Simplify ((14a^2)/(10b^2))÷((21a^2)/(15b^2))

$\frac{14 a^{2}}{10 b^{2}} \div \frac{21 a^{2}}{15 b^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{14 a^{2}}{10 b^{2}} \cdot \frac{15 b^{2}}{21 a^{2}}$

Step 2

Combine.

$\frac{14 a^{2} (15 b^{2})}{10 b^{2} (21 a^{2})}$

Step 3

Cancel the common factor of $14$ and $10$ .

Factor $2$ out of $14 a^{2} (15 b^{2})$ .

$\frac{2 (7 a^{2} (15 b^{2}))}{10 b^{2} (21 a^{2})}$

Cancel the common factors.

Factor $2$ out of $10 b^{2} (21 a^{2})$ .

$\frac{2 (7 a^{2} (15 b^{2}))}{2 (5 b^{2} (21 a^{2}))}$

Cancel the common factor.

$\frac{2 (7 a^{2} (15 b^{2}))}{2 (5 b^{2} (21 a^{2}))}$

Rewrite the expression.

$\frac{7 a^{2} (15 b^{2})}{5 b^{2} (21 a^{2})}$

Step 4

Cancel the common factor of $7$ and $21$ .

Factor $7$ out of $7 a^{2} (15 b^{2})$ .

$\frac{7 (a^{2} (15 b^{2}))}{5 b^{2} (21 a^{2})}$

Cancel the common factors.

Factor $7$ out of $5 b^{2} (21 a^{2})$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{a^{2} (15 b^{2})}{5 b^{2} (3 a^{2})}$

Step 5

Cancel the common factor of $a^{2}$ .

Cancel the common factor.

$\frac{a^{2} (15 b^{2})}{5 b^{2} (3 a^{2})}$

Rewrite the expression.

$\frac{15 b^{2}}{5 b^{2} \cdot (3)}$

Step 6

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

Factor $5$ out of $15 b^{2}$ .

$\frac{5 (3 b^{2})}{5 b^{2} \cdot (3)}$

Cancel the common factors.

Factor $5$ out of $5 b^{2} \cdot (3)$ .

$\frac{5 (3 b^{2})}{5 (b^{2} \cdot (3))}$

Cancel the common factor.

$\frac{5 (3 b^{2})}{5 (b^{2} \cdot (3))}$

Rewrite the expression.

$\frac{3 b^{2}}{b^{2} \cdot (3)}$

Step 7

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 b^{2}}{b^{2} \cdot 3}$

Rewrite the expression.

$\frac{b^{2}}{b^{2}}$

Step 8

Cancel the common factor of $b^{2}$ .

Cancel the common factor.

$\frac{b^{2}}{b^{2}}$

Rewrite the expression.

$1$

Simplify ((14a^2)/(10b^2))÷((21a^2)/(15b^2))

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