 1 = - 1 \cdot 3$

Step 3.2.1.2

Multiply $- 1$ by $3$ .

$9 y - 1 = - 3$

Step 4

Solve for $y$ .

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Step 4.1

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

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Step 4.1.1

Add $1$ to both sides of the equation.

$9 y = - 3 + 1$

Step 4.1.2

Add $- 3$ and $1$ .

$9 y = - 2$

Step 4.2

Divide each term in $9 y = - 2$ by $9$ and simplify.

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Step 4.2.1

Divide each term in $9 y = - 2$ by $9$ .

$\frac{9 y}{9} = \frac{- 2}{9}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $9$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 2}{9}$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 2}{9}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

$y = - \frac{2}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{2}{9}$

Decimal Form:

$y = - 0.\overline{2}$