Basic Math Examples

$(\frac{2}{9} + \frac{4}{9}) (\frac{1}{3} - \frac{9}{10})$

Step 1

Combine the numerators over the common denominator.

$\frac{2 + 4}{9} (\frac{1}{3} - \frac{9}{10})$

Step 2

Add $2$ and $4$ .

$\frac{6}{9} (\frac{1}{3} - \frac{9}{10})$

Step 3

Cancel the common factor of $6$ and $9$ .

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Step 3.1

Factor $3$ out of $6$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $9$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

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

Step 5

To write $- \frac{9}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 6

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

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

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

Step 6.2

Multiply $3$ by $10$ .

$\frac{2}{3} (\frac{10}{30} - \frac{9}{10} \cdot \frac{3}{3})$

Step 6.3

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

$\frac{2}{3} (\frac{10}{30} - \frac{9 \cdot 3}{10 \cdot 3})$

Step 6.4

Multiply $10$ by $3$ .

$\frac{2}{3} (\frac{10}{30} - \frac{9 \cdot 3}{30})$

Step 7

Combine the numerators over the common denominator.

$\frac{2}{3} \cdot \frac{10 - 9 \cdot 3}{30}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $- 9$ by $3$ .

$\frac{2}{3} \cdot \frac{10 - 27}{30}$

Step 8.2

Subtract $27$ from $10$ .

$\frac{2}{3} \cdot \frac{- 17}{30}$

Step 9

Cancel the common factor of $2$ .

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Step 9.1

Factor $2$ out of $30$ .

$\frac{2}{3} \cdot \frac{- 17}{2 (15)}$

Step 9.2

Cancel the common factor.

$\frac{2}{3} \cdot \frac{- 17}{2 \cdot 15}$

Step 9.3

Rewrite the expression.

$\frac{1}{3} \cdot \frac{- 17}{15}$

Step 10

Multiply $\frac{1}{3}$ by $\frac{- 17}{15}$ .

$\frac{- 17}{3 \cdot 15}$

Step 11

Simplify the expression.

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Step 11.1

Multiply $3$ by $15$ .

$\frac{- 17}{45}$

Step 11.2

Move the negative in front of the fraction.

$- \frac{17}{45}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- \frac{17}{45}$

Decimal Form:

$- 0.3\overline{7}$