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.
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.
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
25/5=5
o.O
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 :)
That’s the same as 2/2=1 3/3=1 268/268=1 …
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.
Sonan 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 :)
✅ Math is hard
❌ This math is hard
0.25 / 0.5 = 0.5
0.25 = 0.5 × 0.5
1/4 = 1/2 × 1/2The numbers between zero and one are where all of the fun is!
Divide by 1/2 or multiply with 2/1. Its an equivalent transformation.
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.
Any positive number?
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.
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
N / 1/2 = 2N/2 = 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”)
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.
