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.
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
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
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.
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.
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.
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”)
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