Finite Math Examples

$4 = \frac{k (9) (4)}{{(2)}^{3}}$

Step 1

Rewrite the equation as $\frac{k (9) \cdot 4}{2^{3}} = 4$ .

$\frac{k (9) \cdot 4}{2^{3}} = 4$

Step 2

Multiply both sides of the equation by $\frac{1}{9 \frac{4}{2^{3}}}$ .

$\frac{1}{9 \frac{4}{2^{3}}} \cdot \frac{k \cdot 9 \cdot 4}{2^{3}} = \frac{1}{9 \frac{4}{2^{3}}} \cdot 4$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{1}{9 \frac{4}{2^{3}}} \cdot \frac{k \cdot 9 \cdot 4}{2^{3}}$ .

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Step 3.1.1.1

Simplify terms.

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Step 3.1.1.1.1

Combine.

$\frac{1 (k \cdot 9 \cdot 4)}{9 \frac{4}{2^{3}} \cdot 2^{3}} = \frac{1}{9 \frac{4}{2^{3}}} \cdot 4$

Step 3.1.1.1.2

Cancel the common factor of $9$ .

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Step 3.1.1.1.2.1

Cancel the common factor.

$\frac{1 (k \cdot 9 \cdot 4)}{9 \frac{4}{2^{3}} \cdot 2^{3}} = \frac{1}{9 \frac{4}{2^{3}}} \cdot 4$

Step 3.1.1.1.2.2

Rewrite the expression.

$\frac{1 (k \cdot 4)}{\frac{4}{2^{3}} \cdot 2^{3}} = \frac{1}{9 \frac{4}{2^{3}}} \cdot 4$

Step 3.1.1.1.3

Simplify the expression.

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Step 3.1.1.1.3.1

Raise $2$ to the power of $3$ .

$\frac{1 k \cdot 4}{\frac{4}{8} \cdot 2^{3}} = \frac{1}{9 \frac{4}{2^{3}}} \cdot 4$

Step 3.1.1.1.3.2

Multiply $k$ by $1$ .

$\frac{k \cdot 4}{\frac{4}{8} \cdot 2^{3}} = \frac{1}{9 \frac{4}{2^{3}}} \cdot 4$

Step 3.1.1.1.4

Combine $\frac{4}{8}$ and $2^{3}$ .

$\frac{k \cdot 4}{\frac{4 \cdot 2^{3}}{8}} = \frac{1}{9 \frac{4}{2^{3}}} \cdot 4$

Step 3.1.1.2

Simplify the numerator.

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Step 3.1.1.2.1

Rewrite $4$ as $2^{2}$ .

$\frac{k \cdot 4}{\frac{2^{2} \cdot 2^{3}}{8}} = \frac{1}{9 \frac{4}{2^{3}}} \cdot 4$

Step 3.1.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{k \cdot 4}{\frac{2^{2 + 3}}{8}} = \frac{1}{9 \frac{4}{2^{3}}} \cdot 4$

Step 3.1.1.2.3

Add $2$ and $3$ .

$\frac{k \cdot 4}{\frac{2^{5}}{8}} = \frac{1}{9 \frac{4}{2^{3}}} \cdot 4$

Step 3.1.1.3

Reduce the expression by cancelling the common factors.

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Step 3.1.1.3.1

Raise $2$ to the power of $5$ .

$\frac{k \cdot 4}{\frac{32}{8}} = \frac{1}{9 \frac{4}{2^{3}}} \cdot 4$

Step 3.1.1.3.2

Divide $32$ by $8$ .

$\frac{k \cdot 4}{4} = \frac{1}{9 \frac{4}{2^{3}}} \cdot 4$

Step 3.1.1.3.3

Cancel the common factor of $4$ .

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Step 3.1.1.3.3.1

Cancel the common factor.

$\frac{k \cdot 4}{4} = \frac{1}{9 \frac{4}{2^{3}}} \cdot 4$

Step 3.1.1.3.3.2

Divide $k$ by $1$ .

$k = \frac{1}{9 \frac{4}{2^{3}}} \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{1}{9 \frac{4}{2^{3}}} \cdot 4$ .

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Step 3.2.1.1

Raise $2$ to the power of $3$ .

$k = \frac{1}{9 (\frac{4}{8})} \cdot 4$

Step 3.2.1.2

Combine $9$ and $\frac{4}{8}$ .

$k = \frac{1}{\frac{9 \cdot 4}{8}} \cdot 4$

Step 3.2.1.3

Multiply $9$ by $4$ .

$k = \frac{1}{\frac{36}{8}} \cdot 4$

Step 3.2.1.4

Cancel the common factor of $36$ and $8$ .

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Step 3.2.1.4.1

Factor $4$ out of $36$ .

$k = \frac{1}{\frac{4 (9)}{8}} \cdot 4$

Step 3.2.1.4.2

Cancel the common factors.

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Step 3.2.1.4.2.1

Factor $4$ out of $8$ .

$k = \frac{1}{\frac{4 \cdot 9}{4 \cdot 2}} \cdot 4$

Step 3.2.1.4.2.2

Cancel the common factor.

$k = \frac{1}{\frac{4 \cdot 9}{4 \cdot 2}} \cdot 4$

Step 3.2.1.4.2.3

Rewrite the expression.

$k = \frac{1}{\frac{9}{2}} \cdot 4$

Step 3.2.1.5

Multiply the numerator by the reciprocal of the denominator.

$k = 1 (\frac{2}{9}) \cdot 4$

Step 3.2.1.6

Multiply $\frac{2}{9}$ by $1$ .

$k = \frac{2}{9} \cdot 4$

Step 3.2.1.7

Multiply $\frac{2}{9} \cdot 4$ .

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Step 3.2.1.7.1

Combine $\frac{2}{9}$ and $4$ .

$k = \frac{2 \cdot 4}{9}$

Step 3.2.1.7.2

Multiply $2$ by $4$ .

$k = \frac{8}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$k = \frac{8}{9}$

Decimal Form:

$k = 0.\overline{8}$