Simplify -2/5(10+15m-20n)

$- \frac{2}{5} (10 + 15 m - 20 n)$

Step 1

Apply the distributive property.

$- \frac{2}{5} \cdot 10 - \frac{2}{5} (15 m) - \frac{2}{5} (- 20 n)$

Step 2

Simplify.

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{- 2}{5} \cdot 10 - \frac{2}{5} (15 m) - \frac{2}{5} (- 20 n)$

Factor $5$ out of $10$ .

$\frac{- 2}{5} \cdot (5 (2)) - \frac{2}{5} (15 m) - \frac{2}{5} (- 20 n)$

Cancel the common factor.

$\frac{- 2}{5} \cdot (5 \cdot 2) - \frac{2}{5} (15 m) - \frac{2}{5} (- 20 n)$

Rewrite the expression.

$- 2 \cdot 2 - \frac{2}{5} (15 m) - \frac{2}{5} (- 20 n)$

Multiply $- 2$ by $2$ .

$- 4 - \frac{2}{5} (15 m) - \frac{2}{5} (- 20 n)$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$- 4 + \frac{- 2}{5} (15 m) - \frac{2}{5} (- 20 n)$

Factor $5$ out of $15 m$ .

$- 4 + \frac{- 2}{5} (5 (3 m)) - \frac{2}{5} (- 20 n)$

Cancel the common factor.

$- 4 + \frac{- 2}{5} (5 (3 m)) - \frac{2}{5} (- 20 n)$

Rewrite the expression.

$- 4 - 2 (3 m) - \frac{2}{5} (- 20 n)$

Multiply $3$ by $- 2$ .

$- 4 - 6 m - \frac{2}{5} (- 20 n)$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$- 4 - 6 m + \frac{- 2}{5} (- 20 n)$

Factor $5$ out of $- 20 n$ .

$- 4 - 6 m + \frac{- 2}{5} (5 (- 4 n))$

Cancel the common factor.

$- 4 - 6 m + \frac{- 2}{5} (5 (- 4 n))$

Rewrite the expression.

$- 4 - 6 m - 2 (- 4 n)$

Multiply $- 4$ by $- 2$ .

$- 4 - 6 m + 8 n$

Step 3

Move $- 4$ .

$- 6 m + 8 n - 4$