Finite Math Examples

$x = 1 (\frac{1}{4}) + 2 (\frac{1}{4}) + 3 (\frac{1}{4}) + 4 (\frac{1}{4})$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{1}{4}$ by $1$ .

$x = \frac{1}{4} + 2 (\frac{1}{4}) + 3 (\frac{1}{4}) + 4 (\frac{1}{4})$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $4$ .

$x = \frac{1}{4} + 2 \frac{1}{2 (2)} + 3 (\frac{1}{4}) + 4 (\frac{1}{4})$

Step 1.2.2

Cancel the common factor.

$x = \frac{1}{4} + 2 \frac{1}{2 \cdot 2} + 3 (\frac{1}{4}) + 4 (\frac{1}{4})$

Step 1.2.3

Rewrite the expression.

$x = \frac{1}{4} + \frac{1}{2} + 3 (\frac{1}{4}) + 4 (\frac{1}{4})$

Step 1.3

Combine $3$ and $\frac{1}{4}$ .

$x = \frac{1}{4} + \frac{1}{2} + \frac{3}{4} + 4 (\frac{1}{4})$

Step 1.4

Cancel the common factor of $4$ .

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Step 1.4.1

Cancel the common factor.

$x = \frac{1}{4} + \frac{1}{2} + \frac{3}{4} + 4 (\frac{1}{4})$

Step 1.4.2

Rewrite the expression.

$x = \frac{1}{4} + \frac{1}{2} + \frac{3}{4} + 1$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$x = 1 + \frac{1 + 3}{4} + \frac{1}{2}$

Step 2.2

Add $1$ and $3$ .

$x = 1 + \frac{4}{4} + \frac{1}{2}$

Step 3

Find the common denominator.

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Step 3.1

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

$x = \frac{1}{1} + \frac{4}{4} + \frac{1}{2}$

Step 3.2

Multiply $\frac{1}{1}$ by $\frac{4}{4}$ .

$x = \frac{1}{1} \cdot \frac{4}{4} + \frac{4}{4} + \frac{1}{2}$

Step 3.3

Multiply $\frac{1}{1}$ by $\frac{4}{4}$ .

$x = \frac{4}{4} + \frac{4}{4} + \frac{1}{2}$

Step 3.4

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

$x = \frac{4}{4} + \frac{4}{4} + \frac{1}{2} \cdot \frac{2}{2}$

Step 3.5

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

$x = \frac{4}{4} + \frac{4}{4} + \frac{2}{2 \cdot 2}$

Step 3.6

Multiply $2$ by $2$ .

$x = \frac{4}{4} + \frac{4}{4} + \frac{2}{4}$

Step 4

Combine the numerators over the common denominator.

$x = \frac{4 + 4 + 2}{4}$

Step 5

Simplify by adding numbers.

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Step 5.1

Add $4$ and $4$ .

$x = \frac{8 + 2}{4}$

Step 5.2

Add $8$ and $2$ .

$x = \frac{10}{4}$

Step 6

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

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Step 6.1

Factor $2$ out of $10$ .

$x = \frac{2 (5)}{4}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 5}{2 \cdot 2}$

Step 6.2.2

Cancel the common factor.

$x = \frac{2 \cdot 5}{2 \cdot 2}$

Step 6.2.3

Rewrite the expression.

$x = \frac{5}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{2}$

Decimal Form:

$x = 2.5$

Mixed Number Form:

$x = 2 \frac{1}{2}$