Basic Math Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $2$ by $5$ .

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

Step 4.3

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

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

Step 4.4

Multiply $5$ by $2$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 2$ by $2$ .

$\frac{5 - 4}{10} \cdot \frac{3}{2}$

Step 6.2

Subtract $4$ from $5$ .

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

Step 7

Multiply $\frac{1}{10} \cdot \frac{3}{2}$ .

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Step 7.1

Multiply $\frac{1}{10}$ by $\frac{3}{2}$ .

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

Step 7.2

Multiply $10$ by $2$ .

$\frac{3}{20}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{20}$

Decimal Form:

$0.15$