We can start with what "x" is. Here is how it is defined.

Now let's try and figure out what "x+1" is, by adding 1 to both sides.

Wait a second, this looks a little familiar... where have we seen this before?

Yes! It's just the denominator of the fraction! (remember the dots just mean the pattern keeps going)

So since what is in the blue box and "x+1" are the same thing, we can replace one with the other.

There you go! The denominator is just "x+1".

I hope that answers your question. If you have any other questions or clarifications, just shoot us another email.

Best,

"The Daily Challenge Team

]]>One way to think of fractions (or divides) is as switched-around multiplication problems. So in \(\frac{2}{3},\) the "2" means something altogether that you are sharing, and "3" means the number of groups you are sharing them into. For example,

$$\frac{2 \text{ cookies}}{3 \text{ people}} $$.

The answer to this fraction means how much cookie each person gets. As a multiplication problem, this would be:

And you could represent it as a picture of groups, like this:

What if you divide by a fraction, like

Compare this with

There are half as many people, so each person should get more. How much more? They should get twice as much. This is why

This works no matter if the numerator (top number) of the fraction is 1 or any other number.

This also explains why we have to do the little fraction first; we have to know how many people we are sharing the cookies with before we can begin to figure out how many cookies each person gets.

I hope this helps! Let me know if you have any more questions.

Happy Learning!

The Daily Challenge Team

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