Simplify 4s+1/6s+2 3/5s

$4 s + \frac{1}{6} s + 2 \frac{3}{5} s$

Convert $2 \frac{3}{5}$ to an improper fraction.

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

$4 s + \frac{1}{6} s + (2 + \frac{3}{5}) s$

Add $2$ and $\frac{3}{5}$ .

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

$4 s + \frac{1}{6} s + (2 \cdot \frac{5}{5} + \frac{3}{5}) s$

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

$4 s + \frac{1}{6} s + (\frac{2 \cdot 5}{5} + \frac{3}{5}) s$

Combine the numerators over the common denominator.

$4 s + \frac{1}{6} s + \frac{2 \cdot 5 + 3}{5} s$

Simplify the numerator.

Multiply $2$ by $5$ .

$4 s + \frac{1}{6} s + \frac{10 + 3}{5} s$

Add $10$ and $3$ .

$4 s + \frac{1}{6} s + \frac{13}{5} s$

Simplify each term.

Combine $\frac{1}{6}$ and $s$ .

$4 s + \frac{s}{6} + \frac{13}{5} s$

Combine $\frac{13}{5}$ and $s$ .

$4 s + \frac{s}{6} + \frac{13 s}{5}$

Find the common denominator.

Write $4 s$ as a fraction with denominator $1$ .

$\frac{4 s}{1} + \frac{s}{6} + \frac{13 s}{5}$

Multiply $\frac{4 s}{1}$ by $\frac{30}{30}$ .

$\frac{4 s}{1} \cdot \frac{30}{30} + \frac{s}{6} + \frac{13 s}{5}$

Multiply $\frac{4 s}{1}$ by $\frac{30}{30}$ .

$\frac{4 s \cdot 30}{30} + \frac{s}{6} + \frac{13 s}{5}$

Multiply $\frac{s}{6}$ by $\frac{5}{5}$ .

$\frac{4 s \cdot 30}{30} + \frac{s}{6} \cdot \frac{5}{5} + \frac{13 s}{5}$

Multiply $\frac{s}{6}$ by $\frac{5}{5}$ .

$\frac{4 s \cdot 30}{30} + \frac{s \cdot 5}{6 \cdot 5} + \frac{13 s}{5}$

Multiply $\frac{13 s}{5}$ by $\frac{6}{6}$ .

$\frac{4 s \cdot 30}{30} + \frac{s \cdot 5}{6 \cdot 5} + \frac{13 s}{5} \cdot \frac{6}{6}$

Multiply $\frac{13 s}{5}$ by $\frac{6}{6}$ .

$\frac{4 s \cdot 30}{30} + \frac{s \cdot 5}{6 \cdot 5} + \frac{13 s \cdot 6}{5 \cdot 6}$

Reorder the factors of $6 \cdot 5$ .

$\frac{4 s \cdot 30}{30} + \frac{s \cdot 5}{5 \cdot 6} + \frac{13 s \cdot 6}{5 \cdot 6}$

Multiply $5$ by $6$ .

$\frac{4 s \cdot 30}{30} + \frac{s \cdot 5}{30} + \frac{13 s \cdot 6}{5 \cdot 6}$

Multiply $5$ by $6$ .

$\frac{4 s \cdot 30}{30} + \frac{s \cdot 5}{30} + \frac{13 s \cdot 6}{30}$

Combine the numerators over the common denominator.

$\frac{4 s \cdot 30 + s \cdot 5 + 13 s \cdot 6}{30}$

Simplify each term.

Multiply $30$ by $4$ .

$\frac{120 s + s \cdot 5 + 13 s \cdot 6}{30}$

Move $5$ to the left of $s$ .

$\frac{120 s + 5 \cdot s + 13 s \cdot 6}{30}$

Multiply $6$ by $13$ .

$\frac{120 s + 5 s + 78 s}{30}$

Simplify by adding terms.

Add $120 s$ and $5 s$ .

$\frac{125 s + 78 s}{30}$

Add $125 s$ and $78 s$ .

$\frac{203 s}{30}$

Simplify 4s+1/6s+2 3/5s

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