Basic Math Examples

$\frac{3}{15} + \frac{12}{18}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $3$ and $15$ .

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Step 1.1.1

Factor $3$ out of $3$ .

$\frac{3 (1)}{15} + \frac{12}{18}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $3$ out of $15$ .

$\frac{3 \cdot 1}{3 \cdot 5} + \frac{12}{18}$

Step 1.1.2.2

Cancel the common factor.

$\frac{3 \cdot 1}{3 \cdot 5} + \frac{12}{18}$

Step 1.1.2.3

Rewrite the expression.

$\frac{1}{5} + \frac{12}{18}$

Step 1.2

Cancel the common factor of $12$ and $18$ .

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Step 1.2.1

Factor $6$ out of $12$ .

$\frac{1}{5} + \frac{6 (2)}{18}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $6$ out of $18$ .

$\frac{1}{5} + \frac{6 \cdot 2}{6 \cdot 3}$

Step 1.2.2.2

Cancel the common factor.

$\frac{1}{5} + \frac{6 \cdot 2}{6 \cdot 3}$

Step 1.2.2.3

Rewrite the expression.

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

Step 2

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

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

Step 4.2

Multiply $5$ by $3$ .

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

Step 4.3

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

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

Step 4.4

Multiply $3$ by $5$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $5$ .

$\frac{3 + 10}{15}$

Step 6.2

Add $3$ and $10$ .

$\frac{13}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{15}$

Decimal Form:

$0.8\overline{6}$