how $1/0.5$ is equal to $2$?

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 $2$?

• 1/0.5 is the number of times 0.5 enters in 1. – Tlön Uqbar Orbis Tertius Apr 11 '15 at 13:45
• 2*0.5=1, and your result follows – JonMark Perry Apr 11 '15 at 13:50
• One divided by one half is two. – k170 Apr 11 '15 at 13:54

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.

• thanks for your detailed answer but this was all mathematical justification. – farheen Apr 11 '15 at 23:33
• 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. – farheen Jul 22 '16 at 1:53

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.

• how will you relate this cookie analogy to 1/2=0.5? – farheen Apr 11 '15 at 23:32
• 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. – MJD Apr 12 '15 at 0:47

See Boy.. Lets take a 1 inch Sausage (lol)

Now lets try to do 1/7 ie divide the sausage into 7 parts.. it gives us potions of 0.14"

Now lets try to do 1/3 ie divide the sausage into 3 parts.. it gives us potions of 0.33"

Lets take a 1 inch Sausage Now lets try to do 1/1 ie divide the sausage into 1 parts.. it gives us potions of 1"

Lets take a 1 inch Sausage Now lets try to do 1/0.5 ie divide the sausage into 0.5 equal parts.. it gives us potions of __ ? Wait we cant actually divide a sausage into 0.5 parts. So we divide the sausage into potions of 0.5. Which Gives us 2 parts. yayee!

Also. See the TREND of division results decreasing and then increasing from 1/1.

• Nice answer! It is well written, imaginative, and engaging. Are you a teacher? You sound like it. – The Great Duck Jul 13 '16 at 23:30