Finite Math Examples

$\frac{x}{10} \cdot \frac{25}{100} \cdot \frac{60}{100} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1

Simplify $\frac{x}{10} \cdot \frac{25}{100} \cdot \frac{60}{100} \cdot \frac{75}{100} \cdot 1002$ .

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Step 1.1

Cancel the common factor of $5$ .

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Step 1.1.1

Factor $5$ out of $10$ .

$\frac{x}{5 (2)} \cdot \frac{25}{100} \cdot \frac{60}{100} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.1.2

Factor $5$ out of $25$ .

$\frac{x}{5 \cdot 2} \cdot \frac{5 \cdot 5}{100} \cdot \frac{60}{100} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.1.3

Cancel the common factor.

$\frac{x}{5 \cdot 2} \cdot \frac{5 \cdot 5}{100} \cdot \frac{60}{100} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.1.4

Rewrite the expression.

$\frac{x}{2} \cdot \frac{5}{100} \cdot \frac{60}{100} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.2

Multiply $\frac{x}{2}$ by $\frac{5}{100}$ .

$\frac{x \cdot 5}{2 \cdot 100} \cdot \frac{60}{100} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.3

Multiply $2$ by $100$ .

$\frac{x \cdot 5}{200} \cdot \frac{60}{100} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.4

Cancel the common factor of $5$ .

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Step 1.4.1

Factor $5$ out of $x \cdot 5$ .

$\frac{5 \cdot x}{200} \cdot \frac{60}{100} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.4.2

Factor $5$ out of $100$ .

$\frac{5 \cdot x}{200} \cdot \frac{60}{5 (20)} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.4.3

Cancel the common factor.

$\frac{5 \cdot x}{200} \cdot \frac{60}{5 \cdot 20} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.4.4

Rewrite the expression.

$\frac{x}{200} \cdot \frac{60}{20} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.5

Cancel the common factor of $20$ .

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Step 1.5.1

Factor $20$ out of $200$ .

$\frac{x}{20 (10)} \cdot \frac{60}{20} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.5.2

Factor $20$ out of $60$ .

$\frac{x}{20 \cdot 10} \cdot \frac{20 \cdot 3}{20} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.5.3

Cancel the common factor.

$\frac{x}{20 \cdot 10} \cdot \frac{20 \cdot 3}{20} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.5.4

Rewrite the expression.

$\frac{x}{10} \cdot \frac{3}{20} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.6

Multiply $\frac{x}{10}$ by $\frac{3}{20}$ .

$\frac{x \cdot 3}{10 \cdot 20} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.7

Multiply $10$ by $20$ .

$\frac{x \cdot 3}{200} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.8

Cancel the common factor of $25$ .

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Step 1.8.1

Factor $25$ out of $200$ .

$\frac{x \cdot 3}{25 (8)} \cdot \frac{75}{100} \cdot 1002 = 302$

Step 1.8.2

Factor $25$ out of $75$ .

$\frac{x \cdot 3}{25 \cdot 8} \cdot \frac{25 \cdot 3}{100} \cdot 1002 = 302$

Step 1.8.3

Cancel the common factor.

$\frac{x \cdot 3}{25 \cdot 8} \cdot \frac{25 \cdot 3}{100} \cdot 1002 = 302$

Step 1.8.4

Rewrite the expression.

$\frac{x \cdot 3}{8} \cdot \frac{3}{100} \cdot 1002 = 302$

Step 1.9

Multiply $\frac{x \cdot 3}{8}$ by $\frac{3}{100}$ .

$\frac{x \cdot 3 \cdot 3}{8 \cdot 100} \cdot 1002 = 302$

Step 1.10

Multiply.

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Step 1.10.1

Multiply $3$ by $3$ .

$\frac{x \cdot 9}{8 \cdot 100} \cdot 1002 = 302$

Step 1.10.2

Multiply $8$ by $100$ .

$\frac{x \cdot 9}{800} \cdot 1002 = 302$

Step 1.11

Cancel the common factor of $2$ .

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Step 1.11.1

Factor $2$ out of $800$ .

$\frac{x \cdot 9}{2 (400)} \cdot 1002 = 302$

Step 1.11.2

Factor $2$ out of $1002$ .

$\frac{x \cdot 9}{2 \cdot 400} \cdot (2 \cdot 501) = 302$

Step 1.11.3

Cancel the common factor.

$\frac{x \cdot 9}{2 \cdot 400} \cdot (2 \cdot 501) = 302$

Step 1.11.4

Rewrite the expression.

$\frac{x \cdot 9}{400} \cdot 501 = 302$

Step 1.12

Combine $\frac{x \cdot 9}{400}$ and $501$ .

$\frac{x \cdot 9 \cdot 501}{400} = 302$

Step 1.13

Simplify the expression.

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Step 1.13.1

Multiply $501$ by $9$ .

$\frac{x \cdot 4509}{400} = 302$

Step 1.13.2

Move $4509$ to the left of $x$ .

$\frac{4509 x}{400} = 302$

Step 2

Multiply both sides of the equation by $\frac{400}{4509}$ .

$\frac{400}{4509} \cdot \frac{4509 x}{400} = \frac{400}{4509} \cdot 302$

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 $\frac{400}{4509} \cdot \frac{4509 x}{400}$ .

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Step 3.1.1.1

Cancel the common factor of $400$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{400}{4509} \cdot \frac{4509 x}{400} = \frac{400}{4509} \cdot 302$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{4509} (4509 x) = \frac{400}{4509} \cdot 302$

Step 3.1.1.2

Cancel the common factor of $4509$ .

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Step 3.1.1.2.1

Factor $4509$ out of $4509 x$ .

$\frac{1}{4509} (4509 (x)) = \frac{400}{4509} \cdot 302$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{4509} (4509 x) = \frac{400}{4509} \cdot 302$

Step 3.1.1.2.3

Rewrite the expression.

$x = \frac{400}{4509} \cdot 302$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $\frac{400}{4509} \cdot 302$ .

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Step 3.2.1.1

Combine $\frac{400}{4509}$ and $302$ .

$x = \frac{400 \cdot 302}{4509}$

Step 3.2.1.2

Multiply $400$ by $302$ .

$x = \frac{120800}{4509}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{120800}{4509}$

Decimal Form:

$x = 26.79086271 \dots$

Mixed Number Form:

$x = 26 \frac{3566}{4509}$