Basic Math Examples

\frac{7}{9} + \frac{2}{15}

$\frac{7}{9} + \frac{2}{15}$

Step 1

To write

\frac{7}{9}

$\frac{7}{9}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{7}{9} \cdot \frac{5}{5} + \frac{2}{15}

$\frac{7}{9} \cdot \frac{5}{5} + \frac{2}{15}$

Step 2

To write

\frac{2}{15}

$\frac{2}{15}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{7}{9} \cdot \frac{5}{5} + \frac{2}{15} \cdot \frac{3}{3}

$\frac{7}{9} \cdot \frac{5}{5} + \frac{2}{15} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of

45

$45$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{7}{9}

$\frac{7}{9}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{7 \cdot 5}{9 \cdot 5} + \frac{2}{15} \cdot \frac{3}{3}

$\frac{7 \cdot 5}{9 \cdot 5} + \frac{2}{15} \cdot \frac{3}{3}$

Step 3.2

Multiply

9

$9$ by

5

$5$ .

\frac{7 \cdot 5}{45} + \frac{2}{15} \cdot \frac{3}{3}

$\frac{7 \cdot 5}{45} + \frac{2}{15} \cdot \frac{3}{3}$

Step 3.3

Multiply

\frac{2}{15}

$\frac{2}{15}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{7 \cdot 5}{45} + \frac{2 \cdot 3}{15 \cdot 3}

$\frac{7 \cdot 5}{45} + \frac{2 \cdot 3}{15 \cdot 3}$

Step 3.4

Multiply

15

$15$ by

3

$3$ .

\frac{7 \cdot 5}{45} + \frac{2 \cdot 3}{45}

$\frac{7 \cdot 5}{45} + \frac{2 \cdot 3}{45}$

\frac{7 \cdot 5}{45} + \frac{2 \cdot 3}{45}

$\frac{7 \cdot 5}{45} + \frac{2 \cdot 3}{45}$

Step 4

Combine the numerators over the common denominator.

\frac{7 \cdot 5 + 2 \cdot 3}{45}

$\frac{7 \cdot 5 + 2 \cdot 3}{45}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

7

$7$ by

5

$5$ .

\frac{35 + 2 \cdot 3}{45}

$\frac{35 + 2 \cdot 3}{45}$

Step 5.2

Multiply

2

$2$ by

3

$3$ .

\frac{35 + 6}{45}

$\frac{35 + 6}{45}$

Step 5.3

Add

35

$35$ and

6

$6$ .

\frac{41}{45}

$\frac{41}{45}$

\frac{41}{45}

$\frac{41}{45}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{41}{45}

$\frac{41}{45}$

Decimal Form:

0.9 ¯ 1

$0.9\overline{1}$