Basic Math Examples

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

Step 1

To write $- \frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{5}$ by $\frac{2}{2}$ .

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

Step 3.2

Multiply $5$ by $2$ .

$(- \frac{3 \cdot 2}{10} + \frac{1}{2} \cdot \frac{5}{5}) \cdot \frac{- 2}{3}$

Step 3.3

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$(- \frac{3 \cdot 2}{10} + \frac{5}{2 \cdot 5}) \cdot \frac{- 2}{3}$

Step 3.4

Multiply $2$ by $5$ .

$(- \frac{3 \cdot 2}{10} + \frac{5}{10}) \cdot \frac{- 2}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 3 \cdot 2 + 5}{10} \cdot \frac{- 2}{3}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 3$ by $2$ .

$\frac{- 6 + 5}{10} \cdot \frac{- 2}{3}$

Step 5.2

Add $- 6$ and $5$ .

$\frac{- 1}{10} \cdot \frac{- 2}{3}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $10$ .

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

Step 6.2

Factor $2$ out of $- 2$ .

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

Step 6.3

Cancel the common factor.

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

Step 6.4

Rewrite the expression.

$\frac{- 1}{5} \cdot \frac{- 1}{3}$

Step 7

Multiply $\frac{- 1}{5}$ by $\frac{- 1}{3}$ .

$\frac{- - 1}{5 \cdot 3}$

Step 8

Multiply.

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Step 8.1

Multiply $- 1$ by $- 1$ .

$\frac{1}{5 \cdot 3}$

Step 8.2

Multiply $5$ by $3$ .

$\frac{1}{15}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{15}$

Decimal Form:

$0.0\overline{6}$