Basic Math Examples

\frac{3}{2} + \frac{2}{9}

$\frac{3}{2} + \frac{2}{9}$

Step 1

To write

\frac{3}{2}

$\frac{3}{2}$ as a fraction with a common denominator, multiply by

\frac{9}{9}

$\frac{9}{9}$ .

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

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

Step 2

To write

\frac{2}{9}

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

\frac{2}{2}

$\frac{2}{2}$ .

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

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

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{3}{2}

$\frac{3}{2}$ by

\frac{9}{9}

$\frac{9}{9}$ .

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

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

Step 3.2

Multiply

2

$2$ by

9

$9$ .

\frac{3 \cdot 9}{18} + \frac{2}{9} \cdot \frac{2}{2}

$\frac{3 \cdot 9}{18} + \frac{2}{9} \cdot \frac{2}{2}$

Step 3.3

Multiply

\frac{2}{9}

$\frac{2}{9}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{3 \cdot 9}{18} + \frac{2 \cdot 2}{9 \cdot 2}

$\frac{3 \cdot 9}{18} + \frac{2 \cdot 2}{9 \cdot 2}$

Step 3.4

Multiply

9

$9$ by

2

$2$ .

\frac{3 \cdot 9}{18} + \frac{2 \cdot 2}{18}

$\frac{3 \cdot 9}{18} + \frac{2 \cdot 2}{18}$

\frac{3 \cdot 9}{18} + \frac{2 \cdot 2}{18}

$\frac{3 \cdot 9}{18} + \frac{2 \cdot 2}{18}$

Step 4

Combine the numerators over the common denominator.

\frac{3 \cdot 9 + 2 \cdot 2}{18}

$\frac{3 \cdot 9 + 2 \cdot 2}{18}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

3

$3$ by

9

$9$ .

\frac{27 + 2 \cdot 2}{18}

$\frac{27 + 2 \cdot 2}{18}$

Step 5.2

Multiply

2

$2$ by

2

$2$ .

\frac{27 + 4}{18}

$\frac{27 + 4}{18}$

Step 5.3

Add

27

$27$ and

4

$4$ .

\frac{31}{18}

$\frac{31}{18}$

\frac{31}{18}

$\frac{31}{18}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{31}{18}

$\frac{31}{18}$

Decimal Form:

1.7 ¯ 2

$1.7\overline{2}$

Mixed Number Form:

1 \frac{13}{18}

$1 \frac{13}{18}$