Basic Math Examples

\frac{2}{9} + \frac{5}{6}

$\frac{2}{9} + \frac{5}{6}$

Step 1

To write

\frac{2}{9}

$\frac{2}{9}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{2}{9} \cdot \frac{2}{2} + \frac{5}{6}

$\frac{2}{9} \cdot \frac{2}{2} + \frac{5}{6}$

Step 2

To write

\frac{5}{6}

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

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2}{9} \cdot \frac{2}{2} + \frac{5}{6} \cdot \frac{3}{3}

$\frac{2}{9} \cdot \frac{2}{2} + \frac{5}{6} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of

18

$18$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{2}{9}

$\frac{2}{9}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{2 \cdot 2}{9 \cdot 2} + \frac{5}{6} \cdot \frac{3}{3}

$\frac{2 \cdot 2}{9 \cdot 2} + \frac{5}{6} \cdot \frac{3}{3}$

Step 3.2

Multiply

9

$9$ by

2

$2$ .

\frac{2 \cdot 2}{18} + \frac{5}{6} \cdot \frac{3}{3}

$\frac{2 \cdot 2}{18} + \frac{5}{6} \cdot \frac{3}{3}$

Step 3.3

Multiply

\frac{5}{6}

$\frac{5}{6}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2 \cdot 2}{18} + \frac{5 \cdot 3}{6 \cdot 3}

$\frac{2 \cdot 2}{18} + \frac{5 \cdot 3}{6 \cdot 3}$

Step 3.4

Multiply

6

$6$ by

3

$3$ .

\frac{2 \cdot 2}{18} + \frac{5 \cdot 3}{18}

$\frac{2 \cdot 2}{18} + \frac{5 \cdot 3}{18}$

\frac{2 \cdot 2}{18} + \frac{5 \cdot 3}{18}

$\frac{2 \cdot 2}{18} + \frac{5 \cdot 3}{18}$

Step 4

Combine the numerators over the common denominator.

\frac{2 \cdot 2 + 5 \cdot 3}{18}

$\frac{2 \cdot 2 + 5 \cdot 3}{18}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

2

$2$ by

2

$2$ .

\frac{4 + 5 \cdot 3}{18}

$\frac{4 + 5 \cdot 3}{18}$

Step 5.2

Multiply

5

$5$ by

3

$3$ .

\frac{4 + 15}{18}

$\frac{4 + 15}{18}$

Step 5.3

Add

4

$4$ and

15

$15$ .

\frac{19}{18}

$\frac{19}{18}$

\frac{19}{18}

$\frac{19}{18}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{19}{18}

$\frac{19}{18}$

Decimal Form:

1.0 ¯ 5

$1.0\overline{5}$

Mixed Number Form:

1 \frac{1}{18}

$1 \frac{1}{18}$