Let's assume 1 kilogram is equal to 2.2 pounds.
$1 kg = 2.2 lb$
So we get:
$1/2.2 = lb/kg$
Which means:
$1 : 2.2 = lb : kg$
So if we convert 5 kg to lb and y stands for the pound number, we get:
$1 : 2.2 = ylb : 5kg$
$5kg= y*2.2*lb$
$5(2.2lb)= y*2.2*lb$
$y = 5$
It is really wierd because we all know that it should have been
$kg : lb = 1 : 2.2$
Is there a lack of thinking from me?
On
$1 : 2.2 = lb : kg\tag{1}$
So if we convert 5 kg to lb and y stands for the pound number, we get:
$1 : 2.2 = ylb : 5kg$
This is completely wrong, like saying that $\frac{1}{2}=\frac{5}{2}$
If you want to know how many lb are 5 kg you just multiply the first line by 5
1kg = 2.2lb so 5kg are 11lb
On
Reconsider what it means for an object $\star$ to have a mass $5 kg$?
$$\begin{align*} \text{mass of }\star &= 5\cdot \text{mass of something of }1kg\\ \frac{\text{mass of }\star}{\text{mass of something of }1kg} &= 5 \end{align*}$$
And what it means for 1 kilogram to be equal to 2.2 pounds?
$$\begin{align*} \text{mass of something of }1kg &= 2.2\cdot\text{mass of something of }1lb\\ \frac{\text{mass of something of }1kg}{\text{mass of something of }1lb} &= 2.2\\ \end{align*}$$
So if you know $y\ lb$ and $5kg$ both represent the mass of object $\star$, then
$$\begin{align*} y &= \frac{\text{mass of }\star}{\text{mass of something of }1lb}\\ &= \frac{\text{mass of }\star}{\text{mass of something of }1kg} \cdot \frac{\text{mass of something of }1kg}{\text{mass of something of }1lb}\\ &= 5 \cdot 2.2 \end{align*}$$
You can say one of the followings:
$$\begin{align*} y:5 &= 2.2:1\\ y:5 &= kg:lb\\ y\ lb: 5kg &= 1:1 \end{align*}$$
Well, if $y$ is the number such that $y\,lb=5\,kg$, then you'd have $y\, lb : 5\,kg = 1:1$, no? Because they are supposed to be the same mass. What you should have is that $y\times lb = 5\times kg$, i.e. $$ y:5=kg:lb=2.2:1$$
Or, as some would say in a rather convoluted way, the numerical values are inversely proportional to units of measure.