Basic Math Examples

$\frac{4}{6} + (- \frac{3}{9}) - (- 5)$

Step 1

Remove parentheses.

$\frac{4}{6} - \frac{3}{9} - (- 5)$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{4}{6}$ by $\frac{3}{3}$ .

$\frac{4}{6} \cdot \frac{3}{3} - \frac{3}{9} - (- 5)$

Step 2.2

Multiply $\frac{4}{6}$ by $\frac{3}{3}$ .

$\frac{4 \cdot 3}{6 \cdot 3} - \frac{3}{9} - (- 5)$

Step 2.3

Multiply $\frac{3}{9}$ by $\frac{2}{2}$ .

$\frac{4 \cdot 3}{6 \cdot 3} - (\frac{3}{9} \cdot \frac{2}{2}) - (- 5)$

Step 2.4

Multiply $\frac{3}{9}$ by $\frac{2}{2}$ .

$\frac{4 \cdot 3}{6 \cdot 3} - \frac{3 \cdot 2}{9 \cdot 2} - (- 5)$

Step 2.5

Write $- (- 5)$ as a fraction with denominator $1$ .

$\frac{4 \cdot 3}{6 \cdot 3} - \frac{3 \cdot 2}{9 \cdot 2} + \frac{- (- 5)}{1}$

Step 2.6

Multiply $\frac{- (- 5)}{1}$ by $\frac{18}{18}$ .

$\frac{4 \cdot 3}{6 \cdot 3} - \frac{3 \cdot 2}{9 \cdot 2} + \frac{- (- 5)}{1} \cdot \frac{18}{18}$

Step 2.7

Multiply $\frac{- (- 5)}{1}$ by $\frac{18}{18}$ .

$\frac{4 \cdot 3}{6 \cdot 3} - \frac{3 \cdot 2}{9 \cdot 2} + \frac{- (- 5) \cdot 18}{18}$

Step 2.8

Reorder the factors of $6 \cdot 3$ .

$\frac{4 \cdot 3}{3 \cdot 6} - \frac{3 \cdot 2}{9 \cdot 2} + \frac{- (- 5) \cdot 18}{18}$

Step 2.9

Multiply $3$ by $6$ .

$\frac{4 \cdot 3}{18} - \frac{3 \cdot 2}{9 \cdot 2} + \frac{- (- 5) \cdot 18}{18}$

Step 2.10

Reorder the factors of $9 \cdot 2$ .

$\frac{4 \cdot 3}{18} - \frac{3 \cdot 2}{2 \cdot 9} + \frac{- (- 5) \cdot 18}{18}$

Step 2.11

Multiply $2$ by $9$ .

$\frac{4 \cdot 3}{18} - \frac{3 \cdot 2}{18} + \frac{- (- 5) \cdot 18}{18}$

Step 3

Combine the numerators over the common denominator.

$\frac{4 \cdot 3 - 3 \cdot 2 - (- 5) \cdot 18}{18}$

Step 4

Simplify each term.

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Step 4.1

Multiply $4$ by $3$ .

$\frac{12 - 3 \cdot 2 - (- 5) \cdot 18}{18}$

Step 4.2

Multiply $- 3$ by $2$ .

$\frac{12 - 6 - (- 5) \cdot 18}{18}$

Step 4.3

Multiply $- (- 5) \cdot 18$ .

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Step 4.3.1

Multiply $- 1$ by $- 5$ .

$\frac{12 - 6 + 5 \cdot 18}{18}$

Step 4.3.2

Multiply $5$ by $18$ .

$\frac{12 - 6 + 90}{18}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Subtract $6$ from $12$ .

$\frac{6 + 90}{18}$

Step 5.2

Add $6$ and $90$ .

$\frac{96}{18}$

Step 5.3

Cancel the common factor of $96$ and $18$ .

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Step 5.3.1

Factor $6$ out of $96$ .

$\frac{6 (16)}{18}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $6$ out of $18$ .

$\frac{6 \cdot 16}{6 \cdot 3}$

Step 5.3.2.2

Cancel the common factor.

$\frac{6 \cdot 16}{6 \cdot 3}$

Step 5.3.2.3

Rewrite the expression.

$\frac{16}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{3}$

Decimal Form:

$5.\overline{3}$

Mixed Number Form:

$5 \frac{1}{3}$