Algebra Examples

$\frac{3 a b}{4 x y} \div (- \frac{21 a^{2} b}{10 x^{2} y})$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 a b}{4 x y} (- \frac{10 x^{2} y}{21 a^{2} b})$

Step 2

Rewrite using the commutative property of multiplication.

$- \frac{3 a b}{4 x y} \cdot \frac{10 x^{2} y}{21 a^{2} b}$

Step 3

Cancel the common factor of $3 a b$ .

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Step 3.1

Move the leading negative in $- \frac{3 a b}{4 x y}$ into the numerator.

$\frac{- 3 a b}{4 x y} \cdot \frac{10 x^{2} y}{21 a^{2} b}$

Step 3.2

Factor $3 a b$ out of $- 3 a b$ .

$\frac{3 a b (- 1)}{4 x y} \cdot \frac{10 x^{2} y}{21 a^{2} b}$

Step 3.3

Factor $3 a b$ out of $21 a^{2} b$ .

$\frac{3 a b (- 1)}{4 x y} \cdot \frac{10 x^{2} y}{3 a b (7 a)}$

Step 3.4

Cancel the common factor.

$\frac{3 a b \cdot - 1}{4 x y} \cdot \frac{10 x^{2} y}{3 a b (7 a)}$

Step 3.5

Rewrite the expression.

$\frac{- 1}{4 x y} \cdot \frac{10 x^{2} y}{7 a}$

Step 4

Cancel the common factor of $2 x y$ .

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Step 4.1

Factor $2 x y$ out of $4 x y$ .

$\frac{- 1}{2 x y (2)} \cdot \frac{10 x^{2} y}{7 a}$

Step 4.2

Factor $2 x y$ out of $10 x^{2} y$ .

$\frac{- 1}{2 x y (2)} \cdot \frac{2 x y (5 x)}{7 a}$

Step 4.3

Cancel the common factor.

$\frac{- 1}{2 x y \cdot 2} \cdot \frac{2 x y (5 x)}{7 a}$

Step 4.4

Rewrite the expression.

$\frac{- 1}{2} \cdot \frac{5 x}{7 a}$

Step 5

Multiply $\frac{- 1}{2}$ by $\frac{5 x}{7 a}$ .

$\frac{- (5 x)}{2 (7 a)}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $5$ by $- 1$ .

$\frac{- 5 x}{2 (7 a)}$

Step 6.2

Multiply $7$ by $2$ .

$\frac{- 5 x}{14 a}$

Step 6.3

Move the negative in front of the fraction.

$- \frac{5 x}{14 a}$