Basic Math Examples

\frac{5}{2} - \frac{1}{3}

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

Step 1

To write

\frac{5}{2}

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

\frac{3}{3}

$\frac{3}{3}$ .

\frac{5}{2} \cdot \frac{3}{3} - \frac{1}{3}

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

Step 2

To write

- \frac{1}{3}

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{5}{2} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{2}{2}

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

Step 3

Write each expression with a common denominator of

6

$6$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{5}{2}

$\frac{5}{2}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{5 \cdot 3}{2 \cdot 3} - \frac{1}{3} \cdot \frac{2}{2}

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

Step 3.2

Multiply

2

$2$ by

3

$3$ .

\frac{5 \cdot 3}{6} - \frac{1}{3} \cdot \frac{2}{2}

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

Step 3.3

Multiply

\frac{1}{3}

$\frac{1}{3}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 3.4

Multiply

3

$3$ by

2

$2$ .

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

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

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

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

Step 4

Combine the numerators over the common denominator.

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

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply

5

$5$ by

3

$3$ .

\frac{15 - 2}{6}

$\frac{15 - 2}{6}$

Step 5.2

Subtract

2

$2$ from

15

$15$ .

\frac{13}{6}

$\frac{13}{6}$

\frac{13}{6}

$\frac{13}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{13}{6}

$\frac{13}{6}$

Decimal Form:

2.1 ¯ 6

$2.1\overline{6}$

Mixed Number Form:

2 \frac{1}{6}

$2 \frac{1}{6}$