Basic Math Examples

$\frac{2 y + 3}{4} + \frac{y - 5}{6} = 0$

Step 1

Simplify $\frac{2 y + 3}{4} + \frac{y - 5}{6}$ .

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Step 1.1

To write $\frac{2 y + 3}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 y + 3}{4} \cdot \frac{3}{3} + \frac{y - 5}{6} = 0$

Step 1.2

To write $\frac{y - 5}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 y + 3}{4} \cdot \frac{3}{3} + \frac{y - 5}{6} \cdot \frac{2}{2} = 0$

Step 1.3

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

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Step 1.3.1

Multiply $\frac{2 y + 3}{4}$ by $\frac{3}{3}$ .

$\frac{(2 y + 3) \cdot 3}{4 \cdot 3} + \frac{y - 5}{6} \cdot \frac{2}{2} = 0$

Step 1.3.2

Multiply $4$ by $3$ .

$\frac{(2 y + 3) \cdot 3}{12} + \frac{y - 5}{6} \cdot \frac{2}{2} = 0$

Step 1.3.3

Multiply $\frac{y - 5}{6}$ by $\frac{2}{2}$ .

$\frac{(2 y + 3) \cdot 3}{12} + \frac{(y - 5) \cdot 2}{6 \cdot 2} = 0$

Step 1.3.4

Multiply $6$ by $2$ .

$\frac{(2 y + 3) \cdot 3}{12} + \frac{(y - 5) \cdot 2}{12} = 0$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(2 y + 3) \cdot 3 + (y - 5) \cdot 2}{12} = 0$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{2 y \cdot 3 + 3 \cdot 3 + (y - 5) \cdot 2}{12} = 0$

Step 1.5.2

Multiply $3$ by $2$ .

$\frac{6 y + 3 \cdot 3 + (y - 5) \cdot 2}{12} = 0$

Step 1.5.3

Multiply $3$ by $3$ .

$\frac{6 y + 9 + (y - 5) \cdot 2}{12} = 0$

Step 1.5.4

Apply the distributive property.

$\frac{6 y + 9 + y \cdot 2 - 5 \cdot 2}{12} = 0$

Step 1.5.5

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

$\frac{6 y + 9 + 2 \cdot y - 5 \cdot 2}{12} = 0$

Step 1.5.6

Multiply $- 5$ by $2$ .

$\frac{6 y + 9 + 2 \cdot y - 10}{12} = 0$

Step 1.5.7

Add $6 y$ and $2 y$ .

$\frac{8 y + 9 - 10}{12} = 0$

Step 1.5.8

Subtract $10$ from $9$ .

$\frac{8 y - 1}{12} = 0$

Step 2

Set the numerator equal to zero.

$8 y - 1 = 0$

Step 3

Solve the equation for $y$ .

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Step 3.1

Add $1$ to both sides of the equation.

$8 y = 1$

Step 3.2

Divide each term in $8 y = 1$ by $8$ and simplify.

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Step 3.2.1

Divide each term in $8 y = 1$ by $8$ .

$\frac{8 y}{8} = \frac{1}{8}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $8$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{1}{8}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{1}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{1}{8}$

Decimal Form:

$y = 0.125$