Basic Math Examples

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

Step 1

Cancel the common factor of $4$ and $6$ .

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Step 1.1

Factor $2$ out of $4$ .

$\frac{2 (2)}{6} - \frac{2}{5}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $6$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 3

To write $- \frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

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

Step 4.2

Multiply $3$ by $5$ .

$\frac{2 \cdot 5}{15} - \frac{2}{5} \cdot \frac{3}{3}$

Step 4.3

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

$\frac{2 \cdot 5}{15} - \frac{2 \cdot 3}{5 \cdot 3}$

Step 4.4

Multiply $5$ by $3$ .

$\frac{2 \cdot 5}{15} - \frac{2 \cdot 3}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 \cdot 5 - 2 \cdot 3}{15}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $5$ .

$\frac{10 - 2 \cdot 3}{15}$

Step 6.2

Multiply $- 2$ by $3$ .

$\frac{10 - 6}{15}$

Step 6.3

Subtract $6$ from $10$ .

$\frac{4}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{15}$

Decimal Form:

$0.2\overline{6}$