Hello! Today, we're going to teach you a trick that makes it a lot easier to add together two numbers.

Let's start small, with 2+2.

But before we can solve 2+2, let's take a look at 4+4, because that's just twice as much, right? As you'll learn, it's easier to think of numbers in terms of 4ths rather than 2nds.

So, we all know from elementary school math that 2+2=4 and 4+4=8. But did you know that there's an even simpler way to do this kind of addition, using each number's shape as a guide?

First, let's take a look at what makes 8 the sum of two 4s.

The number 8 is made up of 8 ones, right? Right. But! It is also made up of two 4s. And once you realize that, it becomes a whole lot easier!

Divide each circle within the number 8 into quarters using an Addition Axis. Do you see now how there are two sets of 4 within every 8?

Number the quadrants of the first Axis. There should be four quadrants, because one half of 8 is four.

Next, number the quadrants of the lower Axis.

Now, if you assign a 1 to each quadrant and add them, you will find that each half of the number 8 contains a 4.

And two 4s equals...that's right, 8. Spooky, huh?

So, to add 4 and 4 in a standard equation, assuming you don't know that 8 is the correct solution, you must divide each 4 into quadrants. First, draw a circle around the top of the 4 to completely enclose the little box it has.

Draw in an Addition Axis onto this finished circle.

Number the quadrants of the Axis. There should be four, because there are 4 ones, or 1 four, in the number 4.

Do the same thing to the second 4, starting with enclosing the top.

Then, draw an Axis and number each quadrant. There should be four quadrants.

And you should find, when you add up each quadrant, that the answer is 8. Put an 8 after the equal sign and draw in two Axes and number their quadrants.

Want to check your work? If you draw a line connecting each numbered quadrant in the two 4s to the 8, you will find that each quadrant on the left side of the equal sign has a corresponding quadrant on the right side, proving your answer is correct!

So, now that we've shown an easier way to prove that 4+4=8, let's apply what we learned to 2+2=4.

First, let's look at the 2. We've been taught that 2 is made up of two 1s, right? But let's think of it in terms of quadrants now.

First, let's show you how NOT to do it. In the circle inside each number 2, draw an Axis. You will notice that the Axis looks wrong, and that it's very hard to number each quadrant.

Look at this! Where are you supposed to label quadrants 3 and 4 on this Axis?

Answer: You're not. The number 2 is a special number whose Addition Axis consists of only a single line that divides the circle into two quadrants. Makes sense, right?

On the left side of the equation, you should have two 2s, each with an Axis, and with its two quadrants numbered.

And on the right side, we have the number 4 with Axis and numbered quadrants. Do you see how the same method we used to solve 4+4 solved 2+2? Pretty easy, isn't it?

And again, we can check our work by connecting a line between each numbered quadrant. Each side adds up to 4, because 4=4.

Okay, so now that we've gone through the whole process, and shown how 2+2=4 and 4+4=8, ready to try it on a harder set of numbers?

This method can be used on any two numbers that you need to add, so let's try 13+19. But don't worry, you can put those calculators away! This will only take a moment.

Start by breaking down the number 13. We know that it is made up of two distinct numbers: 10 and 3.

Ignore 3 for now, and look at 10. Because 10 contains a perfect circle, its Addition Axis contains five lines, and divides the circle into 10 quadrants.

The 1 of the number 10 is to be ignored entirely. A 1 is an odd, prime number, and is just a single line. It contains no circles at all and never could.

Number the quadrants and add them up. Are there 10? Good, because this is the number 10.

Now go back to the 3.

The number 3 is the easiest number to draw an Axis on, because it's like the number 2 but with a little more.

Number the quadrants. Quadrants 1 and 2 belong on the inside of the 3's half-circles, just like in the circle of a 2, and then the extra space on the outside of the 3 gets its own third quadrant.

That was 13. Halfway done! Let's take a look at 19, which we also know to consist of 10 and 9.

We already did an Axis and quadrants for the 10 in 13 but let's do it again for 19.

And because the number 9 contains a perfect circle, just like a 10, it deserves an Axis of 5 lines and 10 quadrants. Number them and count them up. Does it equal 9? No, because you have to subtract 1 from the useless stick dangling below the circle.

So now we know that 13=13 and 19=19.

Take your Standard Model equation and transplant it into Axis mode.

Correctly labeled 13 plus correctly labeled 19 should be simple now, because you just have to add up the quadrants.

And when you do, you find that 13+19=32. Horray! Way easier, wasn't it?

But, in case it felt too easy to be true, you can also check your work! Divide 32 into its base parts of 3, 10, 10, 10, and 2.

Give each number its proper Axis.

Number the quadrants.

And draw and add up connecter lines between each quadrant!

Tada! 32=32. The work checks out!

Good luck and good adding!

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