Current Events > No way. Why didn't they teach us this in any math class?

(+) Yeah! (+)

This sounds like one of those tricks they'd teach you in 7th grade math, yet I went all the way through Calculus I without knowing this.

Bump

it's called the commutative and associative properties of multiplication.

they do teach it,

All it is is factoring out .01, and they're the same.

.01(25)(8)

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Fam_Fam posted...

it's called the commutative and associative properties of multiplication.

they do teach it,

Yeah but most people really only learn about those so they know it doesn't matter which number you put first.

Most schools don't really teach how to apply it like this

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Fam_Fam posted...

it's called the commutative and associative properties of multiplication.

they do teach it,

Is it?

8% of 25 would be 0.08 x 25

And the reverse would be .25 x 8

That's not really the commutative property. But I'm a dummy at maths so idk

Comfy_Pillow posted...

Is it?

8% of 25 would be 0.08 x 25

And the reverse would be .25 x 8

That's not really the commutative property. But I'm a dummy at maths so idk

In both of those, youre just multiplying by .01 to make it out of 100. So all this is is swapping the 25 and 8; it doesnt matter which you multiply the .01 to.

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Bananana posted...

In both of those, youre just multiplying by .01

Can you elaborate on this? I'm interested but genuinely don't understand

Comfy_Pillow posted...

Can you elaborate on this? I'm interested but genuinely don't understand

It was said earlier.

(0.08)*(25) ?= (0.25)*(8)
Factor out 0.01 from both sides.

(0.01)*(8)*(25) = (0.01)*(25)*(8)

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Fam_Fam posted...

it's called the commutative and associative properties of multiplication.

they do teach it,

Squall28 posted...

All it is is factoring out .01, and they're the same.

.01(25)(8)

Very true. Yes they taught us those properties. I never noticed the applicability of most of them, because they weren't something that was mentioned when the teacher was teaching us new things. We basically just had to define them in the first 2 weeks of school every year, then never looked at them again.

Neat, and thank you.

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123456789 + 123456789 = 246,913,578
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Smashingpmkns posted...

123456789 + 123456789 = 246,913,578

Is there a trick to that as I would have to write it out personally.

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better proof is

assume x * y/100 = z, x and y can be any number

multiply (x * y/100) by 100/100, which is the same as multiplying it by 1

then you have x/100 * y = z

therefore x * y/100 = x/100 * y
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A great thing to trigger people, on the other hand, is .9... = 1

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10% of 100

is

100% of 10

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commutative property is literally like 3rd grade stuff. And then retaught again basically every year, especially in algebra 1. If you didn't learn that in school you probably didn't pay attention.

Ic3Bullet posted...

Very true. Yes they taught us those properties. I never noticed the applicability of most of them, because they weren't something that was mentioned when the teacher was teaching us new things. We basically just had to define them in the first 2 weeks of school every year, then never looked at them again.

Well the important thing is you know why you can do something as opposed to learning a little math trick like this.

Frankly I've always thought learning stuff like the commutative property was a waste of time. All they did was ask you to recognize it when you see it, and name it.

We know by easy visualization that 2x4 is the same as 4x2. 4 rows of 2 or 2 rows of 4.

Now let's say you factor out. Every spot is now worth 2 instead of 1 but occupies half the volume. If you have cookies in this row, you can just double stack the cookies you already have. Either way you still have 8 cookies.

Understanding the logic behind it is much more important than the name.


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just move the % two spaces over .08 x 25

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Comfy_Pillow posted...

Can you elaborate on this? I'm interested but genuinely don't understand

percent just means you divide sth by 100 (or multiply it by 0.01, same thing)

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Heres one they never explain fully in high school math class for some reason

i^2= -1 because multiplying by i is the same as a rotation by 90 degrees in the complex plane

And why the hell dont they teach more topology in hs?

https://youtu.be/AmgkSdhK4K8

Math is great

Romes187 posted...

Heres one they never explain fully in high school math class for some reason

i^2= -1 because multiplying by i is the same as a rotation by 90 degrees in the complex plane

There's a lot of things they really should teach earlier

Like derivatives could be introduced waaaaay earlier. I mean, they basically already are, as the "rise over run" slopes
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Romes187 posted...

Heres one they never explain fully in high school math class for some reason

i^2= -1 because multiplying by i is the same as a rotation by 90 degrees in the complex plane

I mean...that's the reason the complex plane is set up that way. It's not some hidden property of i.


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Romes187 posted...

Heres one they never explain fully in high school math class for some reason

i^2= -1 because multiplying by i is the same as a rotation by 90 degrees in the complex plane

Eh, it's more that i is defined as i^2 = -1 and then all the complex plane polar coordinate stuff arises from that definition.

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ZeldaMutant posted...

Eh, it's more that i is defined as i^2 = -1 and then all the complex plane polar coordinate stuff arises from that definition.

what I mean is the physical-ness of the property is never explained to young children

Anteaterking posted...

I mean...that's the reason the complex plane is set up that way. It's not some hidden property of i.

the reason imaginary numbers (a dumb name) were discovered was to find roots to equations like x^2+1=0

which leads to the fundamental theorem of algebra

The fact that its a rotation is indeed hidden in a sense. Also of note is in polar coordinates the multiplicative group action on C is converted to an additive action (you add the angles when multiplying the complex numbers)

which has a nice relation to logarithms

math is awesome

If you really want something cool

https://youtu.be/AKotMPGFJYk

thats an example of a principle bundle which is a way to model physical systems at the fundamental Level

bundle physics is the best physics