Finite Math Examples

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{3}{2} \cdot (9 p + 1) + 1) + 1) + 1$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{3}{2} (9 p) + \frac{3}{2} \cdot 1 + 1) + 1) + 1$

Step 1.1.1.2

Multiply $\frac{3}{2} (9 p)$ .

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Step 1.1.1.2.1

Combine $9$ and $\frac{3}{2}$ .

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{9 \cdot 3}{2} p + \frac{3}{2} \cdot 1 + 1) + 1) + 1$

Step 1.1.1.2.2

Multiply $9$ by $3$ .

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27}{2} p + \frac{3}{2} \cdot 1 + 1) + 1) + 1$

Step 1.1.1.2.3

Combine $\frac{27}{2}$ and $p$ .

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3}{2} \cdot 1 + 1) + 1) + 1$

Step 1.1.1.3

Multiply $\frac{3}{2}$ by $1$ .

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3}{2} + 1) + 1) + 1$

Step 1.1.2

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

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3}{2} + \frac{2}{2}) + 1) + 1$

Step 1.1.3

Combine the numerators over the common denominator.

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{3 + 2}{2}) + 1) + 1$

Step 1.1.4

Add $3$ and $2$ .

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot (\frac{27 p}{2} + \frac{5}{2}) + 1) + 1$

Step 1.1.5

Apply the distributive property.

$t = \frac{3}{2} \cdot (\frac{3}{2} \cdot \frac{27 p}{2} + \frac{3}{2} \cdot \frac{5}{2} + 1) + 1$

Step 1.1.6

Multiply $\frac{3}{2} \cdot \frac{27 p}{2}$ .

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Step 1.1.6.1

Multiply $\frac{3}{2}$ by $\frac{27 p}{2}$ .

$t = \frac{3}{2} \cdot (\frac{3 (27 p)}{2 \cdot 2} + \frac{3}{2} \cdot \frac{5}{2} + 1) + 1$

Step 1.1.6.2

Multiply $27$ by $3$ .

$t = \frac{3}{2} \cdot (\frac{81 p}{2 \cdot 2} + \frac{3}{2} \cdot \frac{5}{2} + 1) + 1$

Step 1.1.6.3

Multiply $2$ by $2$ .

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{3}{2} \cdot \frac{5}{2} + 1) + 1$

Step 1.1.7

Multiply $\frac{3}{2} \cdot \frac{5}{2}$ .

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Step 1.1.7.1

Multiply $\frac{3}{2}$ by $\frac{5}{2}$ .

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{3 \cdot 5}{2 \cdot 2} + 1) + 1$

Step 1.1.7.2

Multiply $3$ by $5$ .

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15}{2 \cdot 2} + 1) + 1$

Step 1.1.7.3

Multiply $2$ by $2$ .

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15}{4} + 1) + 1$

Step 1.2

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

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15}{4} + \frac{4}{4}) + 1$

Step 1.3

Combine the numerators over the common denominator.

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{15 + 4}{4}) + 1$

Step 1.4

Add $15$ and $4$ .

$t = \frac{3}{2} \cdot (\frac{81 p}{4} + \frac{19}{4}) + 1$

Step 1.5

Apply the distributive property.

$t = \frac{3}{2} \cdot \frac{81 p}{4} + \frac{3}{2} \cdot \frac{19}{4} + 1$

Step 1.6

Multiply $\frac{3}{2} \cdot \frac{81 p}{4}$ .

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Step 1.6.1

Multiply $\frac{3}{2}$ by $\frac{81 p}{4}$ .

$t = \frac{3 (81 p)}{2 \cdot 4} + \frac{3}{2} \cdot \frac{19}{4} + 1$

Step 1.6.2

Multiply $81$ by $3$ .

$t = \frac{243 p}{2 \cdot 4} + \frac{3}{2} \cdot \frac{19}{4} + 1$

Step 1.6.3

Multiply $2$ by $4$ .

$t = \frac{243 p}{8} + \frac{3}{2} \cdot \frac{19}{4} + 1$

Step 1.7

Multiply $\frac{3}{2} \cdot \frac{19}{4}$ .

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Step 1.7.1

Multiply $\frac{3}{2}$ by $\frac{19}{4}$ .

$t = \frac{243 p}{8} + \frac{3 \cdot 19}{2 \cdot 4} + 1$

Step 1.7.2

Multiply $3$ by $19$ .

$t = \frac{243 p}{8} + \frac{57}{2 \cdot 4} + 1$

Step 1.7.3

Multiply $2$ by $4$ .

$t = \frac{243 p}{8} + \frac{57}{8} + 1$

Step 2

Simplify the expression.

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Step 2.1

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

$t = \frac{243 p}{8} + \frac{57}{8} + \frac{8}{8}$

Step 2.2

Combine the numerators over the common denominator.

$t = \frac{243 p}{8} + \frac{57 + 8}{8}$

Step 2.3

Add $57$ and $8$ .

$t = \frac{243 p}{8} + \frac{65}{8}$