Basic Math Examples

$\frac{3}{8} \div \frac{13}{12} = \frac{3}{8} \cdot \frac{a}{b}$

Step 1

Rewrite the equation as $\frac{3}{8} \cdot \frac{a}{b} = \frac{3}{8} \div \frac{13}{12}$ .

$\frac{3}{8} \cdot \frac{a}{b} = \frac{3}{8} \div \frac{13}{12}$

Step 2

Multiply both sides of the equation by $\frac{8}{3}$ .

$\frac{8}{3} (\frac{3}{8} \cdot \frac{a}{b}) = \frac{8}{3} \cdot \frac{3}{8} \div \frac{13}{12}$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{8}{3} (\frac{3}{8} \cdot \frac{a}{b})$ .

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Step 3.1.1.1

Multiply $\frac{3}{8}$ by $\frac{a}{b}$ .

$\frac{8}{3} \cdot \frac{3 a}{8 b} = \frac{8}{3} \cdot \frac{3}{8} \div \frac{13}{12}$

Step 3.1.1.2

Cancel the common factor of $8$ .

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Step 3.1.1.2.1

Factor $8$ out of $8 b$ .

$\frac{8}{3} \cdot \frac{3 a}{8 (b)} = \frac{8}{3} \cdot \frac{3}{8} \div \frac{13}{12}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{8}{3} \cdot \frac{3 a}{8 b} = \frac{8}{3} \cdot \frac{3}{8} \div \frac{13}{12}$

Step 3.1.1.2.3

Rewrite the expression.

$\frac{1}{3} \cdot \frac{3 a}{b} = \frac{8}{3} \cdot \frac{3}{8} \div \frac{13}{12}$

Step 3.1.1.3

Cancel the common factor of $3$ .

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Step 3.1.1.3.1

Factor $3$ out of $3 a$ .

$\frac{1}{3} \cdot \frac{3 (a)}{b} = \frac{8}{3} \cdot \frac{3}{8} \div \frac{13}{12}$

Step 3.1.1.3.2

Cancel the common factor.

$\frac{1}{3} \cdot \frac{3 a}{b} = \frac{8}{3} \cdot \frac{3}{8} \div \frac{13}{12}$

Step 3.1.1.3.3

Rewrite the expression.

$\frac{a}{b} = \frac{8}{3} \cdot \frac{3}{8} \div \frac{13}{12}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{8}{3} \cdot \frac{3}{8} \div \frac{13}{12}$ .

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Step 3.2.1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{a}{b} = \frac{8}{3} (\frac{3}{8} \cdot \frac{12}{13})$

Step 3.2.1.2

Cancel the common factor of $4$ .

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Step 3.2.1.2.1

Factor $4$ out of $8$ .

$\frac{a}{b} = \frac{8}{3} (\frac{3}{4 (2)} \cdot \frac{12}{13})$

Step 3.2.1.2.2

Factor $4$ out of $12$ .

$\frac{a}{b} = \frac{8}{3} (\frac{3}{4 \cdot 2} \cdot \frac{4 \cdot 3}{13})$

Step 3.2.1.2.3

Cancel the common factor.

$\frac{a}{b} = \frac{8}{3} (\frac{3}{4 \cdot 2} \cdot \frac{4 \cdot 3}{13})$

Step 3.2.1.2.4

Rewrite the expression.

$\frac{a}{b} = \frac{8}{3} (\frac{3}{2} \cdot \frac{3}{13})$

Step 3.2.1.3

Multiply $\frac{3}{2}$ by $\frac{3}{13}$ .

$\frac{a}{b} = \frac{8}{3} \cdot \frac{3 \cdot 3}{2 \cdot 13}$

Step 3.2.1.4

Multiply.

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Step 3.2.1.4.1

Multiply $3$ by $3$ .

$\frac{a}{b} = \frac{8}{3} \cdot \frac{9}{2 \cdot 13}$

Step 3.2.1.4.2

Multiply $2$ by $13$ .

$\frac{a}{b} = \frac{8}{3} \cdot \frac{9}{26}$

Step 3.2.1.5

Cancel the common factor of $2$ .

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Step 3.2.1.5.1

Factor $2$ out of $8$ .

$\frac{a}{b} = \frac{2 (4)}{3} \cdot \frac{9}{26}$

Step 3.2.1.5.2

Factor $2$ out of $26$ .

$\frac{a}{b} = \frac{2 \cdot 4}{3} \cdot \frac{9}{2 \cdot 13}$

Step 3.2.1.5.3

Cancel the common factor.

$\frac{a}{b} = \frac{2 \cdot 4}{3} \cdot \frac{9}{2 \cdot 13}$

Step 3.2.1.5.4

Rewrite the expression.

$\frac{a}{b} = \frac{4}{3} \cdot \frac{9}{13}$

Step 3.2.1.6

Cancel the common factor of $3$ .

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Step 3.2.1.6.1

Factor $3$ out of $9$ .

$\frac{a}{b} = \frac{4}{3} \cdot \frac{3 (3)}{13}$

Step 3.2.1.6.2

Cancel the common factor.

$\frac{a}{b} = \frac{4}{3} \cdot \frac{3 \cdot 3}{13}$

Step 3.2.1.6.3

Rewrite the expression.

$\frac{a}{b} = 4 (\frac{3}{13})$

Step 3.2.1.7

Combine $4$ and $\frac{3}{13}$ .

$\frac{a}{b} = \frac{4 \cdot 3}{13}$

Step 3.2.1.8

Multiply $4$ by $3$ .

$\frac{a}{b} = \frac{12}{13}$

Step 4

Multiply both sides by $b$ .

$\frac{a}{b} b = \frac{12}{13} b$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $b$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{a}{b} b = \frac{12}{13} b$

Step 5.1.1.2

Rewrite the expression.

$a = \frac{12}{13} b$

Step 5.2

Simplify the right side.

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Step 5.2.1

Combine $\frac{12}{13}$ and $b$ .

$a = \frac{12 b}{13}$