Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

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

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.3

Simplify the denominator.

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Step 1.3.1

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.3.2

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

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

Step 1.3.3

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

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Step 1.3.3.1

Multiply $\frac{4}{5}$ by $\frac{2}{2}$ .

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

Step 1.3.3.2

Multiply $5$ by $2$ .

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

Step 1.3.3.3

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

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

Step 1.3.3.4

Multiply $2$ by $5$ .

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

Step 1.3.4

Combine the numerators over the common denominator.

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

Step 1.3.5

Simplify the numerator.

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Step 1.3.5.1

Multiply $4$ by $2$ .

$\frac{2}{3} - (\frac{1}{6} \cdot \frac{1}{\frac{8 - 5}{10}})$

Step 1.3.5.2

Subtract $5$ from $8$ .

$\frac{2}{3} - (\frac{1}{6} \cdot \frac{1}{\frac{3}{10}})$

Step 1.4

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{3} - (\frac{1}{6} (1 (\frac{10}{3})))$

Step 1.5

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

$\frac{2}{3} - (\frac{1}{6} \cdot \frac{10}{3})$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Factor $2$ out of $6$ .

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

Step 1.6.2

Factor $2$ out of $10$ .

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

Step 1.6.3

Cancel the common factor.

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

Step 1.6.4

Rewrite the expression.

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

Step 1.7

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

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

Step 1.8

Multiply $3$ by $3$ .

$\frac{2}{3} - \frac{5}{9}$

Step 2

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

$\frac{2}{3} \cdot \frac{3}{3} - \frac{5}{9}$

Step 3

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$\frac{2 \cdot 3}{3 \cdot 3} - \frac{5}{9}$

Step 3.2

Multiply $3$ by $3$ .

$\frac{2 \cdot 3}{9} - \frac{5}{9}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 - 5}{9}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $3$ .

$\frac{6 - 5}{9}$

Step 5.2

Subtract $5$ from $6$ .

$\frac{1}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{9}$

Decimal Form:

$0.\overline{1}$