Pre-Algebra Examples

$- 10 d^{4} e^{3} f^{5} \div 15 d^{2} e^{2} f$

Step 1

Rewrite the division as a fraction.

$\frac{- 10 d^{4} e^{3} f^{5}}{15 d^{2} e^{2} f}$

Step 2

Cancel the common factor of $- 10$ and $15$ .

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Step 2.1

Factor $5$ out of $- 10 d^{4} e^{3} f^{5}$ .

$\frac{5 (- 2 d^{4} e^{3} f^{5})}{15 d^{2} e^{2} f}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $15 d^{2} e^{2} f$ .

$\frac{5 (- 2 d^{4} e^{3} f^{5})}{5 (3 d^{2} e^{2} f)}$

Step 2.2.2

Cancel the common factor.

$\frac{5 (- 2 d^{4} e^{3} f^{5})}{5 (3 d^{2} e^{2} f)}$

Step 2.2.3

Rewrite the expression.

$\frac{- 2 d^{4} e^{3} f^{5}}{3 d^{2} e^{2} f}$

Step 3

Cancel the common factor of $d^{4}$ and $d^{2}$ .

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Step 3.1

Factor $d^{2}$ out of $- 2 d^{4} e^{3} f^{5}$ .

$\frac{d^{2} (- 2 d^{2} e^{3} f^{5})}{3 d^{2} e^{2} f}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $d^{2}$ out of $3 d^{2} e^{2} f$ .

$\frac{d^{2} (- 2 d^{2} e^{3} f^{5})}{d^{2} (3 e^{2} f)}$

Step 3.2.2

Cancel the common factor.

$\frac{d^{2} (- 2 d^{2} e^{3} f^{5})}{d^{2} (3 e^{2} f)}$

Step 3.2.3

Rewrite the expression.

$\frac{- 2 d^{2} e^{3} f^{5}}{3 e^{2} f}$

Step 4

Cancel the common factor of $e^{3}$ and $e^{2}$ .

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Step 4.1

Factor $e^{2}$ out of $- 2 d^{2} e^{3} f^{5}$ .

$\frac{e^{2} (- 2 d^{2} e f^{5})}{3 e^{2} f}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $e^{2}$ out of $3 e^{2} f$ .

$\frac{e^{2} (- 2 d^{2} e f^{5})}{e^{2} (3 f)}$

Step 4.2.2

Cancel the common factor.

$\frac{e^{2} (- 2 d^{2} e f^{5})}{e^{2} (3 f)}$

Step 4.2.3

Rewrite the expression.

$\frac{- 2 d^{2} e f^{5}}{3 f}$

Step 5

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

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Step 5.1

Factor $f$ out of $- 2 d^{2} e f^{5}$ .

$\frac{f (- 2 d^{2} e f^{4})}{3 f}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $f$ out of $3 f$ .

$\frac{f (- 2 d^{2} e f^{4})}{f \cdot 3}$

Step 5.2.2

Cancel the common factor.

$\frac{f (- 2 d^{2} e f^{4})}{f \cdot 3}$

Step 5.2.3

Rewrite the expression.

$\frac{- 2 d^{2} e f^{4}}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{2 d^{2} e f^{4}}{3}$