Basic Math Examples

$\frac{1}{3} \cdot \frac{4}{4} - \frac{6}{2} + \frac{2}{3} \cdot \frac{6}{3}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $4$ .

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Step 1.1.1

Cancel the common factor.

$\frac{1}{3} \cdot \frac{4}{4} - \frac{6}{2} + \frac{2}{3} \cdot \frac{6}{3}$

Step 1.1.2

Rewrite the expression.

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

Step 1.2

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

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

Step 1.3

Divide $6$ by $2$ .

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

Step 1.4

Multiply $- 1$ by $3$ .

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

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $6$ .

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

Step 1.5.2

Cancel the common factor.

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

Step 1.5.3

Rewrite the expression.

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

Step 1.6

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

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

Step 1.7

Multiply $2$ by $2$ .

$\frac{1}{3} - 3 + \frac{4}{3}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$- 3 + \frac{1 + 4}{3}$

Step 2.2

Add $1$ and $4$ .

$- 3 + \frac{5}{3}$

Step 3

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

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

Step 4

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

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 3$ by $3$ .

$\frac{- 9 + 5}{3}$

Step 6.2

Add $- 9$ and $5$ .

$\frac{- 4}{3}$

Step 7

Move the negative in front of the fraction.

$- \frac{4}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{4}{3}$

Decimal Form:

$- 1.\overline{3}$

Mixed Number Form:

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