Simplify 1/3v+4 5/6v+3

$\frac{1}{3} v + 4 \frac{5}{6} v + 3$

Step 1

Convert $4 \frac{5}{6}$ to an improper fraction.

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

$\frac{1}{3} v + (4 + \frac{5}{6}) v + 3$

Add $4$ and $\frac{5}{6}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{1}{3} v + (4 \cdot \frac{6}{6} + \frac{5}{6}) v + 3$

Combine $4$ and $\frac{6}{6}$ .

$\frac{1}{3} v + (\frac{4 \cdot 6}{6} + \frac{5}{6}) v + 3$

Combine the numerators over the common denominator.

$\frac{1}{3} v + \frac{4 \cdot 6 + 5}{6} v + 3$

Simplify the numerator.

Multiply $4$ by $6$ .

$\frac{1}{3} v + \frac{24 + 5}{6} v + 3$

Add $24$ and $5$ .

$\frac{1}{3} v + \frac{29}{6} v + 3$

Step 2

Simplify each term.

Combine $\frac{1}{3}$ and $v$ .

$\frac{v}{3} + \frac{29}{6} v + 3$

Combine $\frac{29}{6}$ and $v$ .

$\frac{v}{3} + \frac{29 v}{6} + 3$

Step 3

Find the common denominator.

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

$\frac{v}{3} \cdot \frac{2}{2} + \frac{29 v}{6} + 3$

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

$\frac{v \cdot 2}{3 \cdot 2} + \frac{29 v}{6} + 3$

Write $3$ as a fraction with denominator $1$ .

$\frac{v \cdot 2}{3 \cdot 2} + \frac{29 v}{6} + \frac{3}{1}$

Multiply $\frac{3}{1}$ by $\frac{6}{6}$ .

$\frac{v \cdot 2}{3 \cdot 2} + \frac{29 v}{6} + \frac{3}{1} \cdot \frac{6}{6}$

Multiply $\frac{3}{1}$ by $\frac{6}{6}$ .

$\frac{v \cdot 2}{3 \cdot 2} + \frac{29 v}{6} + \frac{3 \cdot 6}{6}$

Reorder the factors of $3 \cdot 2$ .

$\frac{v \cdot 2}{2 \cdot 3} + \frac{29 v}{6} + \frac{3 \cdot 6}{6}$

Multiply $2$ by $3$ .

$\frac{v \cdot 2}{6} + \frac{29 v}{6} + \frac{3 \cdot 6}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{v \cdot 2 + 29 v + 3 \cdot 6}{6}$

Step 5

Simplify each term.

Move $2$ to the left of $v$ .

$\frac{2 \cdot v + 29 v + 3 \cdot 6}{6}$

Multiply $3$ by $6$ .

$\frac{2 v + 29 v + 18}{6}$

Step 6

Add $2 v$ and $29 v$ .

$\frac{31 v + 18}{6}$

Simplify 1/3v+4 5/6v+3

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