Whole Numbers Class 6 PPT

 Page 2


3.1 Addition and Subtraction
Definition: Let a and b be any two whole 
numbers.  If A and B are disjoint sets with a = 
n(A) and b = n(B), then 
( ) B A n b a ? = +
Addition is called a binary operation because two 
numbers are combined to produce a unique 
number. 
Page 3


3.1 Addition and Subtraction
Definition: Let a and b be any two whole 
numbers.  If A and B are disjoint sets with a = 
n(A) and b = n(B), then 
( ) B A n b a ? = +
Addition is called a binary operation because two 
numbers are combined to produce a unique 
number. 
3.1 Addition and Subtraction
Set Model
To find a + b, we need to find two disjoint sets, one 
with a objects and one with b, form their union 
and count their total.
Example: Find 3+2 using the set model.
3
2
3+2=5
Page 4


3.1 Addition and Subtraction
Definition: Let a and b be any two whole 
numbers.  If A and B are disjoint sets with a = 
n(A) and b = n(B), then 
( ) B A n b a ? = +
Addition is called a binary operation because two 
numbers are combined to produce a unique 
number. 
3.1 Addition and Subtraction
Set Model
To find a + b, we need to find two disjoint sets, one 
with a objects and one with b, form their union 
and count their total.
Example: Find 3+2 using the set model.
3
2
3+2=5
Measurement Model
In the measurement model, addition of whole numbers is 
represented by directed arrows of whole number lengths 
along with the whole number line.
0 1 2 3 4 5 6 7 8 9 10 11 12
Example: 2 + 5
Place an arrow length 2 
starting at 0.
2
Then place an arrow length 
5 starting at the end of the 
first arrow.
5 +
The sum is the total 
distance from 0.
Page 5


3.1 Addition and Subtraction
Definition: Let a and b be any two whole 
numbers.  If A and B are disjoint sets with a = 
n(A) and b = n(B), then 
( ) B A n b a ? = +
Addition is called a binary operation because two 
numbers are combined to produce a unique 
number. 
3.1 Addition and Subtraction
Set Model
To find a + b, we need to find two disjoint sets, one 
with a objects and one with b, form their union 
and count their total.
Example: Find 3+2 using the set model.
3
2
3+2=5
Measurement Model
In the measurement model, addition of whole numbers is 
represented by directed arrows of whole number lengths 
along with the whole number line.
0 1 2 3 4 5 6 7 8 9 10 11 12
Example: 2 + 5
Place an arrow length 2 
starting at 0.
2
Then place an arrow length 
5 starting at the end of the 
first arrow.
5 +
The sum is the total 
distance from 0.
Properties
1. Closure Property for Whole-Number Addition
The sum of any two whole numbers is a whole number.
2. Commutative Property for Whole-Number Addition
Let a and b be any whole numbers.  Then a+b=b+a.
3. Associative Property for Whole-Number Addition
Let a, b and c be any whole numbers.  
Then (a+b) + c = a + (b+c).
4. Identity Property for Whole-Number Addition
There is a unique whole number, 0, such that for all 
whole numbers a, a + 0 = 0 + a = a.