please clear my algebra concept

Question

one half times fourteen lowered by the factor of 4 and z

 

1/2(14-4z) this is algebric translation from english.

1. i figure out 1/2*14-4 but afterword i did understand  how this statement directs that bracket is for whole 14-4z
2. next the said factor of 4 and z so how 4 and z get multiplied 

please tell me the meaning of this statement and how statement leads to correct algebric expression 

 

Answer 1

Good morning, Amey!  Thanks for taking the time to write out what you were having difficulty with.  You've run across a tough one from what I can tell that takes a bit to explain and in the end may require your math teacher to reconsider.  I agree that the two points you made could be interpreted differently than shown in the "book" answer.

 

Hearing someone speak that same english expression would probably give you cues that are important for this one. When english words are written down to describe math expressions, you will usually find that commas, word order, phrasing, and "end result" words are very helpful to use to know whether or not specific terms should be grouped. Typically commas are used to indicate where a group is intended. If you happen to leave out any then it could change the meaning.  Make sense?

 

It looks like you understand the "fourteen lowered by" part.  I'd have said "the quantity of" in front of that to be very clear what thing the "one half" was supposed to apply to exactly.  Its not very common to say 1/2 * 14 in any algebraic expression involving a variable.  Key words like sum, product, total, all are also used to help indicate things that should go together. The example you've posted used the word "factor" in a way that I've not seen and seems to be the most confusing part for you.  

 

I agree.  I typically see the word "factor" used when someone is talking about a PART of something that represents a product (result of multiplication) not the RESULT of multiplying two values, which I would also have called a "multiple."  So I would say that 4z would be called a product of factors 4 and z.  4z could also be called a multiple of z or a multiple of 4.  This would definitely be worth having your math teacher explain more fully.  Hope this helps!