Basic Math Examples

$2 \div 0.2 + 0.9 \cdot 3 - {0.4}^{2}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $2 \div 0.2$ by $\frac{\frac{1}{0.2}}{\frac{1}{0.2}}$ .

$2 \div 0.2 \cdot \frac{\frac{1}{0.2}}{\frac{1}{0.2}} + 0.9 \cdot 3 - {0.4}^{2}$

Step 1.2

Multiply $2 \div 0.2$ by $\frac{\frac{1}{0.2}}{\frac{1}{0.2}}$ .

$\frac{2 (\frac{1}{0.2})}{0.2 (\frac{1}{0.2})} + 0.9 \cdot 3 - {0.4}^{2}$

Step 1.3

Write $0.9 \cdot 3$ as a fraction with denominator $1$ .

$\frac{2 (\frac{1}{0.2})}{0.2 (\frac{1}{0.2})} + \frac{0.9 \cdot 3}{1} - {0.4}^{2}$

Step 1.4

Multiply $\frac{0.9 \cdot 3}{1}$ by $\frac{1}{1}$ .

$\frac{2 (\frac{1}{0.2})}{0.2 (\frac{1}{0.2})} + \frac{0.9 \cdot 3}{1} \cdot \frac{1}{1} - {0.4}^{2}$

Step 1.5

Multiply $\frac{0.9 \cdot 3}{1}$ by $\frac{1}{1}$ .

$\frac{2 (\frac{1}{0.2})}{0.2 (\frac{1}{0.2})} + \frac{0.9 \cdot 3}{1} - {0.4}^{2}$

Step 1.6

Write $- {0.4}^{2}$ as a fraction with denominator $1$ .

$\frac{2 (\frac{1}{0.2})}{0.2 (\frac{1}{0.2})} + \frac{0.9 \cdot 3}{1} + \frac{- {0.4}^{2}}{1}$

Step 1.7

Multiply $\frac{- {0.4}^{2}}{1}$ by $\frac{1}{1}$ .

$\frac{2 (\frac{1}{0.2})}{0.2 (\frac{1}{0.2})} + \frac{0.9 \cdot 3}{1} + \frac{- {0.4}^{2}}{1} \cdot \frac{1}{1}$

Step 1.8

Multiply $\frac{- {0.4}^{2}}{1}$ by $\frac{1}{1}$ .

$\frac{2 (\frac{1}{0.2})}{0.2 (\frac{1}{0.2})} + \frac{0.9 \cdot 3}{1} + \frac{- {0.4}^{2}}{1}$

Step 1.9

Combine $0.2$ and $\frac{1}{0.2}$ .

$\frac{2 (\frac{1}{0.2})}{\frac{0.2}{0.2}} + \frac{0.9 \cdot 3}{1} + \frac{- {0.4}^{2}}{1}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 (\frac{1}{0.2})}{\frac{0.2}{0.2}} + \frac{0.9 \cdot 3 - {0.4}^{2}}{1}$

Step 3

Simplify each term.

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Step 3.1

Multiply $0.9$ by $3$ .

$\frac{2 (\frac{1}{0.2})}{\frac{0.2}{0.2}} + \frac{2.7 - {0.4}^{2}}{1}$

Step 3.2

Raise $0.4$ to the power of $2$ .

$\frac{2 (\frac{1}{0.2})}{\frac{0.2}{0.2}} + \frac{2.7 - 1 \cdot 0.16}{1}$

Step 3.3

Multiply $- 1$ by $0.16$ .

$\frac{2 (\frac{1}{0.2})}{\frac{0.2}{0.2}} + \frac{2.7 - 0.16}{1}$

Step 4

Subtract $0.16$ from $2.7$ .

$\frac{2 (\frac{1}{0.2})}{\frac{0.2}{0.2}} + \frac{2.54}{1}$

Step 5

Simplify each term.

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Step 5.1

Cancel the common factor of $0.2$ .

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Step 5.1.1

Cancel the common factor.

$\frac{2 (\frac{1}{0.2})}{\frac{0.2}{0.2}} + \frac{2.54}{1}$

Step 5.1.2

Rewrite the expression.

$\frac{2 (\frac{1}{0.2})}{1} + \frac{2.54}{1}$

Step 5.2

Divide $2 (\frac{1}{0.2})$ by $1$ .

$2 (\frac{1}{0.2}) + \frac{2.54}{1}$

Step 5.3

Cancel the common factor of $0.2$ .

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Step 5.3.1

Factor $0.2$ out of $2$ .

$0.2 (10) \frac{1}{0.2} + \frac{2.54}{1}$

Step 5.3.2

Cancel the common factor.

$0.2 \cdot 10 \frac{1}{0.2} + \frac{2.54}{1}$

Step 5.3.3

Rewrite the expression.

$10 + \frac{2.54}{1}$

Step 5.4

Divide $2.54$ by $1$ .

$10 + 2.54$

Step 6

Add $10$ and $2.54$ .

$12.54$