Simplify -4 3/8v+3/8v-6v

$- 4 \frac{3}{8} v + \frac{3}{8} v - 6 v$

Step 1

Convert $4 \frac{3}{8}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$- (4 + \frac{3}{8}) v + \frac{3}{8} v - 6 v$

Add $4$ and $\frac{3}{8}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- (4 \cdot \frac{8}{8} + \frac{3}{8}) v + \frac{3}{8} v - 6 v$

Combine $4$ and $\frac{8}{8}$ .

$- (\frac{4 \cdot 8}{8} + \frac{3}{8}) v + \frac{3}{8} v - 6 v$

Combine the numerators over the common denominator.

$- \frac{4 \cdot 8 + 3}{8} v + \frac{3}{8} v - 6 v$

Simplify the numerator.

Multiply $4$ by $8$ .

$- \frac{32 + 3}{8} v + \frac{3}{8} v - 6 v$

Add $32$ and $3$ .

$- \frac{35}{8} v + \frac{3}{8} v - 6 v$

Step 2

Simplify each term.

Combine $v$ and $\frac{35}{8}$ .

$- \frac{v \cdot 35}{8} + \frac{3}{8} v - 6 v$

Move $35$ to the left of $v$ .

$- \frac{35 \cdot v}{8} + \frac{3}{8} v - 6 v$

Combine $\frac{3}{8}$ and $v$ .

$- \frac{35 v}{8} + \frac{3 v}{8} - 6 v$

Step 3

Simplify terms.

Combine the numerators over the common denominator.

$- 6 v + \frac{- 35 v + 3 v}{8}$

Add $- 35 v$ and $3 v$ .

$- 6 v + \frac{- 32 v}{8}$

Cancel the common factor of $- 32$ and $8$ .

Factor $8$ out of $- 32 v$ .

$- 6 v + \frac{8 (- 4 v)}{8}$

Cancel the common factors.

Factor $8$ out of $8$ .

$- 6 v + \frac{8 (- 4 v)}{8 (1)}$

Cancel the common factor.

$- 6 v + \frac{8 (- 4 v)}{8 \cdot 1}$

Rewrite the expression.

$- 6 v + \frac{- 4 v}{1}$

Divide $- 4 v$ by $1$ .

$- 6 v - 4 v$

Subtract $4 v$ from $- 6 v$ .

$- 10 v$