Basic Math Examples

\frac{2}{3} + \frac{9}{10}

$\frac{2}{3} + \frac{9}{10}$

Step 1

To write

\frac{2}{3}

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

\frac{10}{10}

$\frac{10}{10}$ .

\frac{2}{3} \cdot \frac{10}{10} + \frac{9}{10}

$\frac{2}{3} \cdot \frac{10}{10} + \frac{9}{10}$

Step 2

To write

\frac{9}{10}

$\frac{9}{10}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2}{3} \cdot \frac{10}{10} + \frac{9}{10} \cdot \frac{3}{3}

$\frac{2}{3} \cdot \frac{10}{10} + \frac{9}{10} \cdot \frac{3}{3}$

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}{3}

$\frac{2}{3}$ by

\frac{10}{10}

$\frac{10}{10}$ .

\frac{2 \cdot 10}{3 \cdot 10} + \frac{9}{10} \cdot \frac{3}{3}

$\frac{2 \cdot 10}{3 \cdot 10} + \frac{9}{10} \cdot \frac{3}{3}$

Step 3.2

Multiply

3

$3$ by

10

$10$ .

\frac{2 \cdot 10}{30} + \frac{9}{10} \cdot \frac{3}{3}

$\frac{2 \cdot 10}{30} + \frac{9}{10} \cdot \frac{3}{3}$

Step 3.3

Multiply

\frac{9}{10}

$\frac{9}{10}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2 \cdot 10}{30} + \frac{9 \cdot 3}{10 \cdot 3}

$\frac{2 \cdot 10}{30} + \frac{9 \cdot 3}{10 \cdot 3}$

Step 3.4

Multiply

10

$10$ by

3

$3$ .

\frac{2 \cdot 10}{30} + \frac{9 \cdot 3}{30}

$\frac{2 \cdot 10}{30} + \frac{9 \cdot 3}{30}$

\frac{2 \cdot 10}{30} + \frac{9 \cdot 3}{30}

$\frac{2 \cdot 10}{30} + \frac{9 \cdot 3}{30}$

Step 4

Combine the numerators over the common denominator.

\frac{2 \cdot 10 + 9 \cdot 3}{30}

$\frac{2 \cdot 10 + 9 \cdot 3}{30}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

2

$2$ by

10

$10$ .

\frac{20 + 9 \cdot 3}{30}

$\frac{20 + 9 \cdot 3}{30}$

Step 5.2

Multiply

9

$9$ by

3

$3$ .

\frac{20 + 27}{30}

$\frac{20 + 27}{30}$

Step 5.3

Add

20

$20$ and

27

$27$ .

\frac{47}{30}

$\frac{47}{30}$

\frac{47}{30}

$\frac{47}{30}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{47}{30}

$\frac{47}{30}$

Decimal Form:

1.5\overline{6}

$1.5\overline{6}$

Mixed Number Form:

1 \frac{17}{30}

$1 \frac{17}{30}$