Basic Math Examples

\frac{3}{5} - \frac{1}{3}

$\frac{3}{5} - \frac{1}{3}$

Step 1

To write

\frac{3}{5}

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

\frac{3}{3}

$\frac{3}{3}$ .

\frac{3}{5} \cdot \frac{3}{3} - \frac{1}{3}

$\frac{3}{5} \cdot \frac{3}{3} - \frac{1}{3}$

Step 2

To write

- \frac{1}{3}

$- \frac{1}{3}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{3}{5} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{5}{5}

$\frac{3}{5} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of

15

$15$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{3}{5}

$\frac{3}{5}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{3 \cdot 3}{5 \cdot 3} - \frac{1}{3} \cdot \frac{5}{5}

$\frac{3 \cdot 3}{5 \cdot 3} - \frac{1}{3} \cdot \frac{5}{5}$

Step 3.2

Multiply

5

$5$ by

3

$3$ .

\frac{3 \cdot 3}{15} - \frac{1}{3} \cdot \frac{5}{5}

$\frac{3 \cdot 3}{15} - \frac{1}{3} \cdot \frac{5}{5}$

Step 3.3

Multiply

\frac{1}{3}

$\frac{1}{3}$ by

\frac{5}{5}

$\frac{5}{5}$ .

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

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

Step 3.4

Multiply

3

$3$ by

5

$5$ .

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

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

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

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

Step 4

Combine the numerators over the common denominator.

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

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply

3

$3$ by

3

$3$ .

\frac{9 - 5}{15}

$\frac{9 - 5}{15}$

Step 5.2

Subtract

5

$5$ from

9

$9$ .

\frac{4}{15}

$\frac{4}{15}$

\frac{4}{15}

$\frac{4}{15}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{4}{15}

$\frac{4}{15}$

Decimal Form:

0.2 ¯ 6

$0.2\overline{6}$