Basic Math Examples

$\frac{1}{3} \cdot (\frac{2}{4} - (\frac{5}{6} + \frac{6}{3} - \frac{3}{4}) + \frac{2}{5} \div \frac{3}{10})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Cancel the common factor of $2$ and $4$ .

Tap for more steps...

Step 1.1.1

Factor $2$ out of $2$ .

$\frac{1}{3} \cdot (\frac{2 (1)}{4} - (\frac{5}{6} + \frac{6}{3} - \frac{3}{4}) + \frac{2}{5} \div \frac{3}{10})$

Step 1.1.2

Cancel the common factors.

Tap for more steps...

Step 1.1.2.1

Factor $2$ out of $4$ .

$\frac{1}{3} \cdot (\frac{2 \cdot 1}{2 \cdot 2} - (\frac{5}{6} + \frac{6}{3} - \frac{3}{4}) + \frac{2}{5} \div \frac{3}{10})$

Step 1.1.2.2

Cancel the common factor.

$\frac{1}{3} \cdot (\frac{2 \cdot 1}{2 \cdot 2} - (\frac{5}{6} + \frac{6}{3} - \frac{3}{4}) + \frac{2}{5} \div \frac{3}{10})$

Step 1.1.2.3

Rewrite the expression.

$\frac{1}{3} \cdot (\frac{1}{2} - (\frac{5}{6} + \frac{6}{3} - \frac{3}{4}) + \frac{2}{5} \div \frac{3}{10})$

Step 1.2

Find the common denominator.

Tap for more steps...

Step 1.2.1

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$\frac{1}{3} \cdot (\frac{1}{2} - (\frac{5}{6} \cdot \frac{2}{2} + \frac{6}{3} - \frac{3}{4}) + \frac{2}{5} \div \frac{3}{10})$

Step 1.2.2

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$\frac{1}{3} \cdot (\frac{1}{2} - (\frac{5 \cdot 2}{6 \cdot 2} + \frac{6}{3} - \frac{3}{4}) + \frac{2}{5} \div \frac{3}{10})$

Step 1.2.3

Multiply $\frac{6}{3}$ by $\frac{4}{4}$ .

$\frac{1}{3} \cdot (\frac{1}{2} - (\frac{5 \cdot 2}{6 \cdot 2} + \frac{6}{3} \cdot \frac{4}{4} - \frac{3}{4}) + \frac{2}{5} \div \frac{3}{10})$

Step 1.2.4

Multiply $\frac{6}{3}$ by $\frac{4}{4}$ .

$\frac{1}{3} \cdot (\frac{1}{2} - (\frac{5 \cdot 2}{6 \cdot 2} + \frac{6 \cdot 4}{3 \cdot 4} - \frac{3}{4}) + \frac{2}{5} \div \frac{3}{10})$

Step 1.2.5

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$\frac{1}{3} \cdot (\frac{1}{2} - (\frac{5 \cdot 2}{6 \cdot 2} + \frac{6 \cdot 4}{3 \cdot 4} - (\frac{3}{4} \cdot \frac{3}{3})) + \frac{2}{5} \div \frac{3}{10})$

Step 1.2.6

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$\frac{1}{3} \cdot (\frac{1}{2} - (\frac{5 \cdot 2}{6 \cdot 2} + \frac{6 \cdot 4}{3 \cdot 4} - \frac{3 \cdot 3}{4 \cdot 3}) + \frac{2}{5} \div \frac{3}{10})$

Step 1.2.7

Reorder the factors of $6 \cdot 2$ .

$\frac{1}{3} \cdot (\frac{1}{2} - (\frac{5 \cdot 2}{2 \cdot 6} + \frac{6 \cdot 4}{3 \cdot 4} - \frac{3 \cdot 3}{4 \cdot 3}) + \frac{2}{5} \div \frac{3}{10})$

Step 1.2.8

Multiply $2$ by $6$ .

$\frac{1}{3} \cdot (\frac{1}{2} - (\frac{5 \cdot 2}{12} + \frac{6 \cdot 4}{3 \cdot 4} - \frac{3 \cdot 3}{4 \cdot 3}) + \frac{2}{5} \div \frac{3}{10})$

Step 1.2.9

Multiply $3$ by $4$ .

$\frac{1}{3} \cdot (\frac{1}{2} - (\frac{5 \cdot 2}{12} + \frac{6 \cdot 4}{12} - \frac{3 \cdot 3}{4 \cdot 3}) + \frac{2}{5} \div \frac{3}{10})$

Step 1.2.10

Reorder the factors of $4 \cdot 3$ .

$\frac{1}{3} \cdot (\frac{1}{2} - (\frac{5 \cdot 2}{12} + \frac{6 \cdot 4}{12} - \frac{3 \cdot 3}{3 \cdot 4}) + \frac{2}{5} \div \frac{3}{10})$

Step 1.2.11

Multiply $3$ by $4$ .

$\frac{1}{3} \cdot (\frac{1}{2} - (\frac{5 \cdot 2}{12} + \frac{6 \cdot 4}{12} - \frac{3 \cdot 3}{12}) + \frac{2}{5} \div \frac{3}{10})$

Step 1.3

Combine the numerators over the common denominator.

$\frac{1}{3} \cdot (\frac{1}{2} - \frac{5 \cdot 2 + 6 \cdot 4 - 3 \cdot 3}{12} + \frac{2}{5} \div \frac{3}{10})$

Step 1.4

Simplify each term.

Tap for more steps...

Step 1.4.1

Multiply $5$ by $2$ .

$\frac{1}{3} \cdot (\frac{1}{2} - \frac{10 + 6 \cdot 4 - 3 \cdot 3}{12} + \frac{2}{5} \div \frac{3}{10})$

Step 1.4.2

Multiply $6$ by $4$ .

$\frac{1}{3} \cdot (\frac{1}{2} - \frac{10 + 24 - 3 \cdot 3}{12} + \frac{2}{5} \div \frac{3}{10})$

Step 1.4.3

Multiply $- 3$ by $3$ .

$\frac{1}{3} \cdot (\frac{1}{2} - \frac{10 + 24 - 9}{12} + \frac{2}{5} \div \frac{3}{10})$

Step 1.5

Add $10$ and $24$ .

$\frac{1}{3} \cdot (\frac{1}{2} - \frac{34 - 9}{12} + \frac{2}{5} \div \frac{3}{10})$

Step 1.6

Subtract $9$ from $34$ .

$\frac{1}{3} \cdot (\frac{1}{2} - \frac{25}{12} + \frac{2}{5} \div \frac{3}{10})$

Step 1.7

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{3} \cdot (\frac{1}{2} - \frac{25}{12} + \frac{2}{5} \cdot \frac{10}{3})$

Step 1.8

Cancel the common factor of $5$ .

Tap for more steps...

Step 1.8.1

Factor $5$ out of $10$ .

$\frac{1}{3} \cdot (\frac{1}{2} - \frac{25}{12} + \frac{2}{5} \cdot \frac{5 (2)}{3})$

Step 1.8.2

Cancel the common factor.

$\frac{1}{3} \cdot (\frac{1}{2} - \frac{25}{12} + \frac{2}{5} \cdot \frac{5 \cdot 2}{3})$

Step 1.8.3

Rewrite the expression.

$\frac{1}{3} \cdot (\frac{1}{2} - \frac{25}{12} + 2 (\frac{2}{3}))$

Step 1.9

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

$\frac{1}{3} \cdot (\frac{1}{2} - \frac{25}{12} + \frac{2 \cdot 2}{3})$

Step 1.10

Multiply $2$ by $2$ .

$\frac{1}{3} \cdot (\frac{1}{2} - \frac{25}{12} + \frac{4}{3})$

Step 2

Find the common denominator.

Tap for more steps...

Step 2.1

Multiply $\frac{1}{2}$ by $\frac{6}{6}$ .

$\frac{1}{3} \cdot (\frac{1}{2} \cdot \frac{6}{6} - \frac{25}{12} + \frac{4}{3})$

Step 2.2

Multiply $\frac{1}{2}$ by $\frac{6}{6}$ .

$\frac{1}{3} \cdot (\frac{6}{2 \cdot 6} - \frac{25}{12} + \frac{4}{3})$

Step 2.3

Multiply $\frac{4}{3}$ by $\frac{4}{4}$ .

$\frac{1}{3} \cdot (\frac{6}{2 \cdot 6} - \frac{25}{12} + \frac{4}{3} \cdot \frac{4}{4})$

Step 2.4

Multiply $\frac{4}{3}$ by $\frac{4}{4}$ .

$\frac{1}{3} \cdot (\frac{6}{2 \cdot 6} - \frac{25}{12} + \frac{4 \cdot 4}{3 \cdot 4})$

Step 2.5

Multiply $2$ by $6$ .

$\frac{1}{3} \cdot (\frac{6}{12} - \frac{25}{12} + \frac{4 \cdot 4}{3 \cdot 4})$

Step 2.6

Multiply $3$ by $4$ .

$\frac{1}{3} \cdot (\frac{6}{12} - \frac{25}{12} + \frac{4 \cdot 4}{12})$

Step 3

Combine the numerators over the common denominator.

$\frac{1}{3} \cdot \frac{6 - 25 + 4 \cdot 4}{12}$

Step 4

Simplify the expression.

Tap for more steps...

Step 4.1

Multiply $4$ by $4$ .

$\frac{1}{3} \cdot \frac{6 - 25 + 16}{12}$

Step 4.2

Subtract $25$ from $6$ .

$\frac{1}{3} \cdot \frac{- 19 + 16}{12}$

Step 4.3

Add $- 19$ and $16$ .

$\frac{1}{3} \cdot \frac{- 3}{12}$

Step 5

Cancel the common factor of $3$ .

Tap for more steps...

Step 5.1

Factor $3$ out of $- 3$ .

$\frac{1}{3} \cdot \frac{3 (- 1)}{12}$

Step 5.2

Cancel the common factor.

$\frac{1}{3} \cdot \frac{3 \cdot - 1}{12}$

Step 5.3

Rewrite the expression.

$\frac{- 1}{12}$

Step 6

Move the negative in front of the fraction.

$- \frac{1}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{12}$

Decimal Form:

$- 0.08\overline{3}$