Chapter 2: Whole Numbers
Introduction to Whole Numbers
What are Whole Numbers?
Whole numbers are a set of numbers that include all natural numbers and zero. They do not have any fractional or decimal parts. Examples of whole numbers are 0, 1, 2, 3, etc.
Importance of Whole Numbers
Whole numbers are used in everyday counting and ordering. They are fundamental in various mathematical operations and concepts.
Successor and Predecessor
Successor
The successor of a whole number is the number that comes immediately after it. For example, the successor of 3 is 4.
Predecessor
The predecessor of a whole number is the number that comes immediately before it. For example, the predecessor of 5 is 4. Note that zero has no predecessor in whole numbers.
Properties of Whole Numbers
Closure Property
Whole numbers are closed under addition and multiplication. This means that the sum or product of any two whole numbers is always a whole number.
Commutative Property
Whole numbers satisfy the commutative property for addition and multiplication. For any two whole numbers (a) and (b):
[ a + b = b + a ]
[ a times b = b times a ]
Associative Property
Whole numbers satisfy the associative property for addition and multiplication. For any three whole numbers (a), (b), and (c):
[ (a + b) + c = a + (b + c) ]
[ (a times b) times c = a times (b times c) ]
Distributive Property
The distributive property of multiplication over addition is applicable to whole numbers. For any three whole numbers (a), (b), and (c):
[ a times (b + c) = (a times b) + (a times c)]
Additive and Multiplicative Identity
Additive Identity
The additive identity for whole numbers is 0. Adding zero to any whole number does not change its value:
[ a + 0 = a ]
Multiplicative Identity
The multiplicative identity for whole numbers is 1. Multiplying any whole number by one does not change its value:
[ a times 1 = a]
Number Line
Representing Whole Numbers on a Number Line
Whole numbers can be represented on a number line. The number line helps to visualize the order and operations of whole numbers.
Operations on Number Line
Addition: To add two whole numbers, start from the first number and move to the right by the number of steps equal to the second number.
Subtraction: To subtract one whole number from another, start from the first number and move to the left by the number of steps equal to the second number.
Activities and Exercises
Practicing Whole Numbers
– Successor and Predecessor Exercises: Identify the successor and predecessor of given whole numbers.
– Properties of Whole Numbers: Solve problems using the closure, commutative, associative, and distributive properties.
Number Line Exercises: Represent whole numbers and perform addition and subtraction on a number line.
Summary
Key Points
– Whole numbers include all natural numbers and zero.
– Successor and predecessor help in understanding the sequence of whole numbers.
– Whole numbers follow closure, commutative, associative, and distributive properties.
– Zero is the additive identity, and one is the multiplicative identity.
– Number lines help in visualizing whole numbers and performing basic operations.
Frequently Asked Questions (FAQs)
Common Questions About Whole Numbers
1. What are whole numbers?
– Whole numbers are a set of numbers including all natural numbers and zero, without any fractions or decimals.
2. What is the successor of a whole number?
– The successor is the number that comes immediately after a given whole number.
3. What is the predecessor of a whole number?
– The predecessor is the number that comes immediately before a given whole number.
4. What are the properties of whole numbers?
– Whole numbers have closure, commutative, associative, and distributive properties.
5. How are whole numbers represented on a number line?
– Whole numbers are represented as equally spaced points on a number line.
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