0.5 / 0.5 = 1, so reducing the top term by half (from 0.5 to 0.25) reduces the result by the same (from 1 to 0.5), makes perfect sense to me. Or, ya know, just remember that dividing by 0.5 is the same as multiplying by 2.
Or even simpler the half of 0.5 fits into 0.25. And we all know a half is 0.5
I was trying to think how to put that into words with an example like, “how many halves fit in 10? It’s 20. So how many halves fit in a quarter? Only half of a half will fit, so 0.5” but I kept screwing up the wording in my head for halves and quarters until I read your reply, so thank you for helping with that clarification. I knew the math was right but couldn’t put it into words the way I wanted.
Dividing any number, except 0, by itself equal 1, so the first part of your argument makes no sense.
If you have 0.5 / 0.5, that equals 1, because it’s a number (except 0), divided by itself. That much we seem to agree on.
So then if we want to get from this to 0.25 / 0.5 as shown in the meme, we have to look at what’s changed and apply that change to each side of the equation. So what changed? The top of the fraction is 0.25 instead of 0.5. Hopefully we can agree that 0.25 is half of 0.5. We halved the top side of the fraction on the left.
Now we want to apply that change on the right side then to keep our equation balanced. For this step, it helps to rewrite 1 on the right side as 1 / 1. Then we halve the top side of that fraction just like we did with the left side, giving us 0.5 / 1, which simplifies to just 0.5.
