how $1/0.5$ 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.

Tags:

Divisibility

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