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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?

vincentlin
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  • When you go from $$ 1:2.2 = lb : kg $$ to $$ 1:2.2 =y lb :5 kg $$ you have multiplied by $\frac{y}{5}$ (the left-hand side you have multiplied by 1), so in essence you have assumed that $y/5 =1$. – Matti P. Jan 08 '21 at 12:27
  • Analogous example but in whole numbers, $$\begin{align} 1 kg &= 1000 g\ g:kg &= 1:1000\ (k &= 1000 :)) \end{align}$$ it's not weird that when the more massive $kg$ is in the denominator, the ratio is less than $1:1$. – peterwhy Jan 08 '21 at 13:40

3 Answers3

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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.

1

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:

$$\begin{align*} y:5 &= 2.2:1\\ y:5 &= kg:lb\\ y\ lb: 5kg &= 1:1 \end{align*}$$

peterwhy
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$1 : 2.2 = lb : kg\tag{1}$

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

Raffaele
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