Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Combine $a$ and $\frac{2}{3}$ .

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

Step 1.2

Move $2$ to the left of $a$ .

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

Step 1.3

Combine $\frac{5}{6}$ and $a$ .

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

Step 2

Find the common denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Reorder the factors of $3 \cdot 2$ .

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

Step 2.4

Multiply $2$ by $3$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Multiply $2$ by $- 2$ .

$\frac{- 4 a + 5 a - 1}{6}$

Step 5

Add $- 4 a$ and $5 a$ .

$\frac{a - 1}{6}$