Basic Math Examples

$0.006 \cdot \frac{1}{3} \div 6 + (0.006 \cdot \frac{1}{3}) \cdot 6$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$\frac{0.006 \cdot \frac{1}{3}}{6} + (0.006 \cdot \frac{1}{3}) \cdot 6$

Step 1.2

Combine $0.006$ and $\frac{1}{3}$ .

$\frac{\frac{0.006}{3}}{6} + (0.006 \cdot \frac{1}{3}) \cdot 6$

Step 1.3

Divide $0.006$ by $3$ .

$\frac{0.002}{6} + (0.006 \cdot \frac{1}{3}) \cdot 6$

Step 1.4

Divide $0.002$ by $6$ .

$0.000\overline{3} + (0.006 \cdot \frac{1}{3}) \cdot 6$

Step 1.5

Cancel the common factor of $0.006$ .

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Step 1.5.1

Factor $0.006$ out of $3$ .

$0.000\overline{3} + 0.006 \cdot \frac{1}{0.006 (500)} \cdot 6$

Step 1.5.2

Cancel the common factor.

$0.000\overline{3} + 0.006 \cdot \frac{1}{0.006 \cdot 500} \cdot 6$

Step 1.5.3

Rewrite the expression.

$0.000\overline{3} + \frac{1}{500} \cdot 6$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Factor $2$ out of $500$ .

$0.000\overline{3} + \frac{1}{2 (250)} \cdot 6$

Step 1.6.2

Factor $2$ out of $6$ .

$0.000\overline{3} + \frac{1}{2 \cdot 250} \cdot (2 \cdot 3)$

Step 1.6.3

Cancel the common factor.

$0.000\overline{3} + \frac{1}{2 \cdot 250} \cdot (2 \cdot 3)$

Step 1.6.4

Rewrite the expression.

$0.000\overline{3} + \frac{1}{250} \cdot 3$

Step 1.7

Combine $\frac{1}{250}$ and $3$ .

$0.000\overline{3} + \frac{3}{250}$

Step 2

To write $0.000\overline{3}$ as a fraction with a common denominator, multiply by $\frac{250}{250}$ .

$0.000\overline{3} \cdot \frac{250}{250} + \frac{3}{250}$

Step 3

Combine fractions.

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Step 3.1

Combine $0.000\overline{3}$ and $\frac{250}{250}$ .

$\frac{0.000\overline{3} \cdot 250}{250} + \frac{3}{250}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{0.000\overline{3} \cdot 250 + 3}{250}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $0.000\overline{3}$ by $250$ .

$\frac{0.08333333 + 3}{250}$

Step 4.2

Add $0.08333333$ and $3$ .

$\frac{3.08333333}{250}$

Step 5

Divide $3.08333333$ by $250$ .

$0.012\overline{3}$