5/6 as a Product of a Whole Number
5/6 as a Product of a Whole Number.
The
whole numbers
are the part of the number system which includes all the positive integers from 0 to infinity. These numbers exist in the number line. Hence, they are all
existent numbers
. Nosotros tin say, all the whole numbers are existent numbers, only not all the real numbers are whole numbers.
Thus, we tin can define whole numbers equally the prepare of natural numbers and 0. Integers are the set of whole numbers and negative of natural numbers. Hence, integers include both positive and negative numbers including 0. Real numbers are the set of all these types of numbers, i.e., natural numbers, whole numbers, integers and fractions.
The complete gear up of natural numbers along with ‘0’ are chosen whole numbers. The examples are: 0, 11, 25, 36, 999, 1200, etc.
Learn more than wellnigh
numbers
here.
 Definition
 Symbol
 Backdrop
 Closure
 Commutative
 Condiment
 Multiplicative
 Associative
 Distributive
 Whole Numbers and Natural numbers
 Solved Examples
 Practice Problems
 Video Lesson
 FAQs
Contents
 1 Whole Numbers Definition
 2 Whole Numbers Properties
 3 Divergence Between Whole Numbers and Natural Numbers
 4 Solved Examples
 5 Video lesson
 6
Ofttimes Asked Questions on Whole Numbers
 6.1 What are whole numbers?
 6.2 Tin whole numbers be negative?
 6.3 What are the properties of whole numbers?
 6.4 Is 10 a whole number?
 6.5 Which numbers are not whole numbers?
 6.6 Are all whole numbers existent numbers?
 6.7 Are all natural numbers, whole numbers?
 6.8 Are natural numbers and counting numbers the aforementioned?
 7 5/6 as a Product of a Whole Number
Whole Numbers Definition
The
whole numbers
are the numbers without fractions and information technology is a collection of positive integers and naught. It is represented past the symbol “W” and the set of numbers are {0, 1, 2, iii, 4, 5, 6, 7, viii, 9,……………}. Null as a whole represents null or a null value.
 Whole Numbers: West = {0, ane, 2, 3, four, five, 6, seven, eight, 9, 10……}
 Natural Numbers: N = {1, 2, 3, 4, v, 6, 7, 8, 9,…}
 Integers: Z = {….nine, 8, 7, vi, 5, 4, 3, 2, ane, 0, 1, ii, three, 4, v, 6, 7, 8, nine,…}
 Counting Numbers: {ane, ii, iii, 4, 5, halfdozen, vii,….}
These numbers are positive integers including aught and do not include partial or decimal parts (3/4, 2.2 and 5.3 are non whole numbers). Also, arithmetic operations such every bit addon, subtraction, multiplication and partition are possible on whole numbers.
Symbol
The symbol to correspond whole numbers is the alphabet ‘W’ in capital letters.
Due west = {0, 1, ii, three, 4, v, 6, 7, 8, 9, 10,…}
Thus, the
whole numbers list
includes 0, i, two, three, 4, v, 6, 7, 8, 9, 10, 11, 12, ….
Facts:
 All the natural numbers are whole numbers
 All counting numbers are whole numbers
 All positive integers including zero are whole numbers
 All whole numbers are real numbers
If you lot still take doubt, What is a whole number in maths? A more comprehensive understanding of the whole numbers tin be obtained from the following nautical chart:
 Whole Numbers and Natural Numbers
 Natural Numbers
 Difference Between Natural and Whole numbers
 Important Questions For Class vi Maths
Whole Numbers Properties
The backdrop of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. Ii whole numbers if added or multiplied will give a whole number itself. Subtraction of two whole numbers may not result in whole numbers, i.e. it tin can be an integer too. Also, the division of two whole numbers results in getting a fraction in some cases. Now, let us run across some more backdrop of whole numbers and their proofs with the help of examples here.
Closure Property
They can be closed nether addon and multiplication, i.due east., if x and y are 2 whole numbers then x. y or x + y is also a whole number.
Instance:
5 and 8 are whole numbers.
five + 8 = 13; a whole number
v × 8 = 40; a whole number
Therefore, the whole numbers are closed nether addition and multiplication.
Commutative Property of Addition and Multiplication
The sum and product of two whole numbers volition be the aforementioned whatsoever the guild they are added or multiplied in, i.eastward., if x and y are two whole numbers, then x + y = y + x and 10 . y = y . x
Example:
Consider two whole numbers 3 and 7.
3 + 7 = 10
seven + 3 = 10
Thus, 3 + 7 = vii + iii .
Also,
three × 7 = 21
7 × iii = 21
Thus, 3 × seven = 7 × 3
Therefore, the whole numbers are commutative under addition and multiplication.
Additive identity
When a whole number is added to 0, its value remains unchanged, i.e., if x is a whole number and then x + 0 = 0 + ten = x
Instance:
Consider two whole numbers 0 and eleven.
0 + 11 = xi
11 + 0 = 11
Here, 0 + xi = 11 + 0 = xi
Therefore, 0 is called the additive identity of whole numbers.
Multiplicative identity
When a whole number is multiplied past i, its value remains unchanged, i.due east., if ten is a whole number so x.1 = x = 1.10
Example:
Consider two whole numbers one and 15.
one × 15 = fifteen
15 × 1 = 15
Here, 1 × xv = fifteen = fifteen × one
Therefore, 1 is the multiplicative identity of whole numbers.
Associative Property
When whole numbers are being added or multiplied equally a fix, they can be grouped in whatever gild, and the result will be the aforementioned, i.e. if x, y and z are whole numbers then x + (y + z) = (x + y) + z and x. (y.z)=(10.y).z
Example:
Consider 3 whole numbers 2, 3, and 4.
ii + (three + 4) = 2 + 7 = 9
(ii + three) + 4 = 5 + 4 = 9
Thus, ii + (three + 4) = (2 + 3) + iv
2 × (3 × 4) = 2 × 12 = 24
(2 × 3) × 4 = 6 × 4 = 24
Here, two × (iii × four) = (2 × 3) × 4
Therefore, the whole numbers are associative nether improver and multiplication.
Distributive Property
If ten, y and z are three whole numbers, the distributive property of multiplication over addition is x. (y + z) = (10.y) + (x.z), similarly, the distributive property of multiplication over subtraction is x. (y – z) = (ten.y) – (x.z)
Instance:
Let the states consider three whole numbers ix, xi and vi.
nine × (11 + 6) = 9 × 17 = 153
(9 × 11) + (9 × 6) = 99 + 54 = 153
Hither, 9 × (11 + 6) = (9 × 11) + (9 × 6)
Also,
ix × (11 – vi) = 9 × 5 = 45
(ix × eleven) – (9 × six) = 99 – 54 = 45
So, nine × (xi – halfdozen) = (9 × xi) – (9 × halfdozen)
Hence, verified the distributive property of whole numbers.
Multiplication by zilch
When a whole number is multiplied to 0, the result is e’er 0, i.e., x.0 = 0.x = 0
Example:
0 × 12 = 0
12 × 0 = 0
Here, 0 × 12 = 12 × 0 = 0
Thus, for any whole number multiplied past 0, the event is e’er 0.
Division by zero
The division of a whole number past o is not defined, i.e., if x is a whole number then x/0 is not defined.
Also, check:
Whole number calculator
Divergence Between Whole Numbers and Natural Numbers
Departure Betwixt Whole Numbers & Natural Numbers 


Whole Numbers  Natural Numbers 
Whole Numbers: {0, ane, two, 3, iv, 5, vi,…..}  Natural Numbers: {1, ii, iii, 4, five, vi,……} 
Counting starts from 0  Counting starts from 1 
All whole numbers are not natural numbers  All Natural numbers are whole numbers 
The below effigy will help u.s. to sympathise the deviation betwixt the whole number and natural numbers :
Can Whole Numbers be negative?
The whole number can’t be negative!
Every bit per definition: {0, 1, ii, 3, 4, 5, 6, 7,……till positive infinity} are whole numbers. At that place is no place for negative numbers.
Is 0 a whole number?
Whole numbers are the set of all the natural numbers including cypher. And then yes, 0 (zip) is non just a whole number merely the first whole number.
Solved Examples
Case one:Are 100, 227, 198, 4321 whole numbers?
Solution:Aye. 100, 227, 198, and 4321 are all whole numbers.
Example 2: Solve x × (5 + 10) using the distributive property.
Solution:
Distributive property of multiplication over the improver of whole numbers is:
x × (y + z) = (x × y) + (x × z)
ten × (v + 10) = (10 × 5) + (ten × 10)
= 50 + 100
= 150
Therefore, 10 × (five + 10) = 150
All the same, we tin can testify several examples of whole numbers using the backdrop of the whole numbers.
Practice Problems
 Write whole numbers between 12 and 25.
 What is the additive changed of the whole number 98?
 How many whole numbers are there between ane and 14?
To larn more than concepts like natural numbers, and real numbers in a more engaging manner, register at BYJU’Due south. Also, watch interesting videos on various maths topics by downloading BYJU’South– The Learning App from Google Play Store or the app store.
Video lesson
Ofttimes Asked Questions on Whole Numbers
What are whole numbers?
The whole numbers are defined equally positive integers including zero. The whole number does not contain any decimal or fractional function. It means that it represents the entire thing without pieces. The set up of whole numbers is mathematically represented as:
W = (0, i, 2, three, 4, 5,……}
Tin whole numbers be negative?
No, the whole numbers cannot exist negative. The whole numbers start from 0, 1, ii, 3, … and so on. All the natural numbers are considered as whole numbers, but all the whole numbers are not natural numbers. Thus, the negative numbers are not considered as whole numbers.
What are the properties of whole numbers?
The properties of whole numbers are:
Whole numbers are closed under addition and multiplication
The addition and multiplication of whole numbers is commutative
The addition and multiplication of whole numbers is associative
It obeys the distributive property of multiplication over addition
The condiment identity of whole numbers is 0
The multiplicative identity of whole numbers is 1
Is 10 a whole number?
x is a whole as well as a natural number. It is written as Ten in words. Although 10 as well represents a whole and not a fraction.
Which numbers are not whole numbers?
The numbers which practise not exist between 0 and infinity are not whole numbers. Negative integers, fractions or rational numbers are not whole numbers. Examples are 1, 5, ½, 9/4, pi, etc. are not whole numbers.
Are all whole numbers existent numbers?
Real numbers are those numbers that include rational numbers, integers, whole numbers and natural numbers. All whole numbers are real numbers just not all existent numbers are whole.
Are all natural numbers, whole numbers?
Natural numbers are those which start from 1 and end at infinity, whereas whole numbers beginning from 0 and end at infinity. All the natural numbers are whole numbers but not all whole numbers are natural.
Are natural numbers and counting numbers the aforementioned?
Natural numbers are the numbers starting from i and extend up to infinity. Counting numbers are used to count the objects or people or anything which is countable. Hence, we e’er start counting from ane.
5/6 as a Product of a Whole Number
Source: https://byjus.com/maths/wholenumbers/