Basic Math Examples

$\frac{1}{3} \div \frac{1}{2} - \frac{1}{5} \cdot \frac{1}{4} + \frac{1}{6}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{3} \cdot 2 - \frac{1}{5} \cdot \frac{1}{4} + \frac{1}{6}$

Step 1.2

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

$\frac{2}{3} - \frac{1}{5} \cdot \frac{1}{4} + \frac{1}{6}$

Step 1.3

Multiply $- \frac{1}{5} \cdot \frac{1}{4}$ .

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Step 1.3.1

Multiply $\frac{1}{4}$ by $\frac{1}{5}$ .

$\frac{2}{3} - \frac{1}{4 \cdot 5} + \frac{1}{6}$

Step 1.3.2

Multiply $4$ by $5$ .

$\frac{2}{3} - \frac{1}{20} + \frac{1}{6}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{2}{3}$ by $\frac{20}{20}$ .

$\frac{2}{3} \cdot \frac{20}{20} - \frac{1}{20} + \frac{1}{6}$

Step 2.2

Multiply $\frac{2}{3}$ by $\frac{20}{20}$ .

$\frac{2 \cdot 20}{3 \cdot 20} - \frac{1}{20} + \frac{1}{6}$

Step 2.3

Multiply $\frac{1}{20}$ by $\frac{3}{3}$ .

$\frac{2 \cdot 20}{3 \cdot 20} - (\frac{1}{20} \cdot \frac{3}{3}) + \frac{1}{6}$

Step 2.4

Multiply $\frac{1}{20}$ by $\frac{3}{3}$ .

$\frac{2 \cdot 20}{3 \cdot 20} - \frac{3}{20 \cdot 3} + \frac{1}{6}$

Step 2.5

Multiply $\frac{1}{6}$ by $\frac{10}{10}$ .

$\frac{2 \cdot 20}{3 \cdot 20} - \frac{3}{20 \cdot 3} + \frac{1}{6} \cdot \frac{10}{10}$

Step 2.6

Multiply $\frac{1}{6}$ by $\frac{10}{10}$ .

$\frac{2 \cdot 20}{3 \cdot 20} - \frac{3}{20 \cdot 3} + \frac{10}{6 \cdot 10}$

Step 2.7

Multiply $3$ by $20$ .

$\frac{2 \cdot 20}{60} - \frac{3}{20 \cdot 3} + \frac{10}{6 \cdot 10}$

Step 2.8

Reorder the factors of $20 \cdot 3$ .

$\frac{2 \cdot 20}{60} - \frac{3}{3 \cdot 20} + \frac{10}{6 \cdot 10}$

Step 2.9

Multiply $3$ by $20$ .

$\frac{2 \cdot 20}{60} - \frac{3}{60} + \frac{10}{6 \cdot 10}$

Step 2.10

Multiply $6$ by $10$ .

$\frac{2 \cdot 20}{60} - \frac{3}{60} + \frac{10}{60}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 \cdot 20 - 3 + 10}{60}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $2$ by $20$ .

$\frac{40 - 3 + 10}{60}$

Step 4.2

Subtract $3$ from $40$ .

$\frac{37 + 10}{60}$

Step 4.3

Add $37$ and $10$ .

$\frac{47}{60}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{47}{60}$

Decimal Form:

$0.78\overline{3}$