Basic Math Examples

$\frac{1}{2} + (\frac{3}{9} - \frac{3}{10})$

Step 1

Remove parentheses.

$\frac{1}{2} + \frac{3}{9} - \frac{3}{10}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{1}{2}$ by $\frac{45}{45}$ .

$\frac{1}{2} \cdot \frac{45}{45} + \frac{3}{9} - \frac{3}{10}$

Step 2.2

Multiply $\frac{1}{2}$ by $\frac{45}{45}$ .

$\frac{45}{2 \cdot 45} + \frac{3}{9} - \frac{3}{10}$

Step 2.3

Multiply $\frac{3}{9}$ by $\frac{10}{10}$ .

$\frac{45}{2 \cdot 45} + \frac{3}{9} \cdot \frac{10}{10} - \frac{3}{10}$

Step 2.4

Multiply $\frac{3}{9}$ by $\frac{10}{10}$ .

$\frac{45}{2 \cdot 45} + \frac{3 \cdot 10}{9 \cdot 10} - \frac{3}{10}$

Step 2.5

Multiply $\frac{3}{10}$ by $\frac{9}{9}$ .

$\frac{45}{2 \cdot 45} + \frac{3 \cdot 10}{9 \cdot 10} - (\frac{3}{10} \cdot \frac{9}{9})$

Step 2.6

Multiply $\frac{3}{10}$ by $\frac{9}{9}$ .

$\frac{45}{2 \cdot 45} + \frac{3 \cdot 10}{9 \cdot 10} - \frac{3 \cdot 9}{10 \cdot 9}$

Step 2.7

Multiply $2$ by $45$ .

$\frac{45}{90} + \frac{3 \cdot 10}{9 \cdot 10} - \frac{3 \cdot 9}{10 \cdot 9}$

Step 2.8

Multiply $9$ by $10$ .

$\frac{45}{90} + \frac{3 \cdot 10}{90} - \frac{3 \cdot 9}{10 \cdot 9}$

Step 2.9

Reorder the factors of $10 \cdot 9$ .

$\frac{45}{90} + \frac{3 \cdot 10}{90} - \frac{3 \cdot 9}{9 \cdot 10}$

Step 2.10

Multiply $9$ by $10$ .

$\frac{45}{90} + \frac{3 \cdot 10}{90} - \frac{3 \cdot 9}{90}$

Step 3

Combine the numerators over the common denominator.

$\frac{45 + 3 \cdot 10 - 3 \cdot 9}{90}$

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $10$ .

$\frac{45 + 30 - 3 \cdot 9}{90}$

Step 4.2

Multiply $- 3$ by $9$ .

$\frac{45 + 30 - 27}{90}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Add $45$ and $30$ .

$\frac{75 - 27}{90}$

Step 5.2

Subtract $27$ from $75$ .

$\frac{48}{90}$

Step 5.3

Cancel the common factor of $48$ and $90$ .

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Step 5.3.1

Factor $6$ out of $48$ .

$\frac{6 (8)}{90}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $6$ out of $90$ .

$\frac{6 \cdot 8}{6 \cdot 15}$

Step 5.3.2.2

Cancel the common factor.

$\frac{6 \cdot 8}{6 \cdot 15}$

Step 5.3.2.3

Rewrite the expression.

$\frac{8}{15}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{15}$

Decimal Form:

$0.5\overline{3}$