Finite Math Examples

$x = \frac{1}{16} + 1 (\frac{1}{4}) + 2 (\frac{3}{8}) + 3 (\frac{1}{4}) + 4 (\frac{1}{16})$

Step 1

Simplify each term.

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Step 1.1

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

$x = \frac{1}{16} + \frac{1}{4} + 2 (\frac{3}{8}) + 3 (\frac{1}{4}) + 4 (\frac{1}{16})$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $8$ .

$x = \frac{1}{16} + \frac{1}{4} + 2 \frac{3}{2 (4)} + 3 (\frac{1}{4}) + 4 (\frac{1}{16})$

Step 1.2.2

Cancel the common factor.

$x = \frac{1}{16} + \frac{1}{4} + 2 \frac{3}{2 \cdot 4} + 3 (\frac{1}{4}) + 4 (\frac{1}{16})$

Step 1.2.3

Rewrite the expression.

$x = \frac{1}{16} + \frac{1}{4} + \frac{3}{4} + 3 (\frac{1}{4}) + 4 (\frac{1}{16})$

Step 1.3

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

$x = \frac{1}{16} + \frac{1}{4} + \frac{3}{4} + \frac{3}{4} + 4 (\frac{1}{16})$

Step 1.4

Cancel the common factor of $4$ .

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Step 1.4.1

Factor $4$ out of $16$ .

$x = \frac{1}{16} + \frac{1}{4} + \frac{3}{4} + \frac{3}{4} + 4 \frac{1}{4 (4)}$

Step 1.4.2

Cancel the common factor.

$x = \frac{1}{16} + \frac{1}{4} + \frac{3}{4} + \frac{3}{4} + 4 \frac{1}{4 \cdot 4}$

Step 1.4.3

Rewrite the expression.

$x = \frac{1}{16} + \frac{1}{4} + \frac{3}{4} + \frac{3}{4} + \frac{1}{4}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$x = \frac{1}{16} + \frac{1 + 3 + 3 + 1}{4}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Add $1$ and $3$ .

$x = \frac{1}{16} + \frac{4 + 3 + 1}{4}$

Step 2.2.2

Add $4$ and $3$ .

$x = \frac{1}{16} + \frac{7 + 1}{4}$

Step 2.2.3

Add $7$ and $1$ .

$x = \frac{1}{16} + \frac{8}{4}$

Step 2.2.4

Divide $8$ by $4$ .

$x = \frac{1}{16} + 2$

Step 3

To write $2$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$x = \frac{1}{16} + 2 \cdot \frac{16}{16}$

Step 4

Combine $2$ and $\frac{16}{16}$ .

$x = \frac{1}{16} + \frac{2 \cdot 16}{16}$

Step 5

Combine the numerators over the common denominator.

$x = \frac{1 + 2 \cdot 16}{16}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $16$ .

$x = \frac{1 + 32}{16}$

Step 6.2

Add $1$ and $32$ .

$x = \frac{33}{16}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{33}{16}$

Decimal Form:

$x = 2.0625$

Mixed Number Form:

$x = 2 \frac{1}{16}$