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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 $2$?

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    $\begingroup$ 1/0.5 is the number of times 0.5 enters in 1. $\endgroup$ Apr 11, 2015 at 13:45
  • $\begingroup$ 2*0.5=1, and your result follows $\endgroup$
    – JMP
    Apr 11, 2015 at 13:50
  • $\begingroup$ One divided by one half is two. $\endgroup$
    – k170
    Apr 11, 2015 at 13:54

6 Answers 6

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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.

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    $\begingroup$ how will you relate this cookie analogy to 1/2=0.5? $\endgroup$
    – farheen
    Apr 11, 2015 at 23:32
  • $\begingroup$ Suppose you have 10 cookies and you want each kid to get 3 cookies. $10\div 3 = 3\frac13$. This means you have enough cookies for 3 kids, and only $\frac13$ of a full share for kid #4. Now suppose you have 1 cookie and you want each kid to get 2 cookies. $1\div 2 = \frac12$. This means you have enough cookies for 0 kids, and only $\frac12$ of a full share for kid #1. $\endgroup$
    – MJD
    Apr 12, 2015 at 0:47
  • $\begingroup$ If you have $1$ cookie and each kid wants only $0$ cookies, how many kids can you serve? All the kids in the world (including those not in this world) :P $\endgroup$ Jul 21, 2021 at 3:46
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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.

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  • $\begingroup$ thanks for your detailed answer but this was all mathematical justification. $\endgroup$
    – farheen
    Apr 11, 2015 at 23:33
  • $\begingroup$ After a very long time I viewed your answer today and I got my answer so I accepted your answer.Thanks to all who tried to make this clear to me. $\endgroup$
    – farheen
    Jul 22, 2016 at 1:53
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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.

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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.

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  • $\begingroup$ Nice answer! It is well written, imaginative, and engaging. Are you a teacher? You sound like it. $\endgroup$
    – user64742
    Jul 13, 2016 at 23:30
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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.

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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"?

  • Answer is represented as $1/2$, each weighs $0.5$ of the original. $1/2=0.5$

Problem 2: "Split a whole into parts each weighing $0.5$ of the original, how many parts were there"?

  • Answer is represented as $1/(0.5)$, need to add $2$ parts to recover original weight. $1/(0.5)=2$
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