Pre-Algebra Examples

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

Step 1

Find the common denominator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Multiply $\frac{3}{5}$ by $\frac{6}{6}$ .

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

Step 1.4

Multiply $\frac{3}{5}$ by $\frac{6}{6}$ .

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

Step 1.5

Multiply $\frac{1}{2}$ by $\frac{15}{15}$ .

$\frac{5 \cdot 5}{6 \cdot 5} - \frac{3 \cdot 6}{5 \cdot 6} + \frac{1}{2} \cdot \frac{15}{15}$

Step 1.6

Multiply $\frac{1}{2}$ by $\frac{15}{15}$ .

$\frac{5 \cdot 5}{6 \cdot 5} - \frac{3 \cdot 6}{5 \cdot 6} + \frac{15}{2 \cdot 15}$

Step 1.7

Reorder the factors of $6 \cdot 5$ .

$\frac{5 \cdot 5}{5 \cdot 6} - \frac{3 \cdot 6}{5 \cdot 6} + \frac{15}{2 \cdot 15}$

Step 1.8

Multiply $5$ by $6$ .

$\frac{5 \cdot 5}{30} - \frac{3 \cdot 6}{5 \cdot 6} + \frac{15}{2 \cdot 15}$

Step 1.9

Multiply $5$ by $6$ .

$\frac{5 \cdot 5}{30} - \frac{3 \cdot 6}{30} + \frac{15}{2 \cdot 15}$

Step 1.10

Multiply $2$ by $15$ .

$\frac{5 \cdot 5}{30} - \frac{3 \cdot 6}{30} + \frac{15}{30}$

Step 2

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 - 3 \cdot 6 + 15}{30}$

Step 3

Simplify each term.

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Step 3.1

Multiply $5$ by $5$ .

$\frac{25 - 3 \cdot 6 + 15}{30}$

Step 3.2

Multiply $- 3$ by $6$ .

$\frac{25 - 18 + 15}{30}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract $18$ from $25$ .

$\frac{7 + 15}{30}$

Step 4.2

Add $7$ and $15$ .

$\frac{22}{30}$

Step 4.3

Cancel the common factor of $22$ and $30$ .

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Step 4.3.1

Factor $2$ out of $22$ .

$\frac{2 (11)}{30}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $2$ out of $30$ .

$\frac{2 \cdot 11}{2 \cdot 15}$

Step 4.3.2.2

Cancel the common factor.

$\frac{2 \cdot 11}{2 \cdot 15}$

Step 4.3.2.3

Rewrite the expression.

$\frac{11}{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{15}$

Decimal Form:

$0.7\overline{3}$