So I'm trying to brush up on my math as an old adult, and I'm currently working through the very basics of math again. I'm trying to truly understand and visualize the various operations I'm engaging in, such as how one "moves" along the number line when one is multiplying two negatives, for example. It's proven more difficult than I thought.
One problem I have is my inability to visualize how I'm moving back and forth on the number line when I'm multiplying $0.5 \times 0.5 = 0.25$. When one multiplies, one is simply doing continuous addition. For example, $3$ times $5$ is merely $3 + 3 + 3 + 3 + 3 = 15,$ or $5 + 5 + 5 = 15$. You're adding a number x amount of times with itself.
This is all fine and dandy with whole numbers, but when I'm multiplying fractions, like $0.5$, I can no longer see how I'm moving along the number lines in regards to continuous addition to explain how I end up with $0.25$!
Is there some kind soul out there who can explain this?
Thanks in advance!
Best Answer
Does it help to think of it as moving halfway to $0.5$ (starting at $0$, of course)? In other words, you're adding in only half of the number $0.5$.