Algebra Examples

$\frac{1}{3} \div \frac{1}{2} + \frac{1}{2} \cdot \frac{3}{5}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

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

Step 1.2

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

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

Step 1.3

Multiply $\frac{1}{2} \cdot \frac{3}{5}$ .

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Step 1.3.1

Multiply $\frac{1}{2}$ by $\frac{3}{5}$ .

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

Step 1.3.2

Multiply $2$ by $5$ .

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

Step 2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $3$ by $10$ .

$\frac{2 \cdot 10}{30} + \frac{3}{10} \cdot \frac{3}{3}$

Step 4.3

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

$\frac{2 \cdot 10}{30} + \frac{3 \cdot 3}{10 \cdot 3}$

Step 4.4

Multiply $10$ by $3$ .

$\frac{2 \cdot 10}{30} + \frac{3 \cdot 3}{30}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 \cdot 10 + 3 \cdot 3}{30}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $10$ .

$\frac{20 + 3 \cdot 3}{30}$

Step 6.2

Multiply $3$ by $3$ .

$\frac{20 + 9}{30}$

Step 6.3

Add $20$ and $9$ .

$\frac{29}{30}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{29}{30}$

Decimal Form:

$0.9\overline{6}$