Simplify ((10ab)/(c^3d))÷((15ab^3)/(7c^3d^4))

$\frac{10 a b}{c^{3} d} \div \frac{15 a b^{3}}{7 c^{3} d^{4}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{10 a b}{c^{3} d} \cdot \frac{7 c^{3} d^{4}}{15 a b^{3}}$

Step 2

Combine.

$\frac{10 a b (7 c^{3} d^{4})}{c^{3} d (15 a b^{3})}$

Step 3

Cancel the common factor of $10$ and $15$ .

Factor $5$ out of $10 a b (7 c^{3} d^{4})$ .

$\frac{5 (2 a b (7 c^{3} d^{4}))}{c^{3} d (15 a b^{3})}$

Cancel the common factors.

Factor $5$ out of $c^{3} d (15 a b^{3})$ .

$\frac{5 (2 a b (7 c^{3} d^{4}))}{5 (c^{3} d (3 a b^{3}))}$

Cancel the common factor.

$\frac{5 (2 a b (7 c^{3} d^{4}))}{5 (c^{3} d (3 a b^{3}))}$

Rewrite the expression.

$\frac{2 a b (7 c^{3} d^{4})}{c^{3} d (3 a b^{3})}$

Step 4

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{2 a b (7 c^{3} d^{4})}{c^{3} d (3 a b^{3})}$

Rewrite the expression.

$\frac{2 b (7 c^{3} d^{4})}{c^{3} d (3 b^{3})}$

Step 5

Cancel the common factor of $b$ and $b^{3}$ .

Factor $b$ out of $2 b (7 c^{3} d^{4})$ .

$\frac{b (2 (7 c^{3} d^{4}))}{c^{3} d (3 b^{3})}$

Cancel the common factors.

Factor $b$ out of $c^{3} d (3 b^{3})$ .

$\frac{b (2 (7 c^{3} d^{4}))}{b (c^{3} d (3 b^{2}))}$

Cancel the common factor.

$\frac{b (2 (7 c^{3} d^{4}))}{b (c^{3} d (3 b^{2}))}$

Rewrite the expression.

$\frac{2 (7 c^{3} d^{4})}{c^{3} d (3 b^{2})}$

Step 6

Cancel the common factor of $c^{3}$ .

Cancel the common factor.

$\frac{2 (7 c^{3} d^{4})}{c^{3} d (3 b^{2})}$

Rewrite the expression.

$\frac{2 (7 d^{4})}{d (3 b^{2})}$

Step 7

Cancel the common factor of $d^{4}$ and $d$ .

Factor $d$ out of $2 (7 d^{4})$ .

$\frac{d (2 (7 d^{3}))}{d (3 b^{2})}$

Cancel the common factors.

Cancel the common factor.

$\frac{d (2 (7 d^{3}))}{d (3 b^{2})}$

Rewrite the expression.

$\frac{2 (7 d^{3})}{3 b^{2}}$

Step 8

Multiply $2$ by $7$ .

$\frac{14 d^{3}}{3 b^{2}}$

Simplify ((10ab)/(c^3d))÷((15ab^3)/(7c^3d^4))

Related Questions

Support LCMGCF.com by disabling your adblocker.