Basic Math Examples

$\frac{\frac{1}{3}}{\frac{3}{8} + 15 \cdot \frac{1}{9}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{3} \cdot \frac{1}{\frac{3}{8} + 15 \cdot \frac{1}{9}}$

Step 2

Simplify the denominator.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

Factor $3$ out of $15$ .

$\frac{1}{3} \cdot \frac{1}{\frac{3}{8} + 3 (5) \cdot \frac{1}{9}}$

Step 2.1.2

Factor $3$ out of $9$ .

$\frac{1}{3} \cdot \frac{1}{\frac{3}{8} + 3 \cdot 5 \cdot \frac{1}{3 \cdot 3}}$

Step 2.1.3

Cancel the common factor.

$\frac{1}{3} \cdot \frac{1}{\frac{3}{8} + 3 \cdot 5 \cdot \frac{1}{3 \cdot 3}}$

Step 2.1.4

Rewrite the expression.

$\frac{1}{3} \cdot \frac{1}{\frac{3}{8} + 5 \cdot \frac{1}{3}}$

Step 2.2

Combine $5$ and $\frac{1}{3}$ .

$\frac{1}{3} \cdot \frac{1}{\frac{3}{8} + \frac{5}{3}}$

Step 2.3

To write $\frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{3} \cdot \frac{1}{\frac{3}{8} \cdot \frac{3}{3} + \frac{5}{3}}$

Step 2.4

To write $\frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{1}{3} \cdot \frac{1}{\frac{3}{8} \cdot \frac{3}{3} + \frac{5}{3} \cdot \frac{8}{8}}$

Step 2.5

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.5.1

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

$\frac{1}{3} \cdot \frac{1}{\frac{3 \cdot 3}{8 \cdot 3} + \frac{5}{3} \cdot \frac{8}{8}}$

Step 2.5.2

Multiply $8$ by $3$ .

$\frac{1}{3} \cdot \frac{1}{\frac{3 \cdot 3}{24} + \frac{5}{3} \cdot \frac{8}{8}}$

Step 2.5.3

Multiply $\frac{5}{3}$ by $\frac{8}{8}$ .

$\frac{1}{3} \cdot \frac{1}{\frac{3 \cdot 3}{24} + \frac{5 \cdot 8}{3 \cdot 8}}$

Step 2.5.4

Multiply $3$ by $8$ .

$\frac{1}{3} \cdot \frac{1}{\frac{3 \cdot 3}{24} + \frac{5 \cdot 8}{24}}$

Step 2.6

Combine the numerators over the common denominator.

$\frac{1}{3} \cdot \frac{1}{\frac{3 \cdot 3 + 5 \cdot 8}{24}}$

Step 2.7

Simplify the numerator.

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Step 2.7.1

Multiply $3$ by $3$ .

$\frac{1}{3} \cdot \frac{1}{\frac{9 + 5 \cdot 8}{24}}$

Step 2.7.2

Multiply $5$ by $8$ .

$\frac{1}{3} \cdot \frac{1}{\frac{9 + 40}{24}}$

Step 2.7.3

Add $9$ and $40$ .

$\frac{1}{3} \cdot \frac{1}{\frac{49}{24}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{3} (1 (\frac{24}{49}))$

Step 4

Multiply $\frac{24}{49}$ by $1$ .

$\frac{1}{3} \cdot \frac{24}{49}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $24$ .

$\frac{1}{3} \cdot \frac{3 (8)}{49}$

Step 5.2

Cancel the common factor.

$\frac{1}{3} \cdot \frac{3 \cdot 8}{49}$

Step 5.3

Rewrite the expression.

$\frac{8}{49}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{49}$

Decimal Form:

$0.16326530 \dots$