Basic Math Examples

$\frac{3 a^{2} b}{7 c^{4}} \div \frac{8 b^{2}}{5 a c^{2}} \div \frac{9 a^{5}}{14 b c}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 a^{2} b}{7 c^{4}} \div \frac{8 b^{2}}{5 a c^{2}} \cdot \frac{14 b c}{9 a^{5}}$

Step 2

Combine.

$\frac{\frac{3 a^{2} b}{7 c^{4}} (14 b c)}{\frac{8 b^{2}}{5 a c^{2}} (9 a^{5})}$

Step 3

Simplify the numerator.

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Step 3.1

Combine $14$ and $\frac{3 a^{2} b}{7 c^{4}}$ .

$\frac{\frac{14 (3 a^{2} b)}{7 c^{4}} (b c)}{\frac{8 b^{2}}{5 a c^{2}} (9 a^{5})}$

Step 3.2

Combine $b$ and $\frac{14 (3 a^{2} b)}{7 c^{4}}$ .

$\frac{\frac{b (14 (3 a^{2} b))}{7 c^{4}} c}{\frac{8 b^{2}}{5 a c^{2}} (9 a^{5})}$

Step 3.3

Combine $\frac{b (14 (3 a^{2} b))}{7 c^{4}}$ and $c$ .

$\frac{\frac{b (14 (3 a^{2} b)) c}{7 c^{4}}}{\frac{8 b^{2}}{5 a c^{2}} (9 a^{5})}$

Step 4

Simplify the denominator.

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Step 4.1

Combine $9$ and $\frac{8 b^{2}}{5 a c^{2}}$ .

$\frac{\frac{b (14 (3 a^{2} b)) c}{7 c^{4}}}{\frac{9 (8 b^{2})}{5 a c^{2}} a^{5}}$

Step 4.2

Combine $\frac{9 (8 b^{2})}{5 a c^{2}}$ and $a^{5}$ .

$\frac{\frac{b (14 (3 a^{2} b)) c}{7 c^{4}}}{\frac{9 (8 b^{2}) a^{5}}{5 a c^{2}}}$

Step 5

Simplify the numerator.

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Step 5.1

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

$\frac{\frac{14 \cdot 3 a^{2} (b^{1} b) c}{7 c^{4}}}{\frac{9 (8 b^{2}) a^{5}}{5 a c^{2}}}$

Step 5.2

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

$\frac{\frac{14 \cdot 3 a^{2} (b^{1} b^{1}) c}{7 c^{4}}}{\frac{9 (8 b^{2}) a^{5}}{5 a c^{2}}}$

Step 5.3

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

$\frac{\frac{14 \cdot 3 a^{2} b^{1 + 1} c}{7 c^{4}}}{\frac{9 (8 b^{2}) a^{5}}{5 a c^{2}}}$

Step 5.4

Add $1$ and $1$ .

$\frac{\frac{14 \cdot 3 a^{2} b^{2} c}{7 c^{4}}}{\frac{9 (8 b^{2}) a^{5}}{5 a c^{2}}}$

Step 5.5

Multiply $14$ by $3$ .

$\frac{\frac{42 a^{2} b^{2} c}{7 c^{4}}}{\frac{9 (8 b^{2}) a^{5}}{5 a c^{2}}}$

Step 6

Multiply $9$ by $8$ .

$\frac{\frac{42 a^{2} b^{2} c}{7 c^{4}}}{\frac{72 b^{2} a^{5}}{5 a c^{2}}}$

Step 7

Simplify the numerator.

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Step 7.1

Reduce the expression $\frac{42 a^{2} b^{2} c}{7 c^{4}}$ by cancelling the common factors.

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Step 7.1.1

Factor $7$ out of $42 a^{2} b^{2} c$ .

$\frac{\frac{7 (6 a^{2} b^{2} c)}{7 c^{4}}}{\frac{72 b^{2} a^{5}}{5 a c^{2}}}$

Step 7.1.2

Factor $7$ out of $7 c^{4}$ .

$\frac{\frac{7 (6 a^{2} b^{2} c)}{7 (c^{4})}}{\frac{72 b^{2} a^{5}}{5 a c^{2}}}$

Step 7.1.3

Cancel the common factor.

$\frac{\frac{7 (6 a^{2} b^{2} c)}{7 c^{4}}}{\frac{72 b^{2} a^{5}}{5 a c^{2}}}$

Step 7.1.4

Rewrite the expression.

$\frac{\frac{6 a^{2} b^{2} c}{c^{4}}}{\frac{72 b^{2} a^{5}}{5 a c^{2}}}$

Step 7.2

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

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Step 7.2.1

Factor $c$ out of $6 a^{2} b^{2} c$ .

$\frac{\frac{c (6 a^{2} b^{2})}{c^{4}}}{\frac{72 b^{2} a^{5}}{5 a c^{2}}}$

Step 7.2.2

Cancel the common factors.

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Step 7.2.2.1

Factor $c$ out of $c^{4}$ .

$\frac{\frac{c (6 a^{2} b^{2})}{c \cdot c^{3}}}{\frac{72 b^{2} a^{5}}{5 a c^{2}}}$

Step 7.2.2.2

Cancel the common factor.

$\frac{\frac{c (6 a^{2} b^{2})}{c \cdot c^{3}}}{\frac{72 b^{2} a^{5}}{5 a c^{2}}}$

Step 7.2.2.3

Rewrite the expression.

$\frac{\frac{6 a^{2} b^{2}}{c^{3}}}{\frac{72 b^{2} a^{5}}{5 a c^{2}}}$

Step 8

Reduce the expression $\frac{72 b^{2} a^{5}}{5 a c^{2}}$ by cancelling the common factors.

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Step 8.1

Factor $a$ out of $72 b^{2} a^{5}$ .

$\frac{\frac{6 a^{2} b^{2}}{c^{3}}}{\frac{a (72 b^{2} a^{4})}{5 a c^{2}}}$

Step 8.2

Factor $a$ out of $5 a c^{2}$ .

$\frac{\frac{6 a^{2} b^{2}}{c^{3}}}{\frac{a (72 b^{2} a^{4})}{a (5 c^{2})}}$

Step 8.3

Cancel the common factor.

$\frac{\frac{6 a^{2} b^{2}}{c^{3}}}{\frac{a (72 b^{2} a^{4})}{a (5 c^{2})}}$

Step 8.4

Rewrite the expression.

$\frac{\frac{6 a^{2} b^{2}}{c^{3}}}{\frac{72 b^{2} a^{4}}{5 c^{2}}}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$\frac{6 a^{2} b^{2}}{c^{3}} \cdot \frac{5 c^{2}}{72 b^{2} a^{4}}$

Step 10

Combine.

$\frac{6 a^{2} b^{2} (5 c^{2})}{c^{3} (72 b^{2} a^{4})}$

Step 11

Cancel the common factor of $6$ and $72$ .

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Step 11.1

Factor $6$ out of $6 a^{2} b^{2} (5 c^{2})$ .

$\frac{6 (a^{2} b^{2} (5 c^{2}))}{c^{3} (72 b^{2} a^{4})}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $6$ out of $c^{3} (72 b^{2} a^{4})$ .

$\frac{6 (a^{2} b^{2} (5 c^{2}))}{6 (c^{3} (12 b^{2} a^{4}))}$

Step 11.2.2

Cancel the common factor.

$\frac{6 (a^{2} b^{2} (5 c^{2}))}{6 (c^{3} (12 b^{2} a^{4}))}$

Step 11.2.3

Rewrite the expression.

$\frac{a^{2} b^{2} (5 c^{2})}{c^{3} (12 b^{2} a^{4})}$

Step 12

Cancel the common factor of $a^{2}$ and $a^{4}$ .

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Step 12.1

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

$\frac{a^{2} (b^{2} (5 c^{2}))}{c^{3} (12 b^{2} a^{4})}$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $a^{2}$ out of $c^{3} (12 b^{2} a^{4})$ .

$\frac{a^{2} (b^{2} (5 c^{2}))}{a^{2} (c^{3} (12 b^{2} a^{2}))}$

Step 12.2.2

Cancel the common factor.

$\frac{a^{2} (b^{2} (5 c^{2}))}{a^{2} (c^{3} (12 b^{2} a^{2}))}$

Step 12.2.3

Rewrite the expression.

$\frac{b^{2} (5 c^{2})}{c^{3} (12 b^{2} a^{2})}$

Step 13

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

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Step 13.1

Cancel the common factor.

$\frac{b^{2} (5 c^{2})}{c^{3} (12 b^{2} a^{2})}$

Step 13.2

Rewrite the expression.

$\frac{5 c^{2}}{c^{3} (12 a^{2})}$

Step 14

Cancel the common factor of $c^{2}$ and $c^{3}$ .

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Step 14.1

Factor $c^{2}$ out of $5 c^{2}$ .

$\frac{c^{2} \cdot 5}{c^{3} (12 a^{2})}$

Step 14.2

Cancel the common factors.

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Step 14.2.1

Factor $c^{2}$ out of $c^{3} (12 a^{2})$ .

$\frac{c^{2} \cdot 5}{c^{2} (c (12 a^{2}))}$

Step 14.2.2

Cancel the common factor.

$\frac{c^{2} \cdot 5}{c^{2} (c (12 a^{2}))}$

Step 14.2.3

Rewrite the expression.

$\frac{5}{c (12 a^{2})}$

Step 15

Move $12$ to the left of $c$ .

$\frac{5}{12 c a^{2}}$