Algebra Examples

$\frac{2}{5} k - \frac{3}{5} + \frac{1}{10} k$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{2}{5}$ and $k$ .

$\frac{2 k}{5} - \frac{3}{5} + \frac{1}{10} k$

Step 1.2

Combine $\frac{1}{10}$ and $k$ .

$\frac{2 k}{5} - \frac{3}{5} + \frac{k}{10}$

Step 2

Find the common denominator.

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Step 2.1

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

$\frac{2 k}{5} \cdot \frac{2}{2} - \frac{3}{5} + \frac{k}{10}$

Step 2.2

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

$\frac{2 k \cdot 2}{5 \cdot 2} - \frac{3}{5} + \frac{k}{10}$

Step 2.3

Multiply $\frac{3}{5}$ by $\frac{2}{2}$ .

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

Step 2.4

Multiply $\frac{3}{5}$ by $\frac{2}{2}$ .

$\frac{2 k \cdot 2}{5 \cdot 2} - \frac{3 \cdot 2}{5 \cdot 2} + \frac{k}{10}$

Step 2.5

Reorder the factors of $5 \cdot 2$ .

$\frac{2 k \cdot 2}{2 \cdot 5} - \frac{3 \cdot 2}{5 \cdot 2} + \frac{k}{10}$

Step 2.6

Multiply $2$ by $5$ .

$\frac{2 k \cdot 2}{10} - \frac{3 \cdot 2}{5 \cdot 2} + \frac{k}{10}$

Step 2.7

Reorder the factors of $5 \cdot 2$ .

$\frac{2 k \cdot 2}{10} - \frac{3 \cdot 2}{2 \cdot 5} + \frac{k}{10}$

Step 2.8

Multiply $2$ by $5$ .

$\frac{2 k \cdot 2}{10} - \frac{3 \cdot 2}{10} + \frac{k}{10}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 k \cdot 2 - 3 \cdot 2 + k}{10}$

Step 4

Simplify each term.

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Step 4.1

Multiply $2$ by $2$ .

$\frac{4 k - 3 \cdot 2 + k}{10}$

Step 4.2

Multiply $- 3$ by $2$ .

$\frac{4 k - 6 + k}{10}$

Step 5

Add $4 k$ and $k$ .

$\frac{5 k - 6}{10}$