Basic Math Examples

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

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

Step 1

Cancel the common factor of

4

$4$ and

6

$6$ .

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Step 1.1

Factor

2

$2$ out of

4

$4$ .

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

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor

2

$2$ out of

6

$6$ .

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

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

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:

$0.2\overline{6}$