1.7: Solving Equations by Multiplication and Division.1.6: Solving Equations by Addition and Subtraction.The first order of business is to introduce the various symbols used to indicate multiplication of two whole numbers. 1.3: Multiplication and Division of Whole Numbers We begin this section by discussing multiplication of whole numbers.1.2: Adding and Subtracting Whole Numbers.1.1: An Introduction to the Whole Numbers.We will use equations to model and solve a number of real-world applications along the way. Finally, we will introduce the concept of a variable, then introduce equations and technique required for their solution. This will lay the foundation for requisite skills with fractional numbers in later chapters. We will also define what is meant by prime and composite numbers, discuss a number of divisibility tests, then show how any composite number can be written uniquely as a product of prime numbers. Along the way we will introduce a number of properties of the whole numbers and show how that can be used to evaluate expressions involving whole number operations. We will then follow with a quick review of addition, subtraction, multiplication, and division skills involving whole numbers that are prerequisite for success in the study of prealgebra. In this first chapter of study, we will introduce the set of natural numbers, then follow with the set of whole numbers. The set of whole numbers is a subset of the integers but does not include the negative integers.\) The whole numbers are the natural numbers together with 0. Whole Numbers begin from 0 and end at infinity. Natural Numbers begin from 0 and counts till infinity. Yes, all Natural Numbers are Whole Numbers but not all Whole Numbers are Natural Numbers. The Letter W represents the Whole Numbers.ģ. We know as per the Distributive Property a.(b+c) =(a.b)+(a.c)Īpplying the Input Numbers in the formula we have the equation as such Solve 8 × (3 + 12) using the Distributive Property? ![]() Difference between Natural Numbers and Whole Numbers Whole NumbersĪll whole numbers are not natural numbersīy referring to the below sections you will better understand the difference between Whole Numbers and Natural Numbers.ġ. a.0=0.a=0ĭivision by Zero: If you divide a Whole Number with Zero the result is undefined, i.e. Multiplication by Zero: If you multiply a Whole Number with Zero the result is always zero. (b.c)=(a.b).cĭistributive Property: If a, b, c are three whole numbers then the distributive property of multiplication over addition is given by a.(b+c) =(a.b)+(a.c), Similarly Distributive Propoerty of Multiplication over Subtraction is given by a.(b-c) = (a.b)-(a.c) If a, b, c are whole numbers then a + (b + c) = (a + b) + c and a. = aĪssociative Property: If you are grouping the whole numbers and adding or multiplying a set the result remains the same irrespective of the order. Let us consider a whole number “a” then a.1 = 1. Multiplicative Identity: Whenever you multiply a whole number with 1 the result remains unchanged. If a is a whole number then a+0 = 0+a = a If a, b are two whole numbers then a+b = b+a, a.b = b.aĪdditive Identity: If a Whole Number is added to 0 the result remains unchanged. If a, b are two whole numbers then a.b and a+b is also a whole number.Ĭommutative Property of Addition and Multiplication: Sum and Product of Two Whole Numbers will be the same no matter the order in which they are added or multiplied. Let us see few more Properties of Whole Numbers by referring below.Ĭlosure Property: Whole Numbers can be closed under addition or multiplication. Division of Whole Numbers can result in a Fraction at times. ![]() ![]() If you Subtract Two Whole Numbers the result may not always be a Whole Number and it can be an Integer too. ![]() When you multiply or add two whole numbers the result will always be a Whole Number. Whole Numbers Properties depend on arithmetic operations such as Addition, Subtraction, Multiplication, Division. All positive integers including zero are whole numbers.The Symbol to denote the Whole Numbers is given by the alphabet W = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,… You can perform all the basic operations such as Addition, Subtraction, Multiplication, and Division. Whole numbers are positive integers along with zero and don’t have fractional or decimal parts. It is denoted by the symbol “W” and is given as Whole Numbers are numbers that don’t have fractions and is a collection of positive integers including zero. Complete Set of Natural Numbers including “0” are called Whole Numbers. Thus, we can say that Whole Numbers are Real Numbers but not all Real Numbers are Whole Numbers. These numbers are present on the number line and are usually called real numbers. Whole Numbers is a part of a number system that includes all the positive integers from 0 to infinity.
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