Algebra Examples

$\frac{9}{10} + \frac{1}{6}$

Step 1

To write $\frac{9}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9}{10} \cdot \frac{3}{3} + \frac{1}{6}$

Step 2

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{9}{10} \cdot \frac{3}{3} + \frac{1}{6} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{9}{10}$ by $\frac{3}{3}$ .

$\frac{9 \cdot 3}{10 \cdot 3} + \frac{1}{6} \cdot \frac{5}{5}$

Step 3.2

Multiply $10$ by $3$ .

$\frac{9 \cdot 3}{30} + \frac{1}{6} \cdot \frac{5}{5}$

Step 3.3

Multiply $\frac{1}{6}$ by $\frac{5}{5}$ .

$\frac{9 \cdot 3}{30} + \frac{5}{6 \cdot 5}$

Step 3.4

Multiply $6$ by $5$ .

$\frac{9 \cdot 3}{30} + \frac{5}{30}$

Step 4

Combine the numerators over the common denominator.

$\frac{9 \cdot 3 + 5}{30}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $9$ by $3$ .

$\frac{27 + 5}{30}$

Step 5.2

Add $27$ and $5$ .

$\frac{32}{30}$

Step 6

Cancel the common factor of $32$ and $30$ .

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Step 6.1

Factor $2$ out of $32$ .

$\frac{2 (16)}{30}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $30$ .

$\frac{2 \cdot 16}{2 \cdot 15}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot 16}{2 \cdot 15}$

Step 6.2.3

Rewrite the expression.

$\frac{16}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{15}$

Decimal Form:

$1.0\overline{6}$

Mixed Number Form:

$1 \frac{1}{15}$