Simplify -1/2a+2/5+5/6a-1/10

$- \frac{1}{2} a + \frac{2}{5} + \frac{5}{6} a - \frac{1}{10}$

Simplify each term.

Combine $a$ and $\frac{1}{2}$ .

$- \frac{a}{2} + \frac{2}{5} + \frac{5}{6} a - \frac{1}{10}$

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

$- \frac{a}{2} + \frac{2}{5} + \frac{5 a}{6} - \frac{1}{10}$

To write $- \frac{a}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{a}{2} \cdot \frac{3}{3} + \frac{5 a}{6} + \frac{2}{5} - \frac{1}{10}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

$- \frac{a \cdot 3}{2 \cdot 3} + \frac{5 a}{6} + \frac{2}{5} - \frac{1}{10}$

Multiply $2$ by $3$ .

$- \frac{a \cdot 3}{6} + \frac{5 a}{6} + \frac{2}{5} - \frac{1}{10}$

Combine the numerators over the common denominator.

$\frac{- a \cdot 3 + 5 a}{6} + \frac{2}{5} - \frac{1}{10}$

Find the common denominator.

Multiply $\frac{- a \cdot 3 + 5 a}{6}$ by $\frac{5}{5}$ .

$\frac{- a \cdot 3 + 5 a}{6} \cdot \frac{5}{5} + \frac{2}{5} - \frac{1}{10}$

Multiply $\frac{- a \cdot 3 + 5 a}{6}$ by $\frac{5}{5}$ .

$\frac{(- a \cdot 3 + 5 a) \cdot 5}{6 \cdot 5} + \frac{2}{5} - \frac{1}{10}$

Multiply $\frac{2}{5}$ by $\frac{6}{6}$ .

$\frac{(- a \cdot 3 + 5 a) \cdot 5}{6 \cdot 5} + \frac{2}{5} \cdot \frac{6}{6} - \frac{1}{10}$

Multiply $\frac{2}{5}$ by $\frac{6}{6}$ .

$\frac{(- a \cdot 3 + 5 a) \cdot 5}{6 \cdot 5} + \frac{2 \cdot 6}{5 \cdot 6} - \frac{1}{10}$

Multiply $\frac{1}{10}$ by $\frac{3}{3}$ .

$\frac{(- a \cdot 3 + 5 a) \cdot 5}{6 \cdot 5} + \frac{2 \cdot 6}{5 \cdot 6} - (\frac{1}{10} \cdot \frac{3}{3})$

Multiply $\frac{1}{10}$ by $\frac{3}{3}$ .

$\frac{(- a \cdot 3 + 5 a) \cdot 5}{6 \cdot 5} + \frac{2 \cdot 6}{5 \cdot 6} - \frac{3}{10 \cdot 3}$

Reorder the factors of $6 \cdot 5$ .

$\frac{(- a \cdot 3 + 5 a) \cdot 5}{5 \cdot 6} + \frac{2 \cdot 6}{5 \cdot 6} - \frac{3}{10 \cdot 3}$

Multiply $5$ by $6$ .

$\frac{(- a \cdot 3 + 5 a) \cdot 5}{30} + \frac{2 \cdot 6}{5 \cdot 6} - \frac{3}{10 \cdot 3}$

Multiply $5$ by $6$ .

$\frac{(- a \cdot 3 + 5 a) \cdot 5}{30} + \frac{2 \cdot 6}{30} - \frac{3}{10 \cdot 3}$

Reorder the factors of $10 \cdot 3$ .

$\frac{(- a \cdot 3 + 5 a) \cdot 5}{30} + \frac{2 \cdot 6}{30} - \frac{3}{3 \cdot 10}$

Multiply $3$ by $10$ .

$\frac{(- a \cdot 3 + 5 a) \cdot 5}{30} + \frac{2 \cdot 6}{30} - \frac{3}{30}$

Combine the numerators over the common denominator.

$\frac{(- a \cdot 3 + 5 a) \cdot 5 + 2 \cdot 6 - 3}{30}$

Simplify each term.

Multiply $3$ by $- 1$ .

$\frac{(- 3 a + 5 a) \cdot 5 + 2 \cdot 6 - 3}{30}$

Add $- 3 a$ and $5 a$ .

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

Multiply $5$ by $2$ .

$\frac{10 a + 2 \cdot 6 - 3}{30}$

Multiply $2$ by $6$ .

$\frac{10 a + 12 - 3}{30}$

Subtract $3$ from $12$ .

$\frac{10 a + 9}{30}$

Simplify -1/2a+2/5+5/6a-1/10

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