Basic Math Examples

\frac{2}{5} + \frac{5}{6}

$\frac{2}{5} + \frac{5}{6}$

Step 1

To write

\frac{2}{5}

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

\frac{6}{6}

$\frac{6}{6}$ .

\frac{2}{5} \cdot \frac{6}{6} + \frac{5}{6}

$\frac{2}{5} \cdot \frac{6}{6} + \frac{5}{6}$

Step 2

To write

\frac{5}{6}

$\frac{5}{6}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{2}{5} \cdot \frac{6}{6} + \frac{5}{6} \cdot \frac{5}{5}

$\frac{2}{5} \cdot \frac{6}{6} + \frac{5}{6} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of

30

$30$ , 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{6}{6}

$\frac{6}{6}$ .

\frac{2 \cdot 6}{5 \cdot 6} + \frac{5}{6} \cdot \frac{5}{5}

$\frac{2 \cdot 6}{5 \cdot 6} + \frac{5}{6} \cdot \frac{5}{5}$

Step 3.2

Multiply

5

$5$ by

6

$6$ .

\frac{2 \cdot 6}{30} + \frac{5}{6} \cdot \frac{5}{5}

$\frac{2 \cdot 6}{30} + \frac{5}{6} \cdot \frac{5}{5}$

Step 3.3

Multiply

\frac{5}{6}

$\frac{5}{6}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{2 \cdot 6}{30} + \frac{5 \cdot 5}{6 \cdot 5}

$\frac{2 \cdot 6}{30} + \frac{5 \cdot 5}{6 \cdot 5}$

Step 3.4

Multiply

6

$6$ by

5

$5$ .

\frac{2 \cdot 6}{30} + \frac{5 \cdot 5}{30}

$\frac{2 \cdot 6}{30} + \frac{5 \cdot 5}{30}$

\frac{2 \cdot 6}{30} + \frac{5 \cdot 5}{30}

$\frac{2 \cdot 6}{30} + \frac{5 \cdot 5}{30}$

Step 4

Combine the numerators over the common denominator.

\frac{2 \cdot 6 + 5 \cdot 5}{30}

$\frac{2 \cdot 6 + 5 \cdot 5}{30}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

2

$2$ by

6

$6$ .

\frac{12 + 5 \cdot 5}{30}

$\frac{12 + 5 \cdot 5}{30}$

Step 5.2

Multiply

5

$5$ by

5

$5$ .

\frac{12 + 25}{30}

$\frac{12 + 25}{30}$

Step 5.3

Add

12

$12$ and

25

$25$ .

\frac{37}{30}

$\frac{37}{30}$

\frac{37}{30}

$\frac{37}{30}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{37}{30}

$\frac{37}{30}$

Decimal Form:

1.2 ¯ 3

$1.2\overline{3}$

Mixed Number Form:

1 \frac{7}{30}

$1 \frac{7}{30}$