Basic Math Examples

$1 - \frac{\sqrt{3}}{3} \div 1 + (1) (\frac{\sqrt{3}}{3})$

Step 1

Find the common denominator.

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Step 1.1

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

$\frac{1}{1} - \frac{\sqrt{3}}{3} \div 1 + (1) (\frac{\sqrt{3}}{3})$

Step 1.2

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

$\frac{1}{1} \cdot \frac{\frac{1}{3}}{\frac{1}{3}} - \frac{\sqrt{3}}{3} \div 1 + (1) (\frac{\sqrt{3}}{3})$

Step 1.3

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

$\frac{\frac{1}{3}}{\frac{1}{3}} - \frac{\sqrt{3}}{3} \div 1 + (1) (\frac{\sqrt{3}}{3})$

Step 1.4

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

$\frac{\frac{1}{3}}{\frac{1}{3}} - (\frac{\sqrt{3}}{3} \div 1 \cdot \frac{\frac{1}{3}}{\frac{1}{3}}) + (1) (\frac{\sqrt{3}}{3})$

Step 1.5

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

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

Step 1.6

Write $(1) (\frac{\sqrt{3}}{3})$ as a fraction with denominator $1$ .

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

Step 1.7

Multiply $\frac{(1) (\frac{\sqrt{3}}{3})}{1}$ by $\frac{\frac{1}{3}}{\frac{1}{3}}$ .

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

Step 1.8

Multiply $\frac{(1) (\frac{\sqrt{3}}{3})}{1}$ by $\frac{\frac{1}{3}}{\frac{1}{3}}$ .

$\frac{\frac{1}{3}}{\frac{1}{3}} - \frac{\frac{\sqrt{3}}{3} \cdot \frac{1}{3}}{\frac{1}{3}} + \frac{\frac{\sqrt{3}}{3} \cdot \frac{1}{3}}{\frac{1}{3}}$

Step 2

Combine the numerators over the common denominator.

$\frac{\frac{1}{3} - \frac{\sqrt{3}}{3} \cdot \frac{1}{3} + \frac{\sqrt{3}}{3} \cdot \frac{1}{3}}{\frac{1}{3}}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- \frac{\sqrt{3}}{3} \cdot \frac{1}{3}$ .

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Step 3.1.1

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

$\frac{\frac{1}{3} - \frac{\sqrt{3}}{3 \cdot 3} + \frac{\sqrt{3}}{3} \cdot \frac{1}{3}}{\frac{1}{3}}$

Step 3.1.2

Multiply $3$ by $3$ .

$\frac{\frac{1}{3} - \frac{\sqrt{3}}{9} + \frac{\sqrt{3}}{3} \cdot \frac{1}{3}}{\frac{1}{3}}$

Step 3.2

Multiply $\frac{\sqrt{3}}{3} \cdot \frac{1}{3}$ .

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Step 3.2.1

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

$\frac{\frac{1}{3} - \frac{\sqrt{3}}{9} + \frac{\sqrt{3}}{3 \cdot 3}}{\frac{1}{3}}$

Step 3.2.2

Multiply $3$ by $3$ .

$\frac{\frac{1}{3} - \frac{\sqrt{3}}{9} + \frac{\sqrt{3}}{9}}{\frac{1}{3}}$

Step 4

Simplify terms.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{\frac{1}{3} + \frac{- \sqrt{3} + \sqrt{3}}{9}}{\frac{1}{3}}$

Step 4.2

Add $- \sqrt{3}$ and $\sqrt{3}$ .

$\frac{\frac{1}{3} + \frac{0}{9}}{\frac{1}{3}}$

Step 4.3

Simplify the expression.

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Step 4.3.1

Divide $0$ by $9$ .

$\frac{\frac{1}{3} + 0}{\frac{1}{3}}$

Step 4.3.2

Add $\frac{1}{3}$ and $0$ .

$\frac{\frac{1}{3}}{\frac{1}{3}}$

Step 4.4

Cancel the common factor of $\frac{1}{3}$ .

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Step 4.4.1

Cancel the common factor.

$\frac{\frac{1}{3}}{\frac{1}{3}}$

Step 4.4.2

Rewrite the expression.

$1$