Algebra Examples

$\frac{2}{30} + \frac{1}{7}$

Step 1

Cancel the common factor of $2$ and $30$ .

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Step 1.1

Factor $2$ out of $2$ .

$\frac{2 (1)}{30} + \frac{1}{7}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $30$ .

$\frac{2 \cdot 1}{2 \cdot 15} + \frac{1}{7}$

Step 1.2.2

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 15} + \frac{1}{7}$

Step 1.2.3

Rewrite the expression.

$\frac{1}{15} + \frac{1}{7}$

Step 2

To write $\frac{1}{15}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{1}{15} \cdot \frac{7}{7} + \frac{1}{7}$

Step 3

To write $\frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{1}{15} \cdot \frac{7}{7} + \frac{1}{7} \cdot \frac{15}{15}$

Step 4

Write each expression with a common denominator of $105$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{15}$ by $\frac{7}{7}$ .

$\frac{7}{15 \cdot 7} + \frac{1}{7} \cdot \frac{15}{15}$

Step 4.2

Multiply $15$ by $7$ .

$\frac{7}{105} + \frac{1}{7} \cdot \frac{15}{15}$

Step 4.3

Multiply $\frac{1}{7}$ by $\frac{15}{15}$ .

$\frac{7}{105} + \frac{15}{7 \cdot 15}$

Step 4.4

Multiply $7$ by $15$ .

$\frac{7}{105} + \frac{15}{105}$

Step 5

Combine the numerators over the common denominator.

$\frac{7 + 15}{105}$

Step 6

Add $7$ and $15$ .

$\frac{22}{105}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{22}{105}$

Decimal Form:

$0.20952380 \dots$