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 well-nigh

numbers

here.

Table of contents:

  • Definition
    • Symbol
  • Backdrop
    • Closure
    • Commutative
    • Condiment
    • Multiplicative
    • Associative
    • Distributive
  • Whole Numbers and Natural numbers
  • Solved Examples
  • Practice Problems
  • Video Lesson
  • FAQs

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, half-dozen, 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 add-on, 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:

Real number system

  • 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 add-on 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 – half-dozen) = (9 × xi) – (9 × half-dozen)

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 :

Whole numbers-Number line

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

  1. Write whole numbers between 12 and 25.
  2. What is the additive changed of the whole number 98?
  3. 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/whole-numbers/