Basic Math Examples

$\frac{0.6 (\frac{365}{360} \cdot 0.13) + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - (0.6 \cdot \frac{365}{360} \cdot 0.13) - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $365$ and $360$ .

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Step 1.1.1

Factor $5$ out of $365$ .

$\frac{0.6 (\frac{5 (73)}{360} \cdot 0.13) + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - (0.6 \cdot \frac{365}{360} \cdot 0.13) - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $5$ out of $360$ .

$\frac{0.6 (\frac{5 \cdot 73}{5 \cdot 72} \cdot 0.13) + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - (0.6 \cdot \frac{365}{360} \cdot 0.13) - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 1.1.2.2

Cancel the common factor.

$\frac{0.6 (\frac{5 \cdot 73}{5 \cdot 72} \cdot 0.13) + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - (0.6 \cdot \frac{365}{360} \cdot 0.13) - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 1.1.2.3

Rewrite the expression.

$\frac{0.6 (\frac{73}{72} \cdot 0.13) + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - (0.6 \cdot \frac{365}{360} \cdot 0.13) - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 1.2

Cancel the common factor of $365$ and $360$ .

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Step 1.2.1

Factor $5$ out of $365$ .

$\frac{0.6 (\frac{73}{72} \cdot 0.13) + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - (0.6 \cdot \frac{5 (73)}{360} \cdot 0.13) - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $5$ out of $360$ .

$\frac{0.6 (\frac{73}{72} \cdot 0.13) + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - (0.6 \cdot \frac{5 \cdot 73}{5 \cdot 72} \cdot 0.13) - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 1.2.2.2

Cancel the common factor.

$\frac{0.6 (\frac{73}{72} \cdot 0.13) + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - (0.6 \cdot \frac{5 \cdot 73}{5 \cdot 72} \cdot 0.13) - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 1.2.2.3

Rewrite the expression.

$\frac{0.6 (\frac{73}{72} \cdot 0.13) + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - (0.6 \cdot \frac{73}{72} \cdot 0.13) - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 2

Simplify the numerator.

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Step 2.1

Cancel the common factor of $0.6$ .

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Step 2.1.1

Factor $0.6$ out of $72$ .

$\frac{0.6 \frac{73}{0.6 (120)} \cdot 0.13 + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - 1 \cdot 0.6 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 2.1.2

Cancel the common factor.

$\frac{0.6 \frac{73}{0.6 \cdot 120} \cdot 0.13 + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - 1 \cdot 0.6 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 2.1.3

Rewrite the expression.

$\frac{\frac{73}{120} \cdot 0.13 + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - 1 \cdot 0.6 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 2.2

Multiply $\frac{73}{120} \cdot 0.13$ .

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Step 2.2.1

Combine $\frac{73}{120}$ and $0.13$ .

$\frac{\frac{73 \cdot 0.13}{120} + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - 1 \cdot 0.6 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 2.2.2

Multiply $73$ by $0.13$ .

$\frac{\frac{9.49}{120} + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - 1 \cdot 0.6 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 2.3

Divide $9.49$ by $120$ .

$\frac{0.07908\overline{3} + 0.0002 (1 - 0.6) - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - 1 \cdot 0.6 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 2.4

Subtract $0.6$ from $1$ .

$\frac{0.07908\overline{3} + 0.0002 \cdot 0.4 - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - 1 \cdot 0.6 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 2.5

Multiply $0.0002$ by $0.4$ .

$\frac{0.07908\overline{3} + 0.00008 - (0.1 + 0.08 \cdot 0.6) \cdot 0}{0.6 - 1 \cdot 0.6 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 2.6

Multiply $0.08$ by $0.6$ .

$\frac{0.07908\overline{3} + 0.00008 - (0.1 + 0.048) \cdot 0}{0.6 - 1 \cdot 0.6 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 2.7

Add $0.1$ and $0.048$ .

$\frac{0.07908\overline{3} + 0.00008 - 1 \cdot 0.148 \cdot 0}{0.6 - 1 \cdot 0.6 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 2.8

Multiply $- 1 \cdot 0.148 \cdot 0$ .

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Step 2.8.1

Multiply $- 1$ by $0.148$ .

$\frac{0.07908\overline{3} + 0.00008 - 0.148 \cdot 0}{0.6 - 1 \cdot 0.6 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 2.8.2

Multiply $- 0.148$ by $0$ .

$\frac{0.07908\overline{3} + 0.00008 + 0}{0.6 - 1 \cdot 0.6 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 2.9

Add $0.07908\overline{3} + 0.00008$ and $0$ .

$\frac{0.07908\overline{3} + 0.00008}{0.6 - 1 \cdot 0.6 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 2.10

Add $0.07908\overline{3}$ and $0.00008$ .

$\frac{0.07916\overline{3}}{0.6 - 1 \cdot 0.6 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 3

Simplify the denominator.

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Step 3.1

Cancel the common factor of $0.6$ .

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Step 3.1.1

Factor $0.6$ out of $- 1 \cdot 0.6$ .

$\frac{0.07916\overline{3}}{0.6 + 0.6 \cdot - 1 \cdot \frac{73}{72} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 3.1.2

Factor $0.6$ out of $72$ .

$\frac{0.07916\overline{3}}{0.6 + 0.6 \cdot - 1 \cdot \frac{73}{0.6 (120)} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 3.1.3

Cancel the common factor.

$\frac{0.07916\overline{3}}{0.6 + 0.6 \cdot - 1 \cdot \frac{73}{0.6 \cdot 120} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 3.1.4

Rewrite the expression.

$\frac{0.07916\overline{3}}{0.6 - 1 \cdot \frac{73}{120} \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 3.2

Rewrite $- 1 (\frac{73}{120})$ as $- (\frac{73}{120})$ .

$\frac{0.07916\overline{3}}{0.6 - (\frac{73}{120}) \cdot 0.13 - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 3.3

Multiply $- \frac{73}{120} \cdot 0.13$ .

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Step 3.3.1

Multiply $0.13$ by $- 1$ .

$\frac{0.07916\overline{3}}{0.6 - 0.13 (\frac{73}{120}) - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 3.3.2

Combine $- 0.13$ and $\frac{73}{120}$ .

$\frac{0.07916\overline{3}}{0.6 + \frac{- 0.13 \cdot 73}{120} - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 3.3.3

Multiply $- 0.13$ by $73$ .

$\frac{0.07916\overline{3}}{0.6 + \frac{- 9.49}{120} - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 3.4

Divide $- 9.49$ by $120$ .

$\frac{0.07916\overline{3}}{0.6 - 0.07908\overline{3} - (0.1 + 0.08 \cdot 0.6) (1 - 0.2)}$

Step 3.5

Multiply $0.08$ by $0.6$ .

$\frac{0.07916\overline{3}}{0.6 - 0.07908\overline{3} - (0.1 + 0.048) (1 - 0.2)}$

Step 3.6

Add $0.1$ and $0.048$ .

$\frac{0.07916\overline{3}}{0.6 - 0.07908\overline{3} - 1 \cdot 0.148 (1 - 0.2)}$

Step 3.7

Multiply $- 1$ by $0.148$ .

$\frac{0.07916\overline{3}}{0.6 - 0.07908\overline{3} - 0.148 (1 - 0.2)}$

Step 3.8

Subtract $0.2$ from $1$ .

$\frac{0.07916\overline{3}}{0.6 - 0.07908\overline{3} - 0.148 \cdot 0.8}$

Step 3.9

Multiply $- 0.148$ by $0.8$ .

$\frac{0.07916\overline{3}}{0.6 - 0.07908\overline{3} - 0.1184}$

Step 3.10

Subtract $0.07908\overline{3}$ from $0.6$ .

$\frac{0.07916\overline{3}}{0.52091\overline{6} - 0.1184}$

Step 3.11

Subtract $0.1184$ from $0.52091\overline{6}$ .

$\frac{0.07916\overline{3}}{0.40251\overline{6}}$

Step 4

Divide $0.07916\overline{3}$ by $0.40251\overline{6}$ .

$0.19667094$