Pre-Algebra Examples

$\frac{40}{7 y^{2}} \div 45 y^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{40}{7 y^{2}}}{45 y^{2}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{40}{7 y^{2}} \cdot \frac{1}{45 y^{2}}$

Step 3

Combine.

$\frac{40 \cdot 1}{7 y^{2} (45 y^{2})}$

Step 4

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

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Step 4.1

Move $y^{2}$ .

$\frac{40 \cdot 1}{7 (y^{2} y^{2}) \cdot 45}$

Step 4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{40 \cdot 1}{7 y^{2 + 2} \cdot 45}$

Step 4.3

Add $2$ and $2$ .

$\frac{40 \cdot 1}{7 y^{4} \cdot 45}$

Step 5

Multiply $40$ by $1$ .

$\frac{40}{7 y^{4} \cdot 45}$

Step 6

Cancel the common factor of $40$ and $45$ .

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Step 6.1

Factor $5$ out of $40$ .

$\frac{5 (8)}{7 y^{4} \cdot 45}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $5$ out of $7 y^{4} \cdot 45$ .

$\frac{5 (8)}{5 (7 y^{4} \cdot 9)}$

Step 6.2.2

Cancel the common factor.

$\frac{5 \cdot 8}{5 (7 y^{4} \cdot 9)}$

Step 6.2.3

Rewrite the expression.

$\frac{8}{7 y^{4} \cdot 9}$

Step 7

Multiply $9$ by $7$ .

$\frac{8}{63 y^{4}}$