Pre-Algebra Examples

$\frac{49 m}{4 n^{2}} \div (- \frac{m}{4 m n})$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{49 m}{4 n^{2}} (- \frac{4 m n}{m})$

Step 2

Rewrite using the commutative property of multiplication.

$- \frac{49 m}{4 n^{2}} \cdot \frac{4 m n}{m}$

Step 3

Cancel the common factor of $m$ .

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Step 3.1

Move the leading negative in $- \frac{49 m}{4 n^{2}}$ into the numerator.

$\frac{- 49 m}{4 n^{2}} \cdot \frac{4 m n}{m}$

Step 3.2

Factor $m$ out of $- 49 m$ .

$\frac{m \cdot - 49}{4 n^{2}} \cdot \frac{4 m n}{m}$

Step 3.3

Cancel the common factor.

$\frac{m \cdot - 49}{4 n^{2}} \cdot \frac{4 m n}{m}$

Step 3.4

Rewrite the expression.

$\frac{- 49}{4 n^{2}} (4 m n)$

Step 4

Cancel the common factor of $4 n$ .

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Step 4.1

Factor $4 n$ out of $4 n^{2}$ .

$\frac{- 49}{4 n (n)} (4 m n)$

Step 4.2

Factor $4 n$ out of $4 m n$ .

$\frac{- 49}{4 n (n)} (4 n (m))$

Step 4.3

Cancel the common factor.

$\frac{- 49}{4 n \cdot n} (4 n m)$

Step 4.4

Rewrite the expression.

$\frac{- 49}{n} m$

Step 5

Combine $\frac{- 49}{n}$ and $m$ .

$\frac{- 49 m}{n}$

Step 6

Move the negative in front of the fraction.

$- \frac{49 m}{n}$