Basic Math Examples

$5 \cdot (\frac{2}{3} + 3) \cdot \frac{6}{11} + \frac{1}{3} - 2$

Step 1

Simplify each term.

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Step 1.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$5 \cdot (\frac{2}{3} + 3 \cdot \frac{3}{3}) \cdot \frac{6}{11} + \frac{1}{3} - 2$

Step 1.2

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

$5 \cdot (\frac{2}{3} + \frac{3 \cdot 3}{3}) \cdot \frac{6}{11} + \frac{1}{3} - 2$

Step 1.3

Combine the numerators over the common denominator.

$5 \cdot \frac{2 + 3 \cdot 3}{3} \cdot \frac{6}{11} + \frac{1}{3} - 2$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $3$ by $3$ .

$5 \cdot \frac{2 + 9}{3} \cdot \frac{6}{11} + \frac{1}{3} - 2$

Step 1.4.2

Add $2$ and $9$ .

$5 \cdot \frac{11}{3} \cdot \frac{6}{11} + \frac{1}{3} - 2$

Step 1.5

Multiply $5 (\frac{11}{3})$ .

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Step 1.5.1

Combine $5$ and $\frac{11}{3}$ .

$\frac{5 \cdot 11}{3} \cdot \frac{6}{11} + \frac{1}{3} - 2$

Step 1.5.2

Multiply $5$ by $11$ .

$\frac{55}{3} \cdot \frac{6}{11} + \frac{1}{3} - 2$

Step 1.6

Cancel the common factor of $11$ .

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Step 1.6.1

Factor $11$ out of $55$ .

$\frac{11 (5)}{3} \cdot \frac{6}{11} + \frac{1}{3} - 2$

Step 1.6.2

Cancel the common factor.

$\frac{11 \cdot 5}{3} \cdot \frac{6}{11} + \frac{1}{3} - 2$

Step 1.6.3

Rewrite the expression.

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

Step 1.7

Cancel the common factor of $3$ .

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Step 1.7.1

Factor $3$ out of $6$ .

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

Step 1.7.2

Cancel the common factor.

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

Step 1.7.3

Rewrite the expression.

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

Step 1.8

Multiply $5$ by $2$ .

$10 + \frac{1}{3} - 2$

Step 2

Find the common denominator.

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Step 2.1

Write $10$ as a fraction with denominator $1$ .

$\frac{10}{1} + \frac{1}{3} - 2$

Step 2.2

Multiply $\frac{10}{1}$ by $\frac{3}{3}$ .

$\frac{10}{1} \cdot \frac{3}{3} + \frac{1}{3} - 2$

Step 2.3

Multiply $\frac{10}{1}$ by $\frac{3}{3}$ .

$\frac{10 \cdot 3}{3} + \frac{1}{3} - 2$

Step 2.4

Write $- 2$ as a fraction with denominator $1$ .

$\frac{10 \cdot 3}{3} + \frac{1}{3} + \frac{- 2}{1}$

Step 2.5

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

$\frac{10 \cdot 3}{3} + \frac{1}{3} + \frac{- 2}{1} \cdot \frac{3}{3}$

Step 2.6

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

$\frac{10 \cdot 3}{3} + \frac{1}{3} + \frac{- 2 \cdot 3}{3}$

Step 3

Combine the numerators over the common denominator.

$\frac{10 \cdot 3 + 1 - 2 \cdot 3}{3}$

Step 4

Simplify each term.

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Step 4.1

Multiply $10$ by $3$ .

$\frac{30 + 1 - 2 \cdot 3}{3}$

Step 4.2

Multiply $- 2$ by $3$ .

$\frac{30 + 1 - 6}{3}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $30$ and $1$ .

$\frac{31 - 6}{3}$

Step 5.2

Subtract $6$ from $31$ .

$\frac{25}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{3}$

Decimal Form:

$8.\overline{3}$

Mixed Number Form:

$8 \frac{1}{3}$