Basic Math Examples

$\frac{3}{0.4} + 2.2 \cdot 10 - 2.1$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{3}{0.4}$ by $\frac{\frac{2}{0.4}}{\frac{2}{0.4}}$ .

$\frac{3}{0.4} \cdot \frac{\frac{2}{0.4}}{\frac{2}{0.4}} + 2.2 \cdot 10 - 2.1$

Step 1.2

Multiply $\frac{3}{0.4}$ by $\frac{\frac{2}{0.4}}{\frac{2}{0.4}}$ .

$\frac{3 (\frac{2}{0.4})}{0.4 (\frac{2}{0.4})} + 2.2 \cdot 10 - 2.1$

Step 1.3

Write $2.2 \cdot 10$ as a fraction with denominator $1$ .

$\frac{3 (\frac{2}{0.4})}{0.4 (\frac{2}{0.4})} + \frac{2.2 \cdot 10}{1} - 2.1$

Step 1.4

Multiply $\frac{2.2 \cdot 10}{1}$ by $\frac{2}{2}$ .

$\frac{3 (\frac{2}{0.4})}{0.4 (\frac{2}{0.4})} + \frac{2.2 \cdot 10}{1} \cdot \frac{2}{2} - 2.1$

Step 1.5

Multiply $\frac{2.2 \cdot 10}{1}$ by $\frac{2}{2}$ .

$\frac{3 (\frac{2}{0.4})}{0.4 (\frac{2}{0.4})} + \frac{2.2 \cdot 10 \cdot 2}{2} - 2.1$

Step 1.6

Write $- 2.1$ as a fraction with denominator $1$ .

$\frac{3 (\frac{2}{0.4})}{0.4 (\frac{2}{0.4})} + \frac{2.2 \cdot 10 \cdot 2}{2} + \frac{- 2.1}{1}$

Step 1.7

Multiply $\frac{- 2.1}{1}$ by $\frac{2}{2}$ .

$\frac{3 (\frac{2}{0.4})}{0.4 (\frac{2}{0.4})} + \frac{2.2 \cdot 10 \cdot 2}{2} + \frac{- 2.1}{1} \cdot \frac{2}{2}$

Step 1.8

Multiply $\frac{- 2.1}{1}$ by $\frac{2}{2}$ .

$\frac{3 (\frac{2}{0.4})}{0.4 (\frac{2}{0.4})} + \frac{2.2 \cdot 10 \cdot 2}{2} + \frac{- 2.1 \cdot 2}{2}$

Step 1.9

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

$\frac{3 (\frac{2}{0.4})}{\frac{0.4 \cdot 2}{0.4}} + \frac{2.2 \cdot 10 \cdot 2}{2} + \frac{- 2.1 \cdot 2}{2}$

Step 1.10

Multiply $0.4$ by $2$ .

$\frac{3 (\frac{2}{0.4})}{\frac{0.8}{0.4}} + \frac{2.2 \cdot 10 \cdot 2}{2} + \frac{- 2.1 \cdot 2}{2}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 (\frac{2}{0.4})}{\frac{0.8}{0.4}} + \frac{2.2 \cdot 10 \cdot 2 - 2.1 \cdot 2}{2}$

Step 3

Simplify each term.

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Step 3.1

Multiply $2.2 \cdot 10 \cdot 2$ .

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Step 3.1.1

Multiply $2.2$ by $10$ .

$\frac{3 (\frac{2}{0.4})}{\frac{0.8}{0.4}} + \frac{22 \cdot 2 - 2.1 \cdot 2}{2}$

Step 3.1.2

Multiply $22$ by $2$ .

$\frac{3 (\frac{2}{0.4})}{\frac{0.8}{0.4}} + \frac{44 - 2.1 \cdot 2}{2}$

Step 3.2

Multiply $- 2.1$ by $2$ .

$\frac{3 (\frac{2}{0.4})}{\frac{0.8}{0.4}} + \frac{44 - 4.2}{2}$

Step 4

Subtract $4.2$ from $44$ .

$\frac{3 (\frac{2}{0.4})}{\frac{0.8}{0.4}} + \frac{39.8}{2}$

Step 5

Simplify each term.

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Step 5.1

Multiply the numerator by the reciprocal of the denominator.

$3 (\frac{2}{0.4}) \frac{0.4}{0.8} + \frac{39.8}{2}$

Step 5.2

Divide $2$ by $0.4$ .

$3 \cdot 5 \frac{0.4}{0.8} + \frac{39.8}{2}$

Step 5.3

Multiply $3$ by $5$ .

$15 (\frac{0.4}{0.8}) + \frac{39.8}{2}$

Step 5.4

Divide $0.4$ by $0.8$ .

$15 \cdot 0.5 + \frac{39.8}{2}$

Step 5.5

Multiply $15$ by $0.5$ .

$7.5 + \frac{39.8}{2}$

Step 5.6

Divide $39.8$ by $2$ .

$7.5 + 19.9$

Step 6

Add $7.5$ and $19.9$ .

$27.4$