Basic Math Examples

$4 \div 0.4 + 0.7 \cdot 7 - {0.2}^{2}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $4 \div 0.4$ by $\frac{\frac{2}{0.4}}{\frac{2}{0.4}}$ .

$4 \div 0.4 \cdot \frac{\frac{2}{0.4}}{\frac{2}{0.4}} + 0.7 \cdot 7 - {0.2}^{2}$

Step 1.2

Multiply $4 \div 0.4$ by $\frac{\frac{2}{0.4}}{\frac{2}{0.4}}$ .

$\frac{4 (\frac{2}{0.4})}{0.4 (\frac{2}{0.4})} + 0.7 \cdot 7 - {0.2}^{2}$

Step 1.3

Write $0.7 \cdot 7$ as a fraction with denominator $1$ .

$\frac{4 (\frac{2}{0.4})}{0.4 (\frac{2}{0.4})} + \frac{0.7 \cdot 7}{1} - {0.2}^{2}$

Step 1.4

Multiply $\frac{0.7 \cdot 7}{1}$ by $\frac{2}{2}$ .

$\frac{4 (\frac{2}{0.4})}{0.4 (\frac{2}{0.4})} + \frac{0.7 \cdot 7}{1} \cdot \frac{2}{2} - {0.2}^{2}$

Step 1.5

Multiply $\frac{0.7 \cdot 7}{1}$ by $\frac{2}{2}$ .

$\frac{4 (\frac{2}{0.4})}{0.4 (\frac{2}{0.4})} + \frac{0.7 \cdot 7 \cdot 2}{2} - {0.2}^{2}$

Step 1.6

Write $- {0.2}^{2}$ as a fraction with denominator $1$ .

$\frac{4 (\frac{2}{0.4})}{0.4 (\frac{2}{0.4})} + \frac{0.7 \cdot 7 \cdot 2}{2} + \frac{- {0.2}^{2}}{1}$

Step 1.7

Multiply $\frac{- {0.2}^{2}}{1}$ by $\frac{2}{2}$ .

$\frac{4 (\frac{2}{0.4})}{0.4 (\frac{2}{0.4})} + \frac{0.7 \cdot 7 \cdot 2}{2} + \frac{- {0.2}^{2}}{1} \cdot \frac{2}{2}$

Step 1.8

Multiply $\frac{- {0.2}^{2}}{1}$ by $\frac{2}{2}$ .

$\frac{4 (\frac{2}{0.4})}{0.4 (\frac{2}{0.4})} + \frac{0.7 \cdot 7 \cdot 2}{2} + \frac{- {0.2}^{2} \cdot 2}{2}$

Step 1.9

Combine $0.4$ and $\frac{2}{0.4}$ .

$\frac{4 (\frac{2}{0.4})}{\frac{0.4 \cdot 2}{0.4}} + \frac{0.7 \cdot 7 \cdot 2}{2} + \frac{- {0.2}^{2} \cdot 2}{2}$

Step 1.10

Multiply $0.4$ by $2$ .

$\frac{4 (\frac{2}{0.4})}{\frac{0.8}{0.4}} + \frac{0.7 \cdot 7 \cdot 2}{2} + \frac{- {0.2}^{2} \cdot 2}{2}$

Step 2

Combine the numerators over the common denominator.

$\frac{4 (\frac{2}{0.4})}{\frac{0.8}{0.4}} + \frac{0.7 \cdot 7 \cdot 2 - {0.2}^{2} \cdot 2}{2}$

Step 3

Simplify each term.

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Step 3.1

Multiply $0.7 \cdot 7 \cdot 2$ .

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Step 3.1.1

Multiply $0.7$ by $7$ .

$\frac{4 (\frac{2}{0.4})}{\frac{0.8}{0.4}} + \frac{4.9 \cdot 2 - {0.2}^{2} \cdot 2}{2}$

Step 3.1.2

Multiply $4.9$ by $2$ .

$\frac{4 (\frac{2}{0.4})}{\frac{0.8}{0.4}} + \frac{9.8 - {0.2}^{2} \cdot 2}{2}$

Step 3.2

Raise $0.2$ to the power of $2$ .

$\frac{4 (\frac{2}{0.4})}{\frac{0.8}{0.4}} + \frac{9.8 - 1 \cdot 0.04 \cdot 2}{2}$

Step 3.3

Multiply $- 1 \cdot 0.04 \cdot 2$ .

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Step 3.3.1

Multiply $- 1$ by $0.04$ .

$\frac{4 (\frac{2}{0.4})}{\frac{0.8}{0.4}} + \frac{9.8 - 0.04 \cdot 2}{2}$

Step 3.3.2

Multiply $- 0.04$ by $2$ .

$\frac{4 (\frac{2}{0.4})}{\frac{0.8}{0.4}} + \frac{9.8 - 0.08}{2}$

Step 4

Subtract $0.08$ from $9.8$ .

$\frac{4 (\frac{2}{0.4})}{\frac{0.8}{0.4}} + \frac{9.72}{2}$

Step 5

Simplify each term.

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Step 5.1

Multiply the numerator by the reciprocal of the denominator.

$4 (\frac{2}{0.4}) \frac{0.4}{0.8} + \frac{9.72}{2}$

Step 5.2

Cancel the common factor of $0.8$ .

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Step 5.2.1

Factor $0.8$ out of $4 (\frac{2}{0.4})$ .

$0.8 (5 (\frac{2}{0.4})) \frac{0.4}{0.8} + \frac{9.72}{2}$

Step 5.2.2

Cancel the common factor.

$0.8 (5 (\frac{2}{0.4})) \frac{0.4}{0.8} + \frac{9.72}{2}$

Step 5.2.3

Rewrite the expression.

$5 (\frac{2}{0.4}) \cdot 0.4 + \frac{9.72}{2}$

Step 5.3

Combine $5$ and $\frac{2}{0.4}$ .

$\frac{5 \cdot 2}{0.4} \cdot 0.4 + \frac{9.72}{2}$

Step 5.4

Multiply $5$ by $2$ .

$\frac{10}{0.4} \cdot 0.4 + \frac{9.72}{2}$

Step 5.5

Combine $\frac{10}{0.4}$ and $0.4$ .

$\frac{10 \cdot 0.4}{0.4} + \frac{9.72}{2}$

Step 5.6

Multiply $10$ by $0.4$ .

$\frac{4}{0.4} + \frac{9.72}{2}$

Step 5.7

Divide $4$ by $0.4$ .

$10 + \frac{9.72}{2}$

Step 5.8

Divide $9.72$ by $2$ .

$10 + 4.86$

Step 6

Add $10$ and $4.86$ .

$14.86$