0.25 / 0.5 = 0.5
0.25 = 0.5 × 0.5
1/4 = 1/2 × 1/2Intuitively speaking, how many times does half of a thing fit into a quarter of a thing? The answer is, exactly one half time.
How many halves fit into a quarter? Half of them
That’s exactly how I think of it, so strange someone downvoted you
Shut up and take my upvote!
Divide by 1/2 or multiply with 2/1. It’s an equivalent transformation.
25/5=5
2.5/0.5=5
o.O
That’s the same as 2/2=1 3/3=1 268/268=1 …
Except that’s not what’s written.
It’s 0.25/0.5
Raising it exponentially would be
2.5/5, or
25/50=50
1/2≠50. Does not compute.
I think, it is the real world logic that makes it hard to grasp. If you divide something with something small it becomes bigger. Mathematically it’s easy and makes sense, but it it’s somehow not intuitive. Especially for young me :)
Multiplication of x times 6:
x * 6 = 1/2 x * 10 + x
This can sometimes be a shortcut for numbers that are easier to divide by 2 than to multiply by 6.
Take half as tens and add the number.
6 * 6 = 30 + 6 = 36
8 * 6 = 40 + 8 = 48
150 * 6 = 750 + 150 = 900
320 = 1600 + 320 = 1920
Etc.
Sleep well.
So an extension of the x * 5 = x/2 * 10 shortcut
Exactly. Multiples of 5 are easy enough in my opinion, but the principle can be used for all kinds of stuff when trying to calculate quickly.
For instance 9x =10x-x is usually faster than 9x (at least for my brain).
I once talked to an old guy who called it “little math”, because it fits in your head instead of having to use paper and pencil at the desk. It must have been taught differently before I was born. I work with numbers, and I’ve often encountered these old geezers who can eyeball a number close enough to make a decision before I can boot my pc and put everything through Excel.
I like that there’s a name for it. I always try to do that if possible. Division by 25? You mean multiply by 4 and divide by 100. Convert miles to km? That’s x + x/2 + x/10.
Not sure if qualify as old geezer, you never know on the internet. I’m old for most people here, but you mention Excel, so you sound closer to my age :)
(1/4) ÷ 1/2 = 2/4 = 1/2 = 0.5
✅ Math is hard
❌ This math is hard
This don’t avoid to sleep not even for 1/2 second. But pick any number. If that number is even, divide it by 2. If it’s odd, multiply it by 3 and add 1. Now repeat the process with your new number. If you keep going, you’ll eventually end up at 1.
You can’t prove that!
Yes, but everyone tried since a century to find a number with which it don’t work, good to avoid sleep.
Any positive number?
N / (1/2) = 2N/1 = 2N
Please use parenthesis to avoid ambiguity. N/1/2 could also mean N/2…
(Also I think you made a typo “2N/2” should be “2N/1”)
thank you very much
p/q=q
So q=√p
Works with a lot of numbers ☝🏻🤓
Ehhh |q| = √p but close enough
If q=√p then -q=√p also.
I worry that people who can get onto the internet find fractions a challenge.
It’s why my favorite way to troll the usual “why isn’t everyone on metric” goombahs is to tell them they’re just too lazy and/or dumb to do math with fractions.
I mean, I’m too lazy, but really - why make life harder than it has to be?
It isn’t actually harder. At all. People just think it is because them funny / signs is different from regular math. So they get put off by it even if they’re actually good at it because they’ve built the idea of hating fractions even though it’s a very intuitive thing.
You take a string, fold it in half, you’ve got a fraction in front of you. The rest follows from that basic principle. But when you put it on paper, the only thing that isn’t obvious is dividing fractions. Even then, you could figure it out on your own with a bit of thought.
Unfortunately, you jam a bunch of kids in a room and make them do boring things, often being taught by someone that isn’t actually good at math, and may have no desire to teach math in the first place, and you get droves of kids that hate math. Someone that likes math, and has spent time playing with it, they’ll have a way of translating it into different terms. Instead, you go by the book regardless of if the book works for kids of a given age.
Fractions are just as easy as decimal. You can’t imagine how many kids struggle with division in decimals, or even just keeping the number line in mind when dealing with them.
The one belt benefit decimal has over fractions is the ability to write things out by line and do most problems (other than division) in a simple box. That goes away once you’re dividing though. Dividing fractions is easier for some.
Also, fractions are easier to estimate with. You can almost always guesstimate what half of a thing will be, so you can almost always keep going until the fraction is too small visually to detect. Eyeballing a tenth of something is not as easy for most people.
Besides, it’s good for your brain. It’s like a muscle in that regard. If you don’t use it, it gets flabby. Flabby brains lead to shitty thinking.
I’m lazy, that’s why I prefer metric. It’s infinitely easier than dealing with fractions.
I don’t think this was shared because people are finding it a “challenge” it just looks funny.
It takes all of a few seconds for your actual mathematical processing to kick in and you go “oh yeah duh” but its just a funky little string of numbers.
It lives in the same camp as how none of the >3 whole multiples of 17 feel like multiples of 17. 68? Preposterous.
This is why “divide by half” and “divide in half” are two different things
x / sqrt(x) = sqrt(x)
Damn who would’ve thought?
