Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

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

Step 1.2

Multiply $\frac{1}{6} \cdot \frac{5}{2}$ .

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Step 1.2.1

Multiply $\frac{1}{6}$ by $\frac{5}{2}$ .

$\frac{2}{3} - \frac{5}{6 \cdot 2}$

Step 1.2.2

Multiply $6$ by $2$ .

$\frac{2}{3} - \frac{5}{12}$

Step 2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{2}{3} \cdot \frac{4}{4} - \frac{5}{12}$

Step 3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$\frac{2 \cdot 4}{3 \cdot 4} - \frac{5}{12}$

Step 3.2

Multiply $3$ by $4$ .

$\frac{2 \cdot 4}{12} - \frac{5}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 - 5}{12}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $4$ .

$\frac{8 - 5}{12}$

Step 5.2

Subtract $5$ from $8$ .

$\frac{3}{12}$

Step 6

Cancel the common factor of $3$ and $12$ .

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Step 6.1

Factor $3$ out of $3$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $12$ .

$\frac{3 \cdot 1}{3 \cdot 4}$

Step 6.2.2

Cancel the common factor.

$\frac{3 \cdot 1}{3 \cdot 4}$

Step 6.2.3

Rewrite the expression.

$\frac{1}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$