Pre-Algebra Examples

$\frac{- 51 m^{2} + 27 m^{2} - 60 m}{- 3 m}$

Step 1

Simplify the numerator.

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Step 1.1

Add $- 51 m^{2}$ and $27 m^{2}$ .

$\frac{- 24 m^{2} - 60 m}{- 3 m}$

Step 1.2

Factor $12 m$ out of $- 24 m^{2} - 60 m$ .

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Step 1.2.1

Factor $12 m$ out of $- 24 m^{2}$ .

$\frac{12 m (- 2 m) - 60 m}{- 3 m}$

Step 1.2.2

Factor $12 m$ out of $- 60 m$ .

$\frac{12 m (- 2 m) + 12 m (- 5)}{- 3 m}$

Step 1.2.3

Factor $12 m$ out of $12 m (- 2 m) + 12 m (- 5)$ .

$\frac{12 m (- 2 m - 5)}{- 3 m}$

Step 2

Cancel the common factor of $12$ and $- 3$ .

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Step 2.1

Factor $3$ out of $12 m (- 2 m - 5)$ .

$\frac{3 (4 m (- 2 m - 5))}{- 3 m}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $- 3 m$ .

$\frac{3 (4 m (- 2 m - 5))}{3 (- m)}$

Step 2.2.2

Cancel the common factor.

$\frac{3 (4 m (- 2 m - 5))}{3 (- m)}$

Step 2.2.3

Rewrite the expression.

$\frac{4 m (- 2 m - 5)}{- m}$

Step 3

Cancel the common factor of $m$ .

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Step 3.1

Cancel the common factor.

$\frac{4 m (- 2 m - 5)}{- m}$

Step 3.2

Rewrite the expression.

$\frac{4 (- 2 m - 5)}{- 1}$

Step 3.3

Move the negative one from the denominator of $\frac{4 (- 2 m - 5)}{- 1}$ .

$- 1 \cdot (4 (- 2 m - 5))$

Step 4

Rewrite $- 1 \cdot (4 (- 2 m - 5))$ as $- (4 (- 2 m - 5))$ .

$- (4 (- 2 m - 5))$

Step 5

Apply the distributive property.

$- (4 (- 2 m) + 4 \cdot - 5)$

Step 6

Multiply $- 2$ by $4$ .

$- (- 8 m + 4 \cdot - 5)$

Step 7

Multiply $4$ by $- 5$ .

$- (- 8 m - 20)$

Step 8

Apply the distributive property.

$- (- 8 m) - - 20$

Step 9

Multiply $- 8$ by $- 1$ .

$8 m - - 20$

Step 10

Multiply $- 1$ by $- 20$ .

$8 m + 20$