Simplify 2/5k-3/5+1/10k

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

Step 1

Simplify each term.

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

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

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

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

Step 2

To write $\frac{2 k}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $5$ by $2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify each term.

Simplify the numerator.

Factor $k$ out of $2 k \cdot 2 + k$ .

Factor $k$ out of $2 k \cdot 2$ .

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

Raise $k$ to the power of $1$ .

$\frac{k (2 \cdot 2) + k^{1}}{10} - \frac{3}{5}$

Factor $k$ out of $k^{1}$ .

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

Factor $k$ out of $k (2 \cdot 2) + k \cdot 1$ .

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

Multiply $2$ by $2$ .

$\frac{k (4 + 1)}{10} - \frac{3}{5}$

Add $4$ and $1$ .

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

Cancel the common factor of $5$ and $10$ .

Factor $5$ out of $k \cdot 5$ .

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

Cancel the common factors.

Factor $5$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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