Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Multiply $4$ by $3$ .

$\frac{y}{3} = \frac{5}{12} - \frac{3}{12}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{y}{3} = \frac{5 - 3}{12}$

Step 2.5

Subtract $3$ from $5$ .

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

Step 2.6

Cancel the common factor of $2$ and $12$ .

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Step 2.6.1

Factor $2$ out of $2$ .

$\frac{y}{3} = \frac{2 (1)}{12}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $2$ out of $12$ .

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

Step 2.6.2.2

Cancel the common factor.

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

Step 2.6.2.3

Rewrite the expression.

$\frac{y}{3} = \frac{1}{6}$

Step 3

Multiply both sides of the equation by $3$ .

$3 \frac{y}{3} = 3 (\frac{1}{6})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1

Cancel the common factor.

$3 \frac{y}{3} = 3 (\frac{1}{6})$

Step 4.1.1.2

Rewrite the expression.

$y = 3 (\frac{1}{6})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Factor $3$ out of $6$ .

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

Step 4.2.1.2

Cancel the common factor.

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

Step 4.2.1.3

Rewrite the expression.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 0.5$