Finite Math Examples

$2 (\frac{3}{10}) - 1 (\frac{4}{10}) - 2 (\frac{2}{10}) + 2 (\frac{1}{10})$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $2$ .

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Step 1.1.1

Factor $2$ out of $10$ .

$2 \frac{3}{2 (5)} - 1 (\frac{4}{10}) - 2 (\frac{2}{10}) + 2 (\frac{1}{10})$

Step 1.1.2

Cancel the common factor.

$2 \frac{3}{2 \cdot 5} - 1 (\frac{4}{10}) - 2 (\frac{2}{10}) + 2 (\frac{1}{10})$

Step 1.1.3

Rewrite the expression.

$\frac{3}{5} - 1 (\frac{4}{10}) - 2 (\frac{2}{10}) + 2 (\frac{1}{10})$

Step 1.2

Cancel the common factor of $4$ and $10$ .

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Step 1.2.1

Factor $2$ out of $4$ .

$\frac{3}{5} - 1 \frac{2 (2)}{10} - 2 (\frac{2}{10}) + 2 (\frac{1}{10})$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $2$ out of $10$ .

$\frac{3}{5} - 1 \frac{2 \cdot 2}{2 \cdot 5} - 2 (\frac{2}{10}) + 2 (\frac{1}{10})$

Step 1.2.2.2

Cancel the common factor.

$\frac{3}{5} - 1 \frac{2 \cdot 2}{2 \cdot 5} - 2 (\frac{2}{10}) + 2 (\frac{1}{10})$

Step 1.2.2.3

Rewrite the expression.

$\frac{3}{5} - 1 (\frac{2}{5}) - 2 (\frac{2}{10}) + 2 (\frac{1}{10})$

Step 1.3

Rewrite $- 1 (\frac{2}{5})$ as $- (\frac{2}{5})$ .

$\frac{3}{5} - (\frac{2}{5}) - 2 (\frac{2}{10}) + 2 (\frac{1}{10})$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $- 2$ .

$\frac{3}{5} - \frac{2}{5} + 2 (- 1) \frac{2}{10} + 2 (\frac{1}{10})$

Step 1.4.2

Factor $2$ out of $10$ .

$\frac{3}{5} - \frac{2}{5} + 2 \cdot - 1 \frac{2}{2 \cdot 5} + 2 (\frac{1}{10})$

Step 1.4.3

Cancel the common factor.

$\frac{3}{5} - \frac{2}{5} + 2 \cdot - 1 \frac{2}{2 \cdot 5} + 2 (\frac{1}{10})$

Step 1.4.4

Rewrite the expression.

$\frac{3}{5} - \frac{2}{5} - 1 (\frac{2}{5}) + 2 (\frac{1}{10})$

Step 1.5

Rewrite $- 1 (\frac{2}{5})$ as $- (\frac{2}{5})$ .

$\frac{3}{5} - \frac{2}{5} - (\frac{2}{5}) + 2 (\frac{1}{10})$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Factor $2$ out of $10$ .

$\frac{3}{5} - \frac{2}{5} - \frac{2}{5} + 2 \frac{1}{2 (5)}$

Step 1.6.2

Cancel the common factor.

$\frac{3}{5} - \frac{2}{5} - \frac{2}{5} + 2 \frac{1}{2 \cdot 5}$

Step 1.6.3

Rewrite the expression.

$\frac{3}{5} - \frac{2}{5} - \frac{2}{5} + \frac{1}{5}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{3 - 2 - 2 + 1}{5}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $2$ from $3$ .

$\frac{1 - 2 + 1}{5}$

Step 2.2.2

Subtract $2$ from $1$ .

$\frac{- 1 + 1}{5}$

Step 2.2.3

Add $- 1$ and $1$ .

$\frac{0}{5}$

Step 2.2.4

Divide $0$ by $5$ .

$0$