Pre-Algebra Examples

$\frac{2 y^{2} - 8 y + 7}{8 y^{5}}$

Step 1

Split the fraction $\frac{2 y^{2} - 8 y + 7}{8 y^{5}}$ into two fractions.

$\frac{2 y^{2} - 8 y}{8 y^{5}} + \frac{7}{8 y^{5}}$

Step 2

Split the fraction $\frac{2 y^{2} - 8 y}{8 y^{5}}$ into two fractions.

$\frac{2 y^{2}}{8 y^{5}} + \frac{- 8 y}{8 y^{5}} + \frac{7}{8 y^{5}}$

Step 3

Cancel the common factor of $2$ and $8$ .

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Step 3.1

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

$\frac{2 (y^{2})}{8 y^{5}} + \frac{- 8 y}{8 y^{5}} + \frac{7}{8 y^{5}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $8 y^{5}$ .

$\frac{2 (y^{2})}{2 (4 y^{5})} + \frac{- 8 y}{8 y^{5}} + \frac{7}{8 y^{5}}$

Step 3.2.2

Cancel the common factor.

$\frac{2 y^{2}}{2 (4 y^{5})} + \frac{- 8 y}{8 y^{5}} + \frac{7}{8 y^{5}}$

Step 3.2.3

Rewrite the expression.

$\frac{y^{2}}{4 y^{5}} + \frac{- 8 y}{8 y^{5}} + \frac{7}{8 y^{5}}$

Step 4

Cancel the common factor of $y^{2}$ and $y^{5}$ .

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Step 4.1

Multiply by $1$ .

$\frac{y^{2} \cdot 1}{4 y^{5}} + \frac{- 8 y}{8 y^{5}} + \frac{7}{8 y^{5}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y^{2}$ out of $4 y^{5}$ .

$\frac{y^{2} \cdot 1}{y^{2} (4 y^{3})} + \frac{- 8 y}{8 y^{5}} + \frac{7}{8 y^{5}}$

Step 4.2.2

Cancel the common factor.

$\frac{y^{2} \cdot 1}{y^{2} (4 y^{3})} + \frac{- 8 y}{8 y^{5}} + \frac{7}{8 y^{5}}$

Step 4.2.3

Rewrite the expression.

$\frac{1}{4 y^{3}} + \frac{- 8 y}{8 y^{5}} + \frac{7}{8 y^{5}}$

Step 5

Cancel the common factor of $- 8$ and $8$ .

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Step 5.1

Factor $8$ out of $- 8 y$ .

$\frac{1}{4 y^{3}} + \frac{8 (- y)}{8 y^{5}} + \frac{7}{8 y^{5}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $8$ out of $8 y^{5}$ .

$\frac{1}{4 y^{3}} + \frac{8 (- y)}{8 (y^{5})} + \frac{7}{8 y^{5}}$

Step 5.2.2

Cancel the common factor.

$\frac{1}{4 y^{3}} + \frac{8 (- y)}{8 y^{5}} + \frac{7}{8 y^{5}}$

Step 5.2.3

Rewrite the expression.

$\frac{1}{4 y^{3}} + \frac{- y}{y^{5}} + \frac{7}{8 y^{5}}$

Step 6

Cancel the common factor of $y$ and $y^{5}$ .

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Step 6.1

Factor $y$ out of $- y$ .

$\frac{1}{4 y^{3}} + \frac{y \cdot - 1}{y^{5}} + \frac{7}{8 y^{5}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$\frac{1}{4 y^{3}} + \frac{y \cdot - 1}{y \cdot y^{4}} + \frac{7}{8 y^{5}}$

Step 6.2.2

Cancel the common factor.

$\frac{1}{4 y^{3}} + \frac{y \cdot - 1}{y \cdot y^{4}} + \frac{7}{8 y^{5}}$

Step 6.2.3

Rewrite the expression.

$\frac{1}{4 y^{3}} + \frac{- 1}{y^{4}} + \frac{7}{8 y^{5}}$

Step 7

Move the negative in front of the fraction.

$\frac{1}{4 y^{3}} - \frac{1}{y^{4}} + \frac{7}{8 y^{5}}$