Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Multiply $2$ by $2$ .

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

Step 4.2

Add $4$ and $1$ .

$\frac{5}{2} \cdot (1 - \frac{1}{5}) \cdot (\frac{2}{3} - 1)$

Step 5

Simplify the expression.

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Step 5.1

Write $1$ as a fraction with a common denominator.

$\frac{5}{2} \cdot (\frac{5}{5} - \frac{1}{5}) \cdot (\frac{2}{3} - 1)$

Step 5.2

Combine the numerators over the common denominator.

$\frac{5}{2} \cdot \frac{5 - 1}{5} \cdot (\frac{2}{3} - 1)$

Step 5.3

Subtract $1$ from $5$ .

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

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Factor $2$ out of $4$ .

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

Step 7.2

Cancel the common factor.

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

Step 7.3

Rewrite the expression.

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

Step 8

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

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

Step 9

Combine $- 1$ and $\frac{3}{3}$ .

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

Step 10

Combine the numerators over the common denominator.

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

Step 11

Simplify the numerator.

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Step 11.1

Multiply $- 1$ by $3$ .

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

Step 11.2

Subtract $3$ from $2$ .

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

Step 12

Move the negative in front of the fraction.

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

Step 13

Multiply $2 (- \frac{1}{3})$ .

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Step 13.1

Multiply $- 1$ by $2$ .

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

Step 13.2

Combine $- 2$ and $\frac{1}{3}$ .

$\frac{- 2}{3}$

Step 14

Move the negative in front of the fraction.

$- \frac{2}{3}$

Step 15

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{3}$

Decimal Form:

$- 0.\overline{6}$