Finite Math Examples

$0 \cdot \frac{27}{125} + 1 \cdot \frac{54}{125} + 2 \cdot \frac{36}{125} + 3 \cdot \frac{8}{125}$

Step 1

Simplify each term.

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Step 1.1

Multiply $0$ by $\frac{27}{125}$ .

$0 + 1 \cdot \frac{54}{125} + 2 \cdot \frac{36}{125} + 3 \cdot \frac{8}{125}$

Step 1.2

Multiply $\frac{54}{125}$ by $1$ .

$0 + \frac{54}{125} + 2 \cdot \frac{36}{125} + 3 \cdot \frac{8}{125}$

Step 1.3

Multiply $2 (\frac{36}{125})$ .

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Step 1.3.1

Combine $2$ and $\frac{36}{125}$ .

$0 + \frac{54}{125} + \frac{2 \cdot 36}{125} + 3 \cdot \frac{8}{125}$

Step 1.3.2

Multiply $2$ by $36$ .

$0 + \frac{54}{125} + \frac{72}{125} + 3 \cdot \frac{8}{125}$

Step 1.4

Multiply $3 (\frac{8}{125})$ .

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Step 1.4.1

Combine $3$ and $\frac{8}{125}$ .

$0 + \frac{54}{125} + \frac{72}{125} + \frac{3 \cdot 8}{125}$

Step 1.4.2

Multiply $3$ by $8$ .

$0 + \frac{54}{125} + \frac{72}{125} + \frac{24}{125}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{54 + 72 + 24}{125}$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $54$ and $72$ .

$\frac{126 + 24}{125}$

Step 2.2.2

Add $126$ and $24$ .

$\frac{150}{125}$

Step 2.3

Cancel the common factor of $150$ and $125$ .

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Step 2.3.1

Factor $25$ out of $150$ .

$\frac{25 (6)}{125}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $25$ out of $125$ .

$\frac{25 \cdot 6}{25 \cdot 5}$

Step 2.3.2.2

Cancel the common factor.

$\frac{25 \cdot 6}{25 \cdot 5}$

Step 2.3.2.3

Rewrite the expression.

$\frac{6}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{6}{5}$

Decimal Form:

$1.2$

Mixed Number Form:

$1 \frac{1}{5}$