You have one apple. You divide it into quarters, so that you have 0.25 of an apple. Now divide it in half. So yes well technically you do have one half of 0.25 (and 0.5 is the answer that a calculator will return) what you actually have is 1/8 of an apple (0.125).
This is what pisses me off about Matt half the time. You end up with something that in the abstract makes sense because it's just numbers, but then if you try to make it make sense in real life it's stupid.
Your confusion comes from the fact that dividing a quarter in half is 0.25/2. That's not what's shown in the comic. Dividing by 0.5 is the same as multiplying by 2. It's just a quirk of syntax, the way we write math. If you spelled it out using English the comic would say "multiplying a quarter by two equals a half". The confusion just stems from someone's unfamiliarity with mathematical notation.
exactly. failure of english, not math. Math allows fairly accurate descriptions of the universe, humans (and especially languages) evolved to adequately percieve the narrow band of qualia that have been relevant to survival
Fractions are just funky when dividing. Dividing by 0.5 is the same multiplying by 2.
Your analogy is really close, but backwards is all. If you have a quarter of an apple. In order to get half a whole apple, you need another quarter. Two quarters make a half, so dividing a quarter by 0.5 gives you 2 quarters. Dividing a quarter by 2 gives you 0.5 of the original quarter which is your 1/8th
100/100 = 1, because any number divided by itself is 1.
And any number multiplied by 1 is still that number.
TBH, I moved the decimal over 2 places on the numerator and denominator and simplified 25/50 to 1/2 because It is easier to do in my head. Some of the other paths are too complicated when I am going to sleep.
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.
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.
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 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.
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")
Edited to add this: Singapore math insists however, that we eliminate the use of visuals in describing arithmetic within the rationals. They encourage that users of common core rely upon the number line, and solely the number line for thorough and most mathematically sound representations of arithmetic, even when involving the division of fractions.
For those not up to speed to with common core, remember how the teacher used to draw a diagram of a bunny hopping from one integer to the next integer to represent adding given integers, such as 4+3, or -2+1? Imagine that representation being used with problems like 1/7 divided by 5/49, and no decimal approximation is allowed. It’s fascinating and truly something to appreciate from the standpoint of someone who truly loves mathematics. I think it makes for great discussions amongst math graduates like myself, and other math enthusiasts. What does that mean for those who are not so enthused? Sometimes it means the teacher receives death threats from angry students. You can’t make everyone happy.
I’m not sure I completely agree with the number-line-only approach, but I’m definitely sympathetic to it. It reinforces the idea that fractions are numbers like any other numbers, and not pieces of pizza.
I get that. I like the number line approach, and respect it, but I have also observed seasoned math coaches fumble the visual explanation of a division by fractions problem where the numerators and denominations were relatively prime. As soon as the guy had drawn the first fraction and began to say, “we’d multiply by the recipro-…”, I could tell it was going to be long problem. He just stood there, and then asked, “well, how would I go about explaining the ‘keep change flip’, if you will?” He ended the problem by saying he might just explain that the distance drawn for the first fraction needs to be repeated on the other side of the fraction to show the multiplication by the denominator of the second fraction, and then that distance could be broken into parts to demonstrate the division by the previous numerator of the second fraction.
Basically he ended the problem by saying, “let’s just reflect it! Then we can break it up.” There wasn’t really a sound justification for the reflection piece of the process, other than saying, “we need to multiply by the reciprocal of the second fraction, so we’ll just have to multiply by its denominator it had, prior to flipping it.”
That was the quietest meeting I have ever seen amongst that group of adults.
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 :)
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.
