Pre-Algebra Examples

$\frac{48 y^{3} + 20 y^{2} + y + 20}{12 y}$

Step 1

Split the fraction $\frac{48 y^{3} + 20 y^{2} + y + 20}{12 y}$ into two fractions.

$\frac{48 y^{3} + 20 y^{2} + y}{12 y} + \frac{20}{12 y}$

Step 2

Split the fraction $\frac{48 y^{3} + 20 y^{2} + y}{12 y}$ into two fractions.

$\frac{48 y^{3} + 20 y^{2}}{12 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 3

Split the fraction $\frac{48 y^{3} + 20 y^{2}}{12 y}$ into two fractions.

$\frac{48 y^{3}}{12 y} + \frac{20 y^{2}}{12 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 4

Cancel the common factor of $48$ and $12$ .

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Step 4.1

Factor $12$ out of $48 y^{3}$ .

$\frac{12 (4 y^{3})}{12 y} + \frac{20 y^{2}}{12 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $12$ out of $12 y$ .

$\frac{12 (4 y^{3})}{12 (y)} + \frac{20 y^{2}}{12 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 4.2.2

Cancel the common factor.

$\frac{12 (4 y^{3})}{12 y} + \frac{20 y^{2}}{12 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 4.2.3

Rewrite the expression.

$\frac{4 y^{3}}{y} + \frac{20 y^{2}}{12 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 5

Cancel the common factor of $y^{3}$ and $y$ .

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Step 5.1

Factor $y$ out of $4 y^{3}$ .

$\frac{y (4 y^{2})}{y} + \frac{20 y^{2}}{12 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Raise $y$ to the power of $1$ .

$\frac{y (4 y^{2})}{y^{1}} + \frac{20 y^{2}}{12 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 5.2.2

Factor $y$ out of $y^{1}$ .

$\frac{y (4 y^{2})}{y \cdot 1} + \frac{20 y^{2}}{12 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 5.2.3

Cancel the common factor.

$\frac{y (4 y^{2})}{y \cdot 1} + \frac{20 y^{2}}{12 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 5.2.4

Rewrite the expression.

$\frac{4 y^{2}}{1} + \frac{20 y^{2}}{12 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 5.2.5

Divide $4 y^{2}$ by $1$ .

$4 y^{2} + \frac{20 y^{2}}{12 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 6

Cancel the common factor of $20$ and $12$ .

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Step 6.1

Factor $4$ out of $20 y^{2}$ .

$4 y^{2} + \frac{4 (5 y^{2})}{12 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $4$ out of $12 y$ .

$4 y^{2} + \frac{4 (5 y^{2})}{4 (3 y)} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 6.2.2

Cancel the common factor.

$4 y^{2} + \frac{4 (5 y^{2})}{4 (3 y)} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 6.2.3

Rewrite the expression.

$4 y^{2} + \frac{5 y^{2}}{3 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 7

Cancel the common factor of $y^{2}$ and $y$ .

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Step 7.1

Factor $y$ out of $5 y^{2}$ .

$4 y^{2} + \frac{y (5 y)}{3 y} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $y$ out of $3 y$ .

$4 y^{2} + \frac{y (5 y)}{y \cdot 3} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 7.2.2

Cancel the common factor.

$4 y^{2} + \frac{y (5 y)}{y \cdot 3} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 7.2.3

Rewrite the expression.

$4 y^{2} + \frac{5 y}{3} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 8

Cancel the common factor of $y$ .

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Step 8.1

Cancel the common factor.

$4 y^{2} + \frac{5 y}{3} + \frac{y}{12 y} + \frac{20}{12 y}$

Step 8.2

Rewrite the expression.

$4 y^{2} + \frac{5 y}{3} + \frac{1}{12} + \frac{20}{12 y}$

Step 9

Cancel the common factor of $20$ and $12$ .

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Step 9.1

Factor $4$ out of $20$ .

$4 y^{2} + \frac{5 y}{3} + \frac{1}{12} + \frac{4 (5)}{12 y}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $4$ out of $12 y$ .

$4 y^{2} + \frac{5 y}{3} + \frac{1}{12} + \frac{4 (5)}{4 (3 y)}$

Step 9.2.2

Cancel the common factor.

$4 y^{2} + \frac{5 y}{3} + \frac{1}{12} + \frac{4 \cdot 5}{4 (3 y)}$

Step 9.2.3

Rewrite the expression.

$4 y^{2} + \frac{5 y}{3} + \frac{1}{12} + \frac{5}{3 y}$