P = V * ( V / R ) = V2 / R

Jerramundi

Senior Member
Location
Chicago
Occupation
Licensed Residential Electrician
Because you would be inserting an extra 1/R in the equation that wasn't there in the first place.
@Carultch is correct. To put it simply, you're inserting an extra R in your V*V/R*R

When we first learned about the Distributive Property way back when, we used to draw arrows to help it make sense, like this:
1602608354957.png
The B and C here are two different values, both "receive" the A.

I think the reason you're getting confused is because the ( V / R ) is spaced out horizontally, because you have to do it that way when typing, and it looks similar to the B + C.

You have to think of the ( V / R ) as ONE number, A FRACTION. So when you distribute the V it actually looks like this:
1602608740846.png 1602609147384.png

When you multiple by a fraction ( V / R ), you have to convert the whole number ( V ) to a fraction too... because those are simply the rules of multiplying fractions. You multiply the top two numbers (i.e. numerators) and the bottom two numbers (i.e. denominators) separately.
1602610133934.png

Any number divided by 1 is equal to itself.
 

myspark

Senior Member
Location
SCV Ca, USA
Occupation
Retired EE
Here's a basic list off mathematical properties/laws:
  • Commutative Property of Addition
  • Commutative Property of Multiplication
  • Associative Property of Addition
  • Associative Property of Multiplication
  • Additive Identity Property
  • Multiplicative Identity Property
  • Additive Inverse Property
  • Multiplicative Inverse Property
  • Multiplicative Property of Zero
  • Additive Property of Zero
  • Substitution Property
  • Distributive Property
  • Division Property
  • Inverse Property of Inequality/Equality
There are more, but it's a good starting point.
Those GUIDELINES are sort of STARE DECISIS (pronounced stah-ree). In Latin means “it’s been done, so that’s the way it shall be.”.
What this implies is ROTE LEARNING.

Basic properties are necessary in early learning of Math.
It is taught in early stages.. . . but in advanced HOTS (Higher Order Thinking Skills) this ROTE LEARNING is simply memorization based on repetition.

This type of learning deprive student the ability to analyze, comprehending, application and evaluation. In other words CRITICAL THINKING is missing.
This is an approach before an exam is conducted often called “CRAMMING”. I know I did it it myself when I was a student. Chances of passing the test is likely. . . but can be forgotten easily.

As a student go into HOTS like higher MATHs. . . as in Algebra, Trigonometry , Differential and Integral Calculus--rote learning becomes a hindrance because lessons are far more engaged in decision-making.

Cumulative Algebra is carried all through the pursuit of higher Math especially this CUMULATIVE CALCULUS--along with other Engineering Fundamentals (FE).
 

Jerramundi

Senior Member
Location
Chicago
Occupation
Licensed Residential Electrician
Those GUIDELINES are sort of STARE DECISIS (pronounced stah-ree). In Latin means “it’s been done, so that’s the way it shall be.”.
What this implies is ROTE LEARNING.
I posted those "guidelines" because it was clear to me that the OP was lacking in an understanding of these "guidelines" and you gotta start somewhere. Why not start with a basic Wikipedia list of Mathematical Principles and go from there? The validity of Wikipedia as a source is often challenged, and sometimes rightfully so, but it still often provides a good "jumping off point."

I don't see what specifying what "type of learning" these fall under accomplishes other than to start a debate about our country's education system, which may be merited in other contexts, but really does nothing to help the OP move forward.
 

myspark

Senior Member
Location
SCV Ca, USA
Occupation
Retired EE
Had a PE tell me one time years ago it’s not what you learned, it what you understood
Exactly.
As Einstein once said:
If everything is understood during the learning process, it becomes really hard to forget.

Education is what remains after everything else is forgotten.

Albert Einstein
 

kreemoweet

Member
Location
Seattle
Occupation
Retired
The "alt" key codes on Windows are not Unicode, it's just some stuff Microsoft thought up one day. The real Unicode
for "superscript 2" is "00B2". On a Linux system, you can enter unicode characters by typing <CTRL>+<SHIFT>+<u>, and
then the 4 digits of the unicode codepoint. Like this: ²
 

synchro

Senior Member
Location
Chicago, IL
Occupation
EE
The "alt" key codes on Windows are not Unicode, it's just some stuff Microsoft thought up one day. The real Unicode
for "superscript 2" is "00B2". On a Linux system, you can enter unicode characters by typing <CTRL>+<SHIFT>+<u>, and
then the 4 digits of the unicode codepoint. Like this: ²
Or on a Mac you enter the hexadecimal digits for Unicode characters with the Option key, provided that you've selected "Unicode Hex Input" in the keyboard preferences.
 
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