What does the term "parallel resistor equivalents" mean?

[Stuartambient]

I am looking at two pairs of parallel resistors.  One is 100 Ohm and 250 Ohm and the other is 350 Ohm and 200 Ohm. I mostly get how parallel resistors work, but I'm being thrown when this term parallel resistor equivalents.  Mostly because I'm not seeing how they are equivalent. 

Hope this is not too silly a question.  Thanks!

[Zero999]

Well 100 Ohm is equivalent to two 200 Ohm resistors connected in parallel.

Quite often you'll see something like R3 = R1|R2 on schematics, which means R3 needs to equal the value of R1 & R2 connected in parallel, so if R1 & R2 are 200 Ohm then R3 = 100 Ohm.

[StillTrying]

Could it mean you use r*r/(r+r) on each pair, which would then leave you with "2 parallel resistor equivalents",
- which you could then use r*r/(r+r) on again. 

Edit: Had r*r/(r+r) upside down. 

[rstofer]

The parallel combination of two resistors is their product over their sum.  So, two 100 Ohm resistors in parallel => (100 * 100) / (100 + 100) or 10,000 / 200 or 50 Ohms.

Here is a crib sheet:
http://www.calvin.edu/~svleest/circuitExamples/equRes/

Look at the 4th sketch, what a mess!  Let's start...

Add up the 3 series resistors on the right edge (3+6+9) = 18 Ohms.  Now calculate that 18 Ohms in parallel with the 5 Ohm resistor (5*18)/(5+18) and let's just call it 3.9 Ohms.

Now combine that 3.9 Ohms wth the 2 & 8 Ohm resistors to get 13.9 Ohms. Calculate the 13.9 Ohms in parallel with the 4 Ohm resistor and get 3.1 Ohms

Finally, combine the 3.1 Ohms with 7 & 1 Ohm resistor to get 11.1 Ohms total equivalent resistance.

That about covers it!
Arithmetic errors are all mine...

[Stuartambient]

I'm about to run out so we'll need to read through the much appreciated responses.  My thinking was that the two pairs of parallel resistors were being called equivalent to each other but now I believe it's showing that after the parallel resistors are reduced to their values in the circuit you can use an equivalent value resistor in a serial hookup.

[Stuartambient]

Could it mean you use r+r/(r*r) on each pair, which would then leave you with "2 parallel resistor equivalents",
- which you could then use r+r/(r*r) on again. 

That might be the formula.  I took for the first parallel 1/100 and 1/250 = 5/500 and 2/500 = 7/500 = 1/.014 = 71.429 Ohms.  Used the same convoluted approach to the second.  So I think the equivalent just means if I replaced the parallel resistors with one serial it should be 71.xx Ohms for the first one.

[StillTrying]

That might be the formula.

Bare in mind that I had r*r/(r+r) upside down. I tend to use 1/r + 1/r = 1/r even when there's just 2 resistors.
Some I can do in my head  50R+100R = ( (100R+100R) + 100R )/3 = 33.3R.

[Stuartambient]

The parallel combination of two resistors is their product over their sum.  So, two 100 Ohm resistors in parallel => (100 * 100) / (100 + 100) or 10,000 / 200 or 50 Ohms.

Here is a crib sheet:
http://www.calvin.edu/~svleest/circuitExamples/equRes/

Good link too, thank you!