When we build integers from natural numbers, we're looking for additive inverse of natural numbers?
What's an additive inverse? Well, for example, the additive inverse of 2 is a numbers 
such that
We call this number -2. So, the real meaning behind the negative sign is "if you add me and my positive counterpart, the result is zero".
So, -5 is the additive inverse of 5, -16 is the additive inverse of 16, and so on, because
Note that this is a symmetrical relation: if -5 is the inverse of 5, it is also true that 5 is the inverse of -5.
So, when you write something like
it means that you want to add 5 and the inverse of the inverse of 4. But given what we just said, the inverse of the inverse of a number is the number itself, which is why subtracting a negative number is the same as adding it.
Answer:
2,090
Step-by-step explanation:
. Now the answers on your paper do not have this choice, but if you think about it, (2-x)=-1(x-2) and (1-x)=-1(x-1). This means that when you have (2-x)/(1-x), this also equals to (x-2)/(x-1), since the -1's cancel out. So, the answer is D.
I hope this was helpful!
Answer:
<em>When 60 beats are heard, Tom hits 15 snare drums, Sam hits 6 kettle drums, and Matt hits 5 bass drums.</em>
Step-by-step explanation:
The Least Common Multiple ( LCM )
The LCM of two integers a,b is the smallest positive integer that is evenly divisible by both a and b.
For example:
LCM(20,8)=40
LCM(35,18)=630
Since Tom, Sam, and Matt are counting drum beats at their own frequency, we must find the least common multiple of all their beats frequency.
Find the LCM of 4,10,12. Follow this procedure:
List prime factorization of all the numbers:
4 = 2*2
10 = 2*5
12 = 2*2*3
Multiply all the factors the greatest times they occur:
LCM=2*2*3*5=60
Thus, when 60 beats are heard, Tom hits 15 snare drums, Sam hits 6 kettle drums, and Matt hits 5 bass drums.
