Basic Math Examples

$\frac{1}{3} \cdot {(1)}^{3} + \frac{5}{2} \cdot {(1)}^{2} - 6 \cdot 1 + 8$

Step 1

Simplify each term.

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Step 1.1

One to any power is one.

$\frac{1}{3} \cdot 1 + \frac{5}{2} \cdot {(1)}^{2} - 6 \cdot 1 + 8$

Step 1.2

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

$\frac{1}{3} + \frac{5}{2} \cdot {(1)}^{2} - 6 \cdot 1 + 8$

Step 1.3

One to any power is one.

$\frac{1}{3} + \frac{5}{2} \cdot 1 - 6 \cdot 1 + 8$

Step 1.4

Multiply $\frac{5}{2}$ by $1$ .

$\frac{1}{3} + \frac{5}{2} - 6 \cdot 1 + 8$

Step 1.5

Multiply $- 6$ by $1$ .

$\frac{1}{3} + \frac{5}{2} - 6 + 8$

Step 2

Find the common denominator.

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Step 2.1

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

$\frac{1}{3} \cdot \frac{2}{2} + \frac{5}{2} - 6 + 8$

Step 2.2

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

$\frac{2}{3 \cdot 2} + \frac{5}{2} - 6 + 8$

Step 2.3

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

$\frac{2}{3 \cdot 2} + \frac{5}{2} \cdot \frac{3}{3} - 6 + 8$

Step 2.4

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

$\frac{2}{3 \cdot 2} + \frac{5 \cdot 3}{2 \cdot 3} - 6 + 8$

Step 2.5

Write $- 6$ as a fraction with denominator $1$ .

$\frac{2}{3 \cdot 2} + \frac{5 \cdot 3}{2 \cdot 3} + \frac{- 6}{1} + 8$

Step 2.6

Multiply $\frac{- 6}{1}$ by $\frac{6}{6}$ .

$\frac{2}{3 \cdot 2} + \frac{5 \cdot 3}{2 \cdot 3} + \frac{- 6}{1} \cdot \frac{6}{6} + 8$

Step 2.7

Multiply $\frac{- 6}{1}$ by $\frac{6}{6}$ .

$\frac{2}{3 \cdot 2} + \frac{5 \cdot 3}{2 \cdot 3} + \frac{- 6 \cdot 6}{6} + 8$

Step 2.8

Write $8$ as a fraction with denominator $1$ .

$\frac{2}{3 \cdot 2} + \frac{5 \cdot 3}{2 \cdot 3} + \frac{- 6 \cdot 6}{6} + \frac{8}{1}$

Step 2.9

Multiply $\frac{8}{1}$ by $\frac{6}{6}$ .

$\frac{2}{3 \cdot 2} + \frac{5 \cdot 3}{2 \cdot 3} + \frac{- 6 \cdot 6}{6} + \frac{8}{1} \cdot \frac{6}{6}$

Step 2.10

Multiply $\frac{8}{1}$ by $\frac{6}{6}$ .

$\frac{2}{3 \cdot 2} + \frac{5 \cdot 3}{2 \cdot 3} + \frac{- 6 \cdot 6}{6} + \frac{8 \cdot 6}{6}$

Step 2.11

Reorder the factors of $3 \cdot 2$ .

$\frac{2}{2 \cdot 3} + \frac{5 \cdot 3}{2 \cdot 3} + \frac{- 6 \cdot 6}{6} + \frac{8 \cdot 6}{6}$

Step 2.12

Multiply $2$ by $3$ .

$\frac{2}{6} + \frac{5 \cdot 3}{2 \cdot 3} + \frac{- 6 \cdot 6}{6} + \frac{8 \cdot 6}{6}$

Step 2.13

Multiply $2$ by $3$ .

$\frac{2}{6} + \frac{5 \cdot 3}{6} + \frac{- 6 \cdot 6}{6} + \frac{8 \cdot 6}{6}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 + 5 \cdot 3 - 6 \cdot 6 + 8 \cdot 6}{6}$

Step 4

Simplify each term.

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Step 4.1

Multiply $5$ by $3$ .

$\frac{2 + 15 - 6 \cdot 6 + 8 \cdot 6}{6}$

Step 4.2

Multiply $- 6$ by $6$ .

$\frac{2 + 15 - 36 + 8 \cdot 6}{6}$

Step 4.3

Multiply $8$ by $6$ .

$\frac{2 + 15 - 36 + 48}{6}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $2$ and $15$ .

$\frac{17 - 36 + 48}{6}$

Step 5.2

Subtract $36$ from $17$ .

$\frac{- 19 + 48}{6}$

Step 5.3

Add $- 19$ and $48$ .

$\frac{29}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{29}{6}$

Decimal Form:

$4.8\overline{3}$

Mixed Number Form:

$4 \frac{5}{6}$