Is $\frac{5x}{3}$ The Same As $\frac{5}{3}x$? I believe they are the same but I'm not sure. Can someone please clarify this for me, and also explain why it would be the same or different.
 A: Depending on your formatting...  
$$\frac{5x}{3}=\frac{5}{3}x$$
Since order wouldn't matter you could think of it as $5\times x \div 3$ is equivalent to $5 \div 3 \times x$
A: $$\frac{5x}{3}=\frac{5}{3}x\ne\frac{5}{3x}$$
I tend to prefer the second over the first.
Both are equivalent to $\frac{1}{3}\cdot5\cdot x$, which can be rearranged in any order:  because multiplication is both commutative and associative, you can change the order of a series of multiplications as you see fit.
A: $\frac{5}{3} x = \frac{5}{3} \frac{x}{1} = \frac{5 \times x}{3 \times 1} = \frac{5 x}{3}$. 
A: First lets just consider 5/3.
Study the graphic for a moment to convince yourself that
$$5\div3$$
$$5\times\frac{1}{3}$$
$$\text{and }\frac{5}{3}$$
are all equivalent expressions.
 
This idea (of equivalence) combined with the Commutative ($ab=ba$) and Associative [(ab)c=a(bc)] Properties gives us.
$$\frac{5x}{3}=(5x)\cdot\frac{1}{3}=5\cdot(x\cdot\frac{1}{3})=5\cdot(\frac{1}{3}\cdot x)=(5\cdot\frac{1}{3})\cdot x=\frac{5}{3}x$$
A: I take a numerical approach here. Lets pretend (x) is just a number like 7. You're asking if:
$$ {5 \times 7 \over 3} = 5 \times {7\over 3} $$
Since the order does not matter here, lets just rewrite the expression on the left; notice that it doesn't matter if you multiply a number before dividing it; or if you divide before multiplying; the answers always the same, so:
$$  (5 \times 7) \div 3 =  5 \times (7 \div 3) %$$
Now we can just rewrite these as fractions if we want to:
$$ {5 \times 7 \over 3} = 5 \times {7 \over 3} $$ 
So you could repeat this reasoning with an x in the place of the 7, and you'll come to the same conclusion :)
