Basic Math Examples

$\frac{y - 2}{3} = \frac{y}{12} + \frac{5}{4}$

Step 1

Multiply both sides by $3$ .

$\frac{y - 2}{3} \cdot 3 = (\frac{y}{12} + \frac{5}{4}) \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{y - 2}{3} \cdot 3 = (\frac{y}{12} + \frac{5}{4}) \cdot 3$

Step 2.1.1.2

Rewrite the expression.

$y - 2 = (\frac{y}{12} + \frac{5}{4}) \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{y}{12} + \frac{5}{4}) \cdot 3$ .

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Step 2.2.1.1

Apply the distributive property.

$y - 2 = \frac{y}{12} \cdot 3 + \frac{5}{4} \cdot 3$

Step 2.2.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.2.1

Factor $3$ out of $12$ .

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

Step 2.2.1.2.2

Cancel the common factor.

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

Step 2.2.1.2.3

Rewrite the expression.

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

Step 2.2.1.3

Multiply $\frac{5}{4} \cdot 3$ .

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Step 2.2.1.3.1

Combine $\frac{5}{4}$ and $3$ .

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

Step 2.2.1.3.2

Multiply $5$ by $3$ .

$y - 2 = \frac{y}{4} + \frac{15}{4}$

Step 3

Solve for $y$ .

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Step 3.1

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

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Step 3.1.1

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

$y - 2 - \frac{y}{4} = \frac{15}{4}$

Step 3.1.2

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

$y \cdot \frac{4}{4} - \frac{y}{4} - 2 = \frac{15}{4}$

Step 3.1.3

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

$\frac{y \cdot 4}{4} - \frac{y}{4} - 2 = \frac{15}{4}$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{y \cdot 4 - y}{4} - 2 = \frac{15}{4}$

Step 3.1.5

Subtract $y$ from $y \cdot 4$ .

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Step 3.1.5.1

Reorder $y$ and $4$ .

$\frac{4 \cdot y - y}{4} - 2 = \frac{15}{4}$

Step 3.1.5.2

Subtract $y$ from $4 \cdot y$ .

$\frac{3 \cdot y}{4} - 2 = \frac{15}{4}$

$\frac{3 y}{4} - 2 = \frac{15}{4}$

Step 3.2

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

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Step 3.2.1

Add $2$ to both sides of the equation.

$\frac{3 y}{4} = \frac{15}{4} + 2$

Step 3.2.2

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

$\frac{3 y}{4} = \frac{15}{4} + 2 \cdot \frac{4}{4}$

Step 3.2.3

Combine $2$ and $\frac{4}{4}$ .

$\frac{3 y}{4} = \frac{15}{4} + \frac{2 \cdot 4}{4}$

Step 3.2.4

Combine the numerators over the common denominator.

$\frac{3 y}{4} = \frac{15 + 2 \cdot 4}{4}$

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply $2$ by $4$ .

$\frac{3 y}{4} = \frac{15 + 8}{4}$

Step 3.2.5.2

Add $15$ and $8$ .

$\frac{3 y}{4} = \frac{23}{4}$

Step 3.3

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

$3 y = 23$

Step 3.4

Divide each term in $3 y = 23$ by $3$ and simplify.

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Step 3.4.1

Divide each term in $3 y = 23$ by $3$ .

$\frac{3 y}{3} = \frac{23}{3}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $3$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{23}{3}$

Step 3.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{23}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{23}{3}$

Decimal Form:

$y = 7.\overline{6}$

Mixed Number Form:

$y = 7 \frac{2}{3}$