Basic Math Examples

$\frac{12}{7 y} \div (- \frac{9 y}{5})$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{12}{7 y} (- \frac{5}{9 y})$

Step 2

Rewrite using the commutative property of multiplication.

$- \frac{12}{7 y} \cdot \frac{5}{9 y}$

Step 3

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1

Move the leading negative in $- \frac{12}{7 y}$ into the numerator.

$\frac{- 12}{7 y} \cdot \frac{5}{9 y}$

Step 3.2

Factor $3$ out of $- 12$ .

$\frac{3 (- 4)}{7 y} \cdot \frac{5}{9 y}$

Step 3.3

Factor $3$ out of $9 y$ .

$\frac{3 (- 4)}{7 y} \cdot \frac{5}{3 (3 y)}$

Step 3.4

Cancel the common factor.

$\frac{3 \cdot - 4}{7 y} \cdot \frac{5}{3 (3 y)}$

Step 3.5

Rewrite the expression.

$\frac{- 4}{7 y} \cdot \frac{5}{3 y}$

Step 4

Multiply $\frac{- 4}{7 y}$ by $\frac{5}{3 y}$ .

$\frac{- 4 \cdot 5}{7 y (3 y)}$

Step 5

Multiply.

Tap for more steps...

Step 5.1

Multiply $- 4$ by $5$ .

$\frac{- 20}{7 y (3 y)}$

Step 5.2

Multiply $3$ by $7$ .

$\frac{- 20}{21 y \cdot y}$

Step 6

Raise $y$ to the power of $1$ .

$\frac{- 20}{21 (y^{1} y)}$

Step 7

Raise $y$ to the power of $1$ .

$\frac{- 20}{21 (y^{1} y^{1})}$

Step 8

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

$\frac{- 20}{21 y^{1 + 1}}$

Step 9

Add $1$ and $1$ .

$\frac{- 20}{21 y^{2}}$

Step 10

Move the negative in front of the fraction.

$- \frac{20}{21 y^{2}}$