Pre-Algebra Examples

$\frac{1}{15} + \frac{1}{5} + \frac{1}{3} + \frac{1}{5} + \frac{1}{15}$

Step 1

Combine the numerators over the common denominator.

$\frac{1 + 1}{15} + \frac{1 + 1}{5} + \frac{1}{3}$

Step 2

Simplify by adding numbers.

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Step 2.1

Add $1$ and $1$ .

$\frac{2}{15} + \frac{1 + 1}{5} + \frac{1}{3}$

Step 2.2

Add $1$ and $1$ .

$\frac{2}{15} + \frac{2}{5} + \frac{1}{3}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{2}{5}$ by $\frac{3}{3}$ .

$\frac{2}{15} + \frac{2}{5} \cdot \frac{3}{3} + \frac{1}{3}$

Step 3.2

Multiply $\frac{2}{5}$ by $\frac{3}{3}$ .

$\frac{2}{15} + \frac{2 \cdot 3}{5 \cdot 3} + \frac{1}{3}$

Step 3.3

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$\frac{2}{15} + \frac{2 \cdot 3}{5 \cdot 3} + \frac{1}{3} \cdot \frac{5}{5}$

Step 3.4

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

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

Step 3.5

Reorder the factors of $5 \cdot 3$ .

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

Step 3.6

Multiply $3$ by $5$ .

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

Step 3.7

Multiply $3$ by $5$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the expression.

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Step 5.1

Multiply $2$ by $3$ .

$\frac{2 + 6 + 5}{15}$

Step 5.2

Add $2$ and $6$ .

$\frac{8 + 5}{15}$

Step 5.3

Add $8$ and $5$ .

$\frac{13}{15}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{15}$

Decimal Form:

$0.8\overline{6}$