My question is how $1/0.5$ is equal to $2$.
I am not asking the mathematical justification that $1/0.5=10/5=2$. I know all this. I just want to know how it is two... a lay man justification. According to my understanding if one says $1/2$ then it means we are dividing something of value $1$ into two parts, so the result is $0.5$ which means each of the two parts has value $0.5$. But if one does $1/0.5$, what does it mean and how it is equal to $2$?
If you have 10 cookies and each kid gets 2 cookies, how many kids can you serve? It's $10\div 2 =5$ kids.
If you have 10 cookies and each kid gets 2.5 cookies, how many kids can you serve? It's $10\div 2.5 =4$ kids.
If you have 1 cookie and each kid gets 0.5 cookies, how many kids can you serve? It's $1\div 0.5 =2$ kids.
You want a "layman justification". Here are a couple of different ways to look at it:
1) By $a$ divided by $b$ we are asking "what do I need to multiply $b$ by to get $a$. And we need to multiply $0.5$ by $2$ to get $1$.
2) You know that $0.5$ is the same as $1/2$ (exactly because you need to multiply $2$ by $0.5$ to get $1$). There is a rule that says $$ \frac{a/b}{c/d} = \frac{a\cdot d}{b\cdot c}. $$ So $$ \frac{1/1}{1/2} = \frac{1\cdot 2}{1\cdot 1} = 2. $$
3) Instead of thinking of $0.5$ as $1$ divided by $2$, just think about $0.5$ as a number of the real number line.
4) You can also think of the number $a$ divded by $b$ as the unique solution to the equation $bx = a$ (that is, an equation in the variable $x$). So you are asking for a solution to $0.5x = 1$.
All this is basically saying the same. I would encourage you to be comfortable with mathematical truth. If you know the mathematical justification for something, then be happy and content with this.
See boy… Let’s take a 1 inch sausage (lol)
Now let’s try to do 1/7, i.e., divide the sausage into 7 parts… it gives us portions of 0.14"
Now let’s try to do 1/3, i.e., divide the sausage into 3 parts… it gives us portions of 0.33"
Let’s take a 1 inch sausage
Now let’s try to do 1/1, i.e., divide the sausage into 1 parts… it gives us portions of 1"
Let’s take a 1 inch sausage
Now let’s try to do 1/0.5, i.e., divide the sausage into 0.5 equal parts… it gives us potions of __ ? Wait we can’t actually divide a sausage into 0.5 parts. So we divide the sausage into portions of 0.5. Which Gives us 2 parts. yayee!
Also, see that the TREND of division results are decreasing and then increasing from 1/1.
Here's the most basic way I can think of to say it. 1/0.5 is asking "How many halves go into 1? The answer is 2.
I wont patronize you, but you can simply think of it as 1 divided in half since 0.5 of any quantity is its half. And so now you count how many pieces are left after dividing or cutting in half and your answer is 2 equal parts.
How about this? I think the best is to view them as answers to two related problems (I would call them "reciprocal problems" to emphasize the relationship between $0.5$ and $2$)
Problem 1: "Split a whole into 2 parts, how much does each part weight"?
Problem 2: "Split a whole into parts each weighing $0.5$ of the original, how many parts were there"?
