…I mean, yeah? If the number is 50 or 10 that works out great. But let’s try that with 7% of 13. Now it’s 13% of 7. Just like you said, “much easier to calculate.”
Okay, choosing prime numbers was intentionally mean on my part. But 3% of 9 becomes 9% of 3. 4% of 2 becomes 2% of 4. Can anyone honestly look me in the eye and tell me that this tip has helped them out in any meaningful way?
Well, single digit percentages are easy. If it helps, move your decimal to the right so 9% becomes 90%. You can probably calculate 90% of 3 because you can do 10% and subtract it and get 2.7. Now move your decimal back to the left and you get 9% of 3 which is 0.27. You can do the same with higher percentages once you learn to break them in to 10% pieces.
I’d… probably use the calculator app before I do all this mental gymnastics
This is not mental gymnastics.
This is a coherent method and makes a lot of sense.
Mental gymnastics is when someone has to lie to themselves to make a point that isn’t correct. Like when people argue that trump was a good president because they can list several good things he did.
Or when people claim something is mental gymnastics when it’s actually called maths.
You’re really asking whether commutativity of multiplication has ever helped anyone? Because that’s what this is.
And yes it has helped me eg. estimate things or whatever along the years – but of course it’s not going to be some sort of magical mathematics trick where just by reversing the numbers it’ll always make things easier to calculate in your head
No, I think we all learned that multiplication is commutative in late elementary school, and obviously that’s an important thing to know.
But I think the original post tried to make it out to be some magical mathematical trick, and I really don’t understand that. Maybe I misunderstood the post.
Edit: wow, “commutative” is a really hard word to spell.
Yeah I think this is more about how you interpreted it, because it doesn’t look like others took it as being an absolute magic trick rule and neither did I.
The Panzer of the Lake didn’t use the word “commutativity” (fuck that really is hard to spell), but it gave out some wisdom that applied that rule by saying that “percentages are reversible”: if the reverse of a percentage would be easier to calculate, you can use it and get the same answer. If it’s not easier, well, then you’re screwed 😁 Oooooor depending on the situation you can use the a × b% = a × b / 100 commutativity trick:
7 × 8% = 0.56
7 × 8 / 100 = 0.56
I’d find 9% of 3 easier for sure. Sometimes it’s easier sometimes it’s not. Just use it when it’s easier.
9% of 3 is easier to estimate because you know it’s “almost 10% of 3”. Or, since 10-1==9, you could think of it as (10% of 3)-(1% of 3) and get the right answer using some other shortcuts. Humans being generally pretty good at base10, this is easy to figure out in your head as (0.3 - 0.03) and get 0.27.
Or, you could do what another commenter suggested and “3% of 9” can broken down as (3/100)•(9/1), becomes, (3•9) / (100•1), becomes 27/100, becomes 0.27. And that can be simplified as xy/100.
Different tools for different jobs. Base10 tricks are good for stuff like figuring out, say, a 15% or 20% tip, because you can easily figure out a 10% tip just by moving the decimal one space to the left, and add half of that (for 15) or double it (for 20). Or half and half again for (almost) 18%. xy/100 is a good trick for figuring out small percentages like sales tax (unless you’re in a place like Mass where it’s 6.25 and you gotta change it now to 625y/10000. At that point I’d just estimate at 6 in my head, or if I had to solve it mentally do (6y100) + ((1y100)/4).
I thought with “reversible” they meant that a number falling 50% and then rising 50% afterwards, it is the same number, which is not true.
10 * 50% = 5
5 * 150% = 7.5
You could also do 6*50 and then divide by 100.
33% of 7 = 7% of 33
Bitch, this only works for certain easy maths.
1% of 33 is .33
.33 × 7 =
.3 x 7 = 2.1
.03 x 7 = .21
21 + 2.1 = 2.31
So
7% of 33 = 2.31
You could also do
33% of 7
10% of 7 is .7
1% of 7 is .07
So 11% is .77
.77 × 3 =
.7 × 3 = 2.1
.07 × 3 = .21
2.1 + .21 = 2.31
That’s pretty damned intensive for a trick that’s supposed to make the maths easier.
Which equals 29^2 x .01
=> ((28 x 30) +1) X .01
=> (840 + 1) x .01
=> 8.41
28 x 30 is an easy mental calculation, as is adding 1, as is moving the decimal place over 2 places. I am teaching this to 4th graders, in two weeks. % to decimal is next week. They can square 2-digit numbers in their heads, already.
Also, a surprising number of people don’t know that precentages are more often than not represented as decimals between 0 and 1 as opposed to actually a number out of 100 when used in calculations (because the concept of a percent doesn’t really exist in math, it’s just a context specific way of formatting a decimal). A lot of people just enter 69 when calculating a formula that operates on a precentage instead of 0.69 which obviously makes the formula useless, or if a formula is supposed to output a precentage, they assume that it output 0.69 percent instead of 69 percent.
