/sci/ - Science & Math

>>5125478
The n example on the right in your picture used the rule in question 3 in the second line.

>>5125476
Not to mention, even using 1 I still don't quite understand it.

>>5125468
It's still an example like that because it's using a number (1).

>>5125463
I can understand an example like that but I don't understand why all fractions by their reciprocal equal 1.

>>5125452
I am pretty sure I understand that example but I don't understand the rule.

>>5125391
>A * (x^y) = A * x * x * x ... (A multiplied by x, done y times)
>A * (x^-y) = A /x /x /x /x ... (A divided by x, done y times) =A /(x * x * x...) = A / (x^y)

Why does the rule work?

>>5125391
>(z/x)/y = (z/x) * (1/y) = (z/(x*y))
(z/x)/y = ((z/x)*1)/y

>>5125391
>(x/y) * (z/k) = (x*z)/(y*k) <-- this is a goofy one to go into full detail on. More or less, you have a fraction of fractions, so you could look at it as getting z/k, multiplying it by x to get (x*z)/k, then dividing by y to get (x*z)/(k*y)
so i go (x*z)/k and divide by y. but that's ((x*z)/k)/y

>>5125297
>If you confuse the number of pieces with the number of cuts the student will confuse multiplication with addition and division with subtraction
Am I doing that?

>>This is why this is an interactive exercise, having the student actually cut and glue either clay blocks or paper.
I don't understand the whole and pieces in the first place.

>>5125297
>This is why some mathematicians make such fucked up teachers...They are more interested in their egos "I'm so smart and your so dumb so just do as I say and call me your highness...look at me mommie, look at me!" Instead of taking the time and creative effort to understand how other people think and tailoring their lessons to the students temperament and ability.
>Go drown in a pool of vomit, you arrogant bowl of fail.
I'm pretty confused. Are you talking to me or someone else?

>>5125252
>If I cut a whole up into some number of pieces, how many time must I glue pieces together to make it whole again?
You need to glue it by the number of pieces you cut it up by.

>The amount I cut is always equal to the amount I glue if I want my whole back.
What do you mean the amount you glue? And glue "back"? Back from what?

>A multiple number of wholes are each cut up the same amount of times.
Wait, I can't go further until I know which parts of the equation are the "wholes".

>>5125259
>Dont be 2 years old and ask why for everything. Explain exactly what you don't understand, otherwise no one can understand what you don't understand and we can't help you.
What exactly I don't understand is the parts that I quote or say I don't understand.

>>5125241
I'm more confused than ever now.

>>5125249
>right loudly "n*1/n"
Where did we get to n*1/n? I don't get what part you mean. Which part are you explaining and why n*1/n?

>if you part a pie in n pieces and keep the n pieces, you still get 1 pie.
By what do you mean "keep"? In the thing that you are explaining, is the mathematical concept based on "keeping" something?

>>5125240
>3/1*1/3 is the same as 3*1 over 1*3 based on how fractions work.
This goes to question 3 in my original post. I can't get the next parts of your post.

>>5125233
>>5125233
>Because 3 in fractional form is 3/1 and 3/1*1/3 is 3*1/1*3 which is 3/3 which is 1.
Why?

>>5125179
Yeah, I'm aware that 3 x 1/3 = 1 because 3/3=1. But why? Why is it that all fractions multiplied by their reciprocal = 1?

Also, I didn't get what you were talking about with b).

>>5125185
Saying the same thing as what? I don't understand what you mean here.

1. Something multiplied by it's reciprocal equals 1.

2. Something divided by a number is the same as it being multiplied by its reciprocal.

3. A fraction multiplied by another fraction is the same as their numerators multiplied together divided by their denominators multiplied by each other.

4. A number multiplied by a number divided by a number multiplied by a number is the same as one of the numerators divided by the product of the denominators and the total of that multiplied by the other numerator.

5. A number to the power of a negative number is the same as it's reciprocal to the power of the same power with the opposite sign.

6. A number to the power of a fraction is the same as the root of that number to the degree of the denominator (not sure if I wrote that right) and the product of that to the power of the numerator.

Can anyone explain why instead of just using examples because I can see that examples and proofs work, I just don't understand why they work.