Intuitively 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
✅ Math is hard
❌ This math is hard
0.25 / 0.5 = 0.5
0.25 = 0.5 × 0.5
1/4 = 1/2 × 1/2p/q=q
So q=√p
Works with a lot of numbers ☝🏻🤓
Ehhh |q| = √p but close enough
If q=√p then -q=√p also.
This is why “divide by half” and “divide in half” are two different things
It won’t keep you up if you just think of Divide as just multiplying by the fraction
Yeah I was gonna comment that 0.25*(1/0.5) = 0.5 doesn’t look nearly as weird
I didn’t specify fully, but I was just thinking 1/4 * 2/1
Imo, as soon as you write it as 0.25 multiplied by a fraction it works, because you can then easily see that it’s the same as (1/4)*2
The math looks perfectly fine. But when people phrase “half of a quarter” I think they have (1/2)*(1/4) in mind, instead of 0.25/0.5
But this isn’t “half of a quarter” this is “the reciprocal of a half, of a quarter”
Half of a quarter is 0.25/2 or 0.25*1/2
I know, but to me this meme doesn’t make sense to me unless I assume the person reading the math Expression is interpreting its real world application.
25 / 5 = 5 and nobodies head exploded. That’s just evaluating a math Expression. .25 / .5 = .5 is the same. It’s not a “my brain can’t comprehend how to evaluate expressions” as the meme suggests.
However, if someone who doesnt do much algebra thought to themselves “I need half of a quarter”, then I could understand why their brain might “hurt” as the meme suggests, for a similar reason why adding 20 degree Celsius water to 20 degree Celsius water doesn’t make 40 degree Celsius wate
I’m probably reading into it too much, but the meme just doesn’t feel like a “mind fuck that keeps me up at night”. I’m looking for reasons to try and explain it, but it’s just a math expression at the end of the day
I think the meme is an exaggeration of the situation for comedic effect. It just looks silly at first glance, I don’t believe the OP is kept up at night by this, and is rather making a remark about how it doesn’t instantly feel intuitive as a result (to use the 20 Celsius water example, its the same kind of momentary “wtf?” as 40 Celsius water not being twice as hot as 20 Celsius water. After a moment you remember “oh derp yeah we’re missing 273.15 kelvin in this picture lol”)
I think you nailed the confusion in this meme.
To simplify: it’s confusing that ½ = 0.5, but 1/2 ≠ 1/0.5
If you give half a person a quarter of a thing, how much would you be giving a full person? That’s right baby, half a thing. Don’t sweat it.
I worry that people who can get onto the internet find fractions a challenge.
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.
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.
x / sqrt(x) = sqrt(x)
Damn who would’ve thought?
Divide by 1/2 or multiply with 2/1. It’s an equivalent transformation.
I just think of division as how many times the right expression fits inside the left expression. 0.5 fits into 0.25 only 0.5 aka 1/2 times, because only half of it fits.
Precisely this. The people not getting the OP are why Common Core was developed.
1×2=2
Wow. Much brain. Maths wow.
The numbers between zero and one are where all of the fun is!
This just comes down to the fact that “dividing by a fraction is the same as multiplying by the inverse of the fraction” is an easy rule to follow but not particularly intuitive. In natural language, when most people hear “divide by half” they’re actually picturing “divide by two” in their head.
