Whole numbers Lesson - Definition, Symbol, Properties and Examples

Lesson Overview

• Definition of Whole Numbers
• Whole Numbers on Number Line
• Properties of Whole Numbers
• Difference between Whole Numbers and Natural Numbers
• Whole Number Assessment

Whole numbers represent complete units without fractions or decimals. They are the positive integers along with zero, forming an infinite sequence that stretches from 0 to infinity. Whole numbers are essential for basic arithmetic operations, laying the groundwork for more advanced mathematical concepts.

Definition of Whole Numbers

A whole number is any non-negative number that does not include a fraction or decimal part. So, whole numbers are the set of natural numbers (counting numbers) including zero.

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Whole Numbers Quiz Questions And Answers

Key characteristics:

• Whole numbers are always greater than or equal to zero.
• They represent complete units.
• The set of whole numbers extends indefinitely.

Example:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12…

Whole numbers are fundamental for:

• Counting objects
• Measuring quantities
• Performing basic arithmetic operations (addition, subtraction, multiplication, division)
• Building a foundation for understanding more complex mathematical concepts.

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GRADE 6 MATH UNIT 2 WHOLE NUMBERS (25 MARKS)

Whole Numbers on Number Line

The number line is a graphical representation where numbers are placed at equal intervals along a straight line, extending infinitely in both directions.  

When we focus on whole numbers, we use the number line to represent the set of non-negative integers: {0, 1, 2, 3, 4, 5...}.

• The Origin: The number line starts with zero (0), which is called the origin.  
• Positive Direction: To the right of the origin, we mark equally spaced points, each representing a whole number in increasing order (1, 2, 3, and so on). This is the positive direction.
• No End: The number line extends infinitely to the right, indicating that the set of whole numbers is infinite.

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Natural, Whole, and Integer Numbers Quiz

Properties of Whole Numbers

Whole numbers have properties that govern how they behave in mathematical operations. Understanding these properties is essential for performing calculations correctly. 

1. Closure Property

• Addition: The sum of any two whole numbers is always a whole number.
  
  • Example: 5 + 3 = 8 (8 is a whole number)
    
• Multiplication: The product of any two whole numbers is always a whole number.
  
  • Example: 7 x 4 = 28 (28 is a whole number)
    
• Subtraction and Division: Whole numbers are NOT closed under subtraction and division.
  
  • Example: 3 - 5 = -2 (-2 is not a whole number)
  • Example: 10 ÷ 3 = 3.33... (3.33... is not a whole number)
    

2. Commutative Property

• Addition: The order in which you add two whole numbers does not affect the sum.
  
  • Example: 2 + 9 = 9 + 2 = 11
    
• Multiplication: The order in which you multiply two whole numbers does not affect the product.
  
  • Example: 6 x 3 = 3 x 6 = 18 
    

3. Associative Property

• Addition: When adding three or more whole numbers, the grouping of the numbers does not affect the sum.
  
  • Example: (4 + 5) + 2 = 4 + (5 + 2) = 11
    
• Multiplication: When multiplying three or more whole numbers, the grouping of the numbers does not affect the product.
  
  • Example: (2 x 3) x 5 = 2 x (3 x 5) = 30
    

4. Distributive Property

Multiplication distributes over addition and subtraction.  

• Example: 5 x (2 + 3) = (5 x 2) + (5 x 3) = 25
• Example: 8 x (7 - 3) = (8 x 7) - (8 x 3) = 32
  

5. Identity Property

• Additive Identity: The sum of any whole number and 0 is the whole number itself. 0 is the additive identity.
  
  • Example: 9 + 0 = 9
    
• Multiplicative Identity: The product of any whole number and 1 is the whole number itself. 1 is the multiplicative identity.
  
  • Example: 5 x 1 = 5

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PLACE VALUE OF WHOLE NUMBERS

Difference between Whole Numbers and Natural Numbers

Although closely related, whole numbers and natural numbers have a subtle yet important distinction.

Whole Number Assessment

1. Simplify: 8 x (5 + 3)

• Distribute: 8 x 5 + 8 x 3
• Calculate: 40 + 24
• Result: 64
  

2. Calculate: 12 + 7 + 8

• Group: (12 + 8) + 7
• Calculate: 20 + 7
• Result: 27
  

3. Find the value of 'x': x + 9 = 15

• Isolate 'x': x = 15 - 9
• Calculate: x = 6
  

4. Is 36 divisible by 3?

• Sum the digits: 3 + 6 = 9
• Check if the sum is divisible by 3: 9 is divisible by 3
• Result: Yes, 36 is divisible by 3.
  

5. A baker has 24 cookies and wants to arrange them equally on 4 plates. How many cookies will be on each plate?

• Divide: 24 cookies / 4 plates
• Calculate: 6 cookies/plate
• Result: Each plate will have 6 cookies.

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Rounding to whole numbers