I have read these definitions but I am not sure that I understand them.
Could someone give the intuition behind these definitions?
2026-03-29 18:32:44.1774809164
What it means that multiplication is stretching and addition is sliding the number line?
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Imagine the number line as a long strip. This strip goes through an infinitely tiny slit that shows exactly one point - number - on the line.
Now, suppose the integers are all one centimeter apart on the strip. Then, if you pulled the strip three centimeters to the left, the number showing through the slit would increase by three. Thus, addition can be viewed as "sliding" the number line to the left.
Now, suppose we started pulling the ends of the strip apart, stretching it, while making sure that 0 doesn't move. If we stretch it twice, now there are two centimeters between integers. Since 0 didn't move, we now have half as much numbers between it and our slit, so the number shown on the slit is halved.
Note, as has been pointed out in comments, these are NOT formal definitions; just intuition/visualization.