Addition meaning and properties
I suppose you have 5 fingers in each hand.
If you put your two hands together, you make a new set of fingers out of the first two (the hands)
How many fingers in the new set, count them: 10. When you count by 1, you are in fact adding 1 to the previous result
You could see this new number of fingers as some combination (putting together, gathering) of the two numbers 5.
Mathematically you call this operation (combination) addition
The simplest things are sometimes the hardest to explain, or put into words.
Terminology: words
Let a and b be two numbers (Please do not ask me about their values: make up your own.)
The addition operation is symbolized by the + sign.
Addition of a and b, or of b to a is written as a+b.
The result of the operation is called its sum
If I write a+ b= c, where c is some number
b is called the addend ( it is short for addendum), c is the sum . For some authors both a and b are called addends. You could say that any number involved in an addition (operation) is an addend.
Properties
2+3= 3+2=5
For arbitrary numbers (numbers you may choose), you can write
a+b=b+a
The order of the terms (which comes first, and which second) has changed but the result is the same. This is a property that is common to (shared with) all additions. It has received a scientific name, commutativity.
The addition is a commutative operation and we write a+b=b+a
Now imagine you have to add three or more numbers
2+5 +17
You can do that in two steps
Add 2 and 5, then add the result to 17
(2+5)+17
You can also add in another way: add 5 and 17, then add the result to 2, which you write as 2+(5+17)
Let's compare the results of the two ways
(2+5)+17=7+17=24
2+ (5+17)=2+22=24
The two sums are identical. (2+5)+17=2+(5+17)=24
For other undisclosed numbers we can write
(a+b)+c=a +(b+c)
This property is verified by all sets of three numbers. It is a general property called associativity
There is another property
Neutral element.
In every set of numbers that has addition as a rule there is an element, call it e, such that
for any number a of the set a+e=e+a=a
the element e is called the neutral element, in that when added to a number it gives you back that number. For real numbers, the neutral element is the number 0.
Summary of words introduced :
To add, addition, terms, addends, result, sum, commutativity, commutative property, associativity, associative property, neutral element.
I will stop here, believing that you have ADDED many new terms (words) to you vocabulary.
×