Algebra Examples

$\frac{5}{6} + \frac{7}{10}$

Step 1

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

$\frac{5}{6} \cdot \frac{5}{5} + \frac{7}{10}$

Step 2

To write $\frac{7}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{6} \cdot \frac{5}{5} + \frac{7}{10} \cdot \frac{3}{3}$

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

$\frac{5 \cdot 5}{6 \cdot 5} + \frac{7}{10} \cdot \frac{3}{3}$

Step 3.2

Multiply $6$ by $5$ .

$\frac{5 \cdot 5}{30} + \frac{7}{10} \cdot \frac{3}{3}$

Step 3.3

Multiply $\frac{7}{10}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 5}{30} + \frac{7 \cdot 3}{10 \cdot 3}$

Step 3.4

Multiply $10$ by $3$ .

$\frac{5 \cdot 5}{30} + \frac{7 \cdot 3}{30}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 + 7 \cdot 3}{30}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5$ by $5$ .

$\frac{25 + 7 \cdot 3}{30}$

Step 5.2

Multiply $7$ by $3$ .

$\frac{25 + 21}{30}$

Step 5.3

Add $25$ and $21$ .

$\frac{46}{30}$

Step 6

Cancel the common factor of $46$ and $30$ .

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Step 6.1

Factor $2$ out of $46$ .

$\frac{2 (23)}{30}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $30$ .

$\frac{2 \cdot 23}{2 \cdot 15}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot 23}{2 \cdot 15}$

Step 6.2.3

Rewrite the expression.

$\frac{23}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{23}{15}$

Decimal Form:

$1.5\overline{3}$

Mixed Number Form:

$1 \frac{8}{15}$