Simplify ((5m)/(6n))÷((15m^2)/8)

$\frac{5 m}{6 n} \div \frac{15 m^{2}}{8}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 m}{6 n} \cdot \frac{8}{15 m^{2}}$

Step 2

Combine.

$\frac{5 m \cdot 8}{6 n (15 m^{2})}$

Step 3

Cancel the common factor of $5$ and $15$ .

Factor $5$ out of $5 m \cdot 8$ .

$\frac{5 (m \cdot 8)}{6 n (15 m^{2})}$

Cancel the common factors.

Factor $5$ out of $6 n (15 m^{2})$ .

$\frac{5 (m \cdot 8)}{5 (6 n (3 m^{2}))}$

Cancel the common factor.

$\frac{5 (m \cdot 8)}{5 (6 n (3 m^{2}))}$

Rewrite the expression.

$\frac{m \cdot 8}{6 n (3 m^{2})}$

$\frac{m \cdot 8}{6 n (3 m^{2})}$

$\frac{m \cdot 8}{6 n (3 m^{2})}$

Step 4

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

Factor $m$ out of $m \cdot 8$ .

$\frac{m (8)}{6 n (3 m^{2})}$

Cancel the common factors.

Factor $m$ out of $6 n (3 m^{2})$ .

$\frac{m (8)}{m (6 n (3 m))}$

Cancel the common factor.

$\frac{m \cdot 8}{m (6 n (3 m))}$

Rewrite the expression.

$\frac{8}{6 n (3 m)}$

$\frac{8}{6 n (3 m)}$

$\frac{8}{6 n (3 m)}$

Step 5

Cancel the common factor of $8$ and $6$ .

Factor $2$ out of $8$ .

$\frac{2 (4)}{6 n (3 m)}$

Cancel the common factors.

Factor $2$ out of $6 n (3 m)$ .

$\frac{2 (4)}{2 (3 n (3 m))}$

Cancel the common factor.

$\frac{2 \cdot 4}{2 (3 n (3 m))}$

Rewrite the expression.

$\frac{4}{3 n (3 m)}$

$\frac{4}{3 n (3 m)}$

$\frac{4}{3 n (3 m)}$

Step 6

Multiply $3$ by $3$ .

$\frac{4}{9 n m}$

Related Questions