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 you nailed the confusion in this meme.
To simplify: it’s confusing that ½ = 0.5, but 1/2 ≠ 1/0.5
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”)
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.
The numbers between zero and one are where all of the fun is!
1×2=2
Wow. Much brain. Maths wow.
25/5=5
2.5/0.5=5
o.O
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 :)
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.
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.
