Basic Math Examples

$5 y^{2} \div 35 y^{6} - 40 y^{5} + 30 y^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$\frac{5 y^{2}}{35 y^{6}} - 40 y^{5} + 30 y^{2}$

Step 1.2

Cancel the common factor of $5$ and $35$ .

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Step 1.2.1

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

$\frac{5 (y^{2})}{35 y^{6}} - 40 y^{5} + 30 y^{2}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $5$ out of $35 y^{6}$ .

$\frac{5 (y^{2})}{5 (7 y^{6})} - 40 y^{5} + 30 y^{2}$

Step 1.2.2.2

Cancel the common factor.

$\frac{5 y^{2}}{5 (7 y^{6})} - 40 y^{5} + 30 y^{2}$

Step 1.2.2.3

Rewrite the expression.

$\frac{y^{2}}{7 y^{6}} - 40 y^{5} + 30 y^{2}$

Step 1.3

Cancel the common factor of $y^{2}$ and $y^{6}$ .

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Step 1.3.1

Multiply by $1$ .

$\frac{y^{2} \cdot 1}{7 y^{6}} - 40 y^{5} + 30 y^{2}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $y^{2}$ out of $7 y^{6}$ .

$\frac{y^{2} \cdot 1}{y^{2} (7 y^{4})} - 40 y^{5} + 30 y^{2}$

Step 1.3.2.2

Cancel the common factor.

$\frac{y^{2} \cdot 1}{y^{2} (7 y^{4})} - 40 y^{5} + 30 y^{2}$

Step 1.3.2.3

Rewrite the expression.

$\frac{1}{7 y^{4}} - 40 y^{5} + 30 y^{2}$

Step 2

Move $\frac{1}{7 y^{4}}$ .

$- 40 y^{5} + 30 y^{2} + \frac{1}{7 y^{4}}$