Finite Math Examples

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

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

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

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

Step 1.1.1.2

Multiply

\frac{3}{2} (9 p)

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

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Step 1.1.1.2.1

Combine

9

$9$ and

\frac{3}{2}

$\frac{3}{2}$ .

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

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

Step 1.1.1.2.2

Multiply

9

$9$ by

3

$3$ .

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

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

Step 1.1.1.2.3

Combine

\frac{27}{2}

$\frac{27}{2}$ and

p

$p$ .

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

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

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

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

Step 1.1.1.3

Multiply

\frac{3}{2}

$\frac{3}{2}$ by

1

$1$ .

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

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

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

$1$ 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

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

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

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

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

$8$ .

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