Basic Math Examples

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

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

Step 1

Find the common denominator.

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Step 1.1

Multiply

4 \div 0.4

$4 \div 0.4$ by

\frac{\frac{2}{0.4}}{\frac{2}{0.4}}

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

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

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

Step 1.2

Multiply

4 \div 0.4

$4 \div 0.4$ by

\frac{\frac{2}{0.4}}{\frac{2}{0.4}}

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

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

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

Step 1.3

Write

0.7 \cdot 7

$0.7 \cdot 7$ as a fraction with denominator

1

$1$ .

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

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

Step 1.4

Multiply

\frac{0.7 \cdot 7}{1}

$\frac{0.7 \cdot 7}{1}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\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}

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

Step 1.5

Multiply

\frac{0.7 \cdot 7}{1}

$\frac{0.7 \cdot 7}{1}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.6

Write

- {0.2}^{2}

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

1

$1$ .

\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}

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

Step 1.7

Multiply

\frac{- {0.2}^{2}}{1}

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

\frac{2}{2}

$\frac{2}{2}$ .

\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}

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

Step 1.8

Multiply

\frac{- {0.2}^{2}}{1}

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

\frac{2}{2}

$\frac{2}{2}$ .

\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}

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

Step 1.9

Combine

0.4

$0.4$ and

\frac{2}{0.4}

$\frac{2}{0.4}$ .

\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}

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

Step 1.10

Multiply

0.4

$0.4$ by

2

$2$ .

\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}

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

\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}

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

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}

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

Step 3

Simplify each term.

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Step 3.1

Multiply

0.7 \cdot 7 \cdot 2

$0.7 \cdot 7 \cdot 2$ .

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Step 3.1.1

Multiply

0.7

$0.7$ by

7

$7$ .

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

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

Step 3.1.2

Multiply

4.9

$4.9$ by

2

$2$ .

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

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

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

$0.2$ to the power of

2

$2$ .

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

$- 1 \cdot 0.04 \cdot 2$ .

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Step 3.3.1

Multiply

- 1

$- 1$ by

0.04

$0.04$ .

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

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

Step 3.3.2

Multiply

- 0.04

$- 0.04$ by

2

$2$ .

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

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

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

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

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

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

Step 4

Subtract

0.08

$0.08$ from

9.8

$9.8$ .

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

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

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}

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

Step 5.2

Cancel the common factor of

0.8

$0.8$ .

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Step 5.2.1

Factor

0.8

$0.8$ out of

4 (\frac{2}{0.4})

$4 (\frac{2}{0.4})$ .

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

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

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

$4.86$ .

$14.86$