Let’s talk about divisibility and division two concepts that can make your head spin like a top on a rollercoaster (or maybe just give you a mild headache). Don’t Worry, because we’re here to break it down in simple terms.

To kick things off: what is divisibility? Well, let’s say you have 12 cookies and want to share them with your friends. If each friend gets an equal number of cookies (no cheating!), then the total number of cookies must be divisible by the number of friends. In other words, if there are n cookies and m friends, we can write this as:

n = m * k

where k is some whole number (also known as an integer). If you’re wondering what that asterisk (*) means, it’s just a fancy way to say “multiply.” So in our cookie example, if there are 12 cookies and 4 friends, then we can write:

12 = 4 * k

where k is some whole number. If you divide both sides of this equation by 4 (which means multiplying the left side by 1/4), you get:

3 = k

So each friend gets 3 cookies, and there are no leftovers! This is what we mean when we say that 12 is divisible by 4. In other words, 4 is a divisor of 12 (because it goes into 12 an equal number of times), and 12 is a multiple of 4 (because you can get 12 by multiplying 4 with some whole number).

Now division. This is where things start to get tricky, because not all numbers are divisible by other numbers. For example, if we try to share 5 cookies among 3 friends using the same method as before (i.e., dividing both sides of an equation), we end up with:

1 = k

But this doesn’t make sense! We can’t divide a whole cookie into equal parts and still have one leftover. So what gives? Well, it turns out that division is not always possible (at least not using the same method as multiplication). This is why we say that 5 is not divisible by 3.

But don’t worry there are other ways to think about division! For example, if you have a recipe for making 12 cupcakes and want to make half as many (i.e., 6), then you can divide both sides of an equation like this:

12 = n * k

where n is the original number of cupcakes and k is some whole number. If we set n=12 and k=2, then we get:

12 = 2 * 6

So if you divide both sides by 2 (which means multiplying the left side by 1/2), you get:

6 = k

And there you have it half as many cupcakes! This is what we mean when we say that division can be thought of as “undoing” multiplication. In other words, if you start with a product (i.e., the result of multiplying two numbers), then dividing one of those numbers by another number gives you back the original factor.

Remember: not all numbers are divisible by others, but we can always think about division as “undoing” multiplication (at least for whole numbers). And if you ever find yourself struggling with these concepts, just remember that cookies and cupcakes make everything better.