Basic Math Examples

\frac{2}{5} + \frac{5}{2}

$\frac{2}{5} + \frac{5}{2}$

Step 1

To write

\frac{2}{5}

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{2}{5} \cdot \frac{2}{2} + \frac{5}{2}

$\frac{2}{5} \cdot \frac{2}{2} + \frac{5}{2}$

Step 2

To write

\frac{5}{2}

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

\frac{5}{5}

$\frac{5}{5}$ .

\frac{2}{5} \cdot \frac{2}{2} + \frac{5}{2} \cdot \frac{5}{5}

$\frac{2}{5} \cdot \frac{2}{2} + \frac{5}{2} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of

10

$10$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{2}{5}

$\frac{2}{5}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{2 \cdot 2}{5 \cdot 2} + \frac{5}{2} \cdot \frac{5}{5}

$\frac{2 \cdot 2}{5 \cdot 2} + \frac{5}{2} \cdot \frac{5}{5}$

Step 3.2

Multiply

5

$5$ by

2

$2$ .

\frac{2 \cdot 2}{10} + \frac{5}{2} \cdot \frac{5}{5}

$\frac{2 \cdot 2}{10} + \frac{5}{2} \cdot \frac{5}{5}$

Step 3.3

Multiply

\frac{5}{2}

$\frac{5}{2}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{2 \cdot 2}{10} + \frac{5 \cdot 5}{2 \cdot 5}

$\frac{2 \cdot 2}{10} + \frac{5 \cdot 5}{2 \cdot 5}$

Step 3.4

Multiply

2

$2$ by

5

$5$ .

\frac{2 \cdot 2}{10} + \frac{5 \cdot 5}{10}

$\frac{2 \cdot 2}{10} + \frac{5 \cdot 5}{10}$

\frac{2 \cdot 2}{10} + \frac{5 \cdot 5}{10}

$\frac{2 \cdot 2}{10} + \frac{5 \cdot 5}{10}$

Step 4

Combine the numerators over the common denominator.

\frac{2 \cdot 2 + 5 \cdot 5}{10}

$\frac{2 \cdot 2 + 5 \cdot 5}{10}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

2

$2$ by

2

$2$ .

\frac{4 + 5 \cdot 5}{10}

$\frac{4 + 5 \cdot 5}{10}$

Step 5.2

Multiply

5

$5$ by

5

$5$ .

\frac{4 + 25}{10}

$\frac{4 + 25}{10}$

Step 5.3

Add

4

$4$ and

25

$25$ .

\frac{29}{10}

$\frac{29}{10}$

\frac{29}{10}

$\frac{29}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{29}{10}

$\frac{29}{10}$

Decimal Form:

2.9

$2.9$

Mixed Number Form:

2 \frac{9}{10}

$2 \frac{9}{10}$