Basic Math Examples

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

Step 1

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

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

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

Step 2.2

Multiply $2$ by $2$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Add $1$ and $2$ .

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

Step 5

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{3}{4} (\frac{1}{9} - 1 \cdot \frac{9}{9})$

Step 6

Combine $- 1$ and $\frac{9}{9}$ .

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

Step 7

Combine the numerators over the common denominator.

$\frac{3}{4} \cdot \frac{1 - 1 \cdot 9}{9}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $- 1$ by $9$ .

$\frac{3}{4} \cdot \frac{1 - 9}{9}$

Step 8.2

Subtract $9$ from $1$ .

$\frac{3}{4} \cdot \frac{- 8}{9}$

Step 9

Cancel the common factor of $3$ .

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Step 9.1

Factor $3$ out of $9$ .

$\frac{3}{4} \cdot \frac{- 8}{3 (3)}$

Step 9.2

Cancel the common factor.

$\frac{3}{4} \cdot \frac{- 8}{3 \cdot 3}$

Step 9.3

Rewrite the expression.

$\frac{1}{4} \cdot \frac{- 8}{3}$

Step 10

Cancel the common factor of $4$ .

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Step 10.1

Factor $4$ out of $- 8$ .

$\frac{1}{4} \cdot \frac{4 (- 2)}{3}$

Step 10.2

Cancel the common factor.

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

Step 10.3

Rewrite the expression.

$\frac{- 2}{3}$

Step 11

Move the negative in front of the fraction.

$- \frac{2}{3}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{3}$

Decimal Form:

$- 0.\overline{6}$