presentation on natural numbers

• Math Article

Natural Numbers

Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity and are also used for counting purpose. It does not include zero (0). In fact, 1,2,3,4,5,6,7,8,9…., are also called counting numbers .

Natural numbers are  part of real numbers,  that include only the positive integers i.e. 1, 2, 3, 4,5,6, ………. excluding zero, fractions, decimals and negative numbers.

Note: Natural numbers do not include negative numbers or zero.

In this article, you will learn more about natural numbers with respect to their definition, comparison with whole numbers, representation in the number line, properties, etc.

Natural Number Definition

As explained in the introduction part, natural numbers are the numbers which are positive integers and includes numbers from 1 till infinity(∞). These numbers are countable and are generally used for calculation purpose.  The set of natural numbers is represented by the letter “ N ”.

N = {1,2,3,4,5,6,7,8,9,10…….}

Natural Numbers and Whole Numbers

Natural numbers include all the whole numbers excluding the number 0. In other words, all natural numbers are whole numbers, but all whole numbers are not natural numbers.

• Natural Numbers = {1,2,3,4,5,6,7,8,9,…..}
• Whole Numbers = {0,1,2,3,4,5,7,8,9,….}

Check out the difference between natural and whole numbers to know more about the differentiating properties of these two sets of numbers.

The above representation of sets shows two regions. A ∩ B i.e. intersection of natural numbers and whole numbers (1, 2, 3, 4, 5, 6, ……..) and the green region showing A-B, i.e. part of the whole number (0).

Thus, a whole number is “a part of Integers consisting of all the natural number including 0.”

Is ‘0’ a Natural Number?

The answer to this question is ‘No’. As we know already, natural numbers start with 1 to infinity and are positive integers. But when we combine 0 with a positive integer such as 10, 20, etc. it becomes a natural number. In fact, 0 is a whole number which has a null value.

Every Natural Number is a Whole Number. True or False?

Every natural number is a whole number. The statement is true because natural numbers are the positive integers that start from 1 and goes till infinity whereas whole numbers also include all the positive integers along with 0.

Representing Natural Numbers on a Number Line

Natural numbers representation on a number line is as follows:

The above number line represents natural numbers and whole numbers. All the integers on the right-hand side of 0 represent the natural numbers, thus forming an infinite set of numbers. When 0 is included, these numbers become whole numbers which are also an infinite set of numbers.

Set of Natural Numbers

In a set notation, the symbol of natural number is “N” and it is represented as given below.

N = Set of all numbers starting from 1.

In Roster Form:

N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ………………………………}

In Set Builder Form:

N = {x : x is an integer starting from 1}

Natural Numbers Examples

The natural numbers include the positive integers (also known as non-negative integers) and a few examples include 1, 2, 3, 4, 5, 6, …∞.  In other words, natural numbers are a set of all the whole numbers excluding 0.

23, 56, 78, 999, 100202, etc. are all examples of natural numbers.

Properties of Natural Numbers

Natural numbers properties are segregated into four main properties which include:

• Closure property
• Commutative property
• Associative property
• Distributive property 

Each of these properties is explained below in detail.

Closure Property

Natural numbers are always closed under addition and multiplication. The addition and multiplication of two or more natural numbers will always yield a natural number. In the case of subtraction and division, natural numbers do not obey closure property, which means subtracting or dividing two natural numbers might not give a natural number as a result.

• Addition: 1 + 2 = 3, 3 + 4 = 7, etc. In each of these cases, the resulting number is always a natural number.
• Multiplication: 2 × 3 = 6, 5 × 4 = 20, etc. In this case also, the resultant is always a natural number.
• Subtraction: 9 – 5 = 4, 3 – 5 = -2, etc. In this case, the result may or may not be a natural number.
• Division: 10 ÷ 5 = 2, 10 ÷ 3 = 3.33, etc. In this case, also, the resultant number may or may not be a natural number.

Note: Closure property does not hold, if any of the numbers in case of multiplication and division, is not a natural number. But for addition and subtraction, if the result is a positive number, then only closure property exists.

For example: 

• -2 x 3 = -6; Not a natural number
• 6/-2 = -3; Not a natural number
• Associative Property

The associative property holds true in case of addition and multiplication of natural numbers i.e. a + ( b + c ) = ( a + b ) + c and a × ( b × c ) = ( a × b ) × c. On the other hand, for subtraction and division of natural numbers, the associative property does not hold true . An example of this is given below.

• Addition: a + ( b + c ) = ( a + b ) + c => 3 + (15 + 1 ) = 19 and (3 + 15 ) + 1 = 19.
• Multiplication: a × ( b × c ) = ( a × b ) × c => 3 × (15 × 1 ) = 45 and ( 3 × 15 ) × 1 = 45.
• Subtraction: a – ( b – c ) ≠ ( a – b ) – c => 2 – (15 – 1 ) = – 12 and ( 2 – 15 ) – 1 = – 14.
• Division: a ÷ ( b ÷ c ) ≠ ( a ÷ b ) ÷ c => 2 ÷( 3 ÷ 6 ) = 4 and ( 2 ÷ 3 ) ÷ 6 = 0.11.
• Commutative Property

For commutative property

• Addition and multiplication of natural numbers show the commutative property. For example, x + y = y + x and a × b = b × a
• Subtraction and division of natural numbers do not show the commutative property. For example, x – y ≠ y – x and x ÷ y ≠ y ÷ x
• Distributive Property
• Multiplication of natural numbers is always distributive over addition. For example, a × (b + c) = ab + ac
• Multiplication of natural numbers is also distributive over subtraction. For example, a × (b – c) = ab – ac

Read More Here:

Operations With Natural Numbers

An overview of algebraic operation with natural numbers i.e. addition, subtraction, multiplication and division, along with their respective properties are summarized in the table given below.

Video Lesson on Numbers

Solved Examples

Question 1: Sort out the natural numbers from the following list: 20, 1555, 63.99, 5/2, 60, −78, 0, −2, −3/2

Solution: Natural numbers from the above list are 20, 1555 and 60.

Question 2: What are the first 10 natural numbers?

Solution: The first 10 natural numbers on the number line are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Question 3: Is the number 0 a natural number?

Solution: 0 is not a natural number. It is a whole number. Natural numbers only include positive integers.

Stay tuned with BYJU’S and keep learning various other Maths topics in a simple and easily understandable way . Also, get other maths study materials, video lessons, practice questions, etc. by registering at BYJU’S.

Frequently Asked Questions on Natural Numbers

What are natural numbers.

Natural numbers are the positive integers or non-negative integers which start from 1 and ends at infinity, such as:

1,2,3,4,5,6,7,8,9,10,……,∞.

Is 0 a Natural Number?

Zero does not have a positive or negative value. Since all the natural numbers are positive integers, hence we cannot say zero is a natural number. Although zero is called a whole number.

What are the first ten Natural Numbers?

The first ten natural numbers are: 1,2,3,4,5,6,7,8,9, and 10.

What is the difference between Natural numbers and Whole numbers?

Natural numbers include only positive integers and starts from 1 till infinity. Whereas whole numbers are the combination of zero and natural numbers, as it starts from 0 and ends at infinite value.

What are the examples of Natural numbers?

The examples of natural numbers are 5, 7, 21, 24, 99, 101, etc.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

Visit BYJU’S for all Maths related queries and study materials

Your result is as below

Request OTP on Voice Call

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Post My Comment

I like your answers for my mathematics Project Work

• Share Share

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

• School Guide
• Mathematics
• Number System and Arithmetic
• Trigonometry
• Probability
• Mensuration
• Maths Formulas
• Class 8 Maths Notes
• Class 9 Maths Notes
• Class 10 Maths Notes
• Class 11 Maths Notes
• Class 12 Maths Notes
• CBSE Class 9 Maths Revision Notes

Chapter 1: Number System

• Number System in Maths

Natural Numbers | Definition, Examples, Properties

• Whole Numbers | Definition, Properties and Examples
• Rational Number: Definition, Examples, Irrationals, Exercises
• Irrational Numbers- Definition, Identification, Examples, Symbol, Properties
• Real Numbers
• Decimal Expansion of Real Numbers
• Decimal Expansions of Rational Numbers
• Representation of Rational Numbers on the Number Line | Class 8 Maths
• Represent √3 on the number line
• Operations on Real Numbers
• Rationalization of Denominators
• Laws of Exponents for Real Numbers

Chapter 2: Polynomials

• Polynomials in One Variable - Polynomials | Class 9 Maths
• Polynomial Formula
• Types of Polynomials
• Zeros of Polynomial
• Factorization of Polynomial
• Remainder Theorem
• Factor Theorem
• Algebraic Identities

Chapter 3: Coordinate Geometry

• Coordinate Geometry
• Cartesian Coordinate System in Maths
• Cartesian Plane

Chapter 4: Linear equations in two variables

• Linear Equations in One Variable
• Linear Equation in Two Variables
• Graph of Linear Equations in Two Variables
• Graphical Methods of Solving Pair of Linear Equations in Two Variables
• Equations of Lines Parallel to the x-axis and y-axis

Chapter 5: Introduction to Euclid's Geometry

• Euclidean Geometry
• Equivalent Version of Euclid’s Fifth Postulate

Chapter 6: Lines and Angles

• Lines and Angles
• Types of Angles
• Pairs of Angles - Lines & Angles
• Transversal Lines
• Angle Sum Property of a Triangle

Chapter 7: Triangles

• Triangles in Geometry
• Congruence of Triangles |SSS, SAS, ASA, and RHS Rules
• Theorem - Angle opposite to equal sides of an isosceles triangle are equal | Class 9 Maths
• Triangle Inequality

Chapter 8: Quadrilateral

• Angle Sum Property of a Quadrilateral
• Quadrilateral - Definition, Properties, Types, Formulas, Examples
• Introduction to Parallelogram: Properties, Types, and Theorem
• Rhombus: Definition, Properties, Formula, Examples
• Kite - Quadrilaterals
• Properties of Parallelograms
• Mid Point Theorem

Chapter 9: Areas of Parallelograms and Triangles

• Area of Triangle | Formula and Examples
• Area of Parallelogram
• Figures on the Same Base and between the Same Parallels

Chapter 10: Circles

• Circles in Maths
• Radius of Circle
• Tangent to a Circle
• What is the longest chord of a Circle?
• Circumference of Circle - Definition, Perimeter Formula, and Examples
• Angle subtended by an arc at the centre of a circle
• What is Cyclic Quadrilateral
• Theorem - The sum of opposite angles of a cyclic quadrilateral is 180° | Class 9 Maths

Chapter 11: Construction

• Basic Constructions - Angle Bisector, Perpendicular Bisector, Angle of 60°
• Construction of Triangles

Chapter 12: Heron's Formula

• Area of Equilateral Triangle
• Area of Isosceles Triangle
• Heron's Formula
• Applications of Heron's Formula
• Area of Quadrilateral
• Area of Polygons

Chapter 13: Surface Areas and Volumes

• Surface Area of Cuboid
• Volume of Cuboid | Formula and Examples
• Surface Area of Cube
• Volume of a Cube
• Surface Area of Cylinder (CSA and TSA) |Formula, Derivation, Examples
• Volume of Cylinder
• Surface Area of Cone
• Volume of Cone | Formula, Derivation and Examples
• Surface Area of Sphere | CSA, TSA, Formula and Derivation
• Volume of a Sphere
• Surface Area of a Hemisphere
• Volume of Hemisphere

Chapter 14: Statistics

• Collection and Presentation of Data
• Graphical Representation of Data
• Bar graphs and Histograms
• Central Tendency
• Mean, Median and Mode

Chapter 15: Probability

• Experimental Probability
• Empirical Probability
• CBSE Class 9 Maths Formulas
• NCERT Solutions for Class 9 Maths
• RD Sharma Class 9 Solutions

Natural Numbers are all positive integers from 1 to infinity and are a component of the number system. Natural numbers are also called counting numbers because they are used for counting of various things.

Illustration of Natural Numbers

Let’s learn more about natural numbers, their properties, and examples in detail in this article.

What are Natural Numbers?

Natural numbers or counting numbers are those integers that begin with 1 and go up to infinity.

Only positive integers, such as 1, 2, 3, 4, 5, 6, etc., are included in the set of natural numbers. Natural numbers start from 1 and go up to ∞.

Set of Natural Numbers

In mathematics, the set of natural numbers is expressed as 1, 2, 3, … The set of natural numbers is represented by the symbol N. N = {1, 2, 3, 4, 5, … ∞}. A collection of elements is referred to as a set ( numbers in this context). The smallest element in N is 1, and the next element in terms of 1 and N for any element in N. 2 is 1 greater than 1, 3 is 1 greater than 2, and so on. The below table explains the different set forms of natural numbers.

Natural numbers are the subset of whole numbers, and whole numbers are the subset of integers. Similarly, integers are the subset of real numbers. The below-given diagram explains the relationship w.r.t. the sets of natural numbers, whole numbers, integers, and real numbers.

Types of Natural Numbers

Odd natural numbers.

Odd natural numbers are integers greater than zero that cannot be divided evenly by 2, resulting in a remainder of 1 when divided by 2. Examples of odd natural numbers include 1, 3, 5, 7, 9, 11, and so on.

Even natural numbers

Even natural numbers are whole numbers that are divisible by 2 without leaving a remainder. In other words, they are integers greater than zero that can be expressed in the form 2n, where n is an integer. Examples of even natural numbers include 2, 4, 6, 8, 10, and so on.

Natural Numbers from 1 to 100

As Natural Numbers are also called counting numbers, thus natural numbers from 1 to 100 are:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.

Does 0 belong to Natural numbers?

Natural numbers are counting numbers that start from 1 and go till ∞ and every successor is greater than its predecessor. Thus, 0 is not a natural number. The number 0 precisely belongs to the Whole number.

Natural Numbers and Whole Numbers

The set of whole numbers is identical to the set of natural numbers, with the exception that it includes a 0 as an extra number.

W = {0, 1, 2, 3, 4, 5, …} and N = {1, 2, 3, 4, 5, …}

Difference Between Natural Numbers and Whole Numbers

Let’s discuss the differences between natural numbers and whole numbers.

Natural Numbers on Number Line

Natural numbers are represented by all positive integers or integers on the right-hand side of 0, whereas whole numbers are represented by all positive integers plus zero.

Here is how we represent natural numbers and whole numbers on the number line:

Representation of Natural Numbers on Number Line

Properties of Natural Numbers

All the natural numbers have these properties in common :

• Closure property
• Commutative property
• Associative property
• Distributive property

Let’s learn about these properties in the table below.

Note: Subtraction and Division may not result in a natural number. Associative Property does not hold true for subtraction and division.

Operations With Natural Numbers

We can add, subtract, multiply, and divide the natural numbers together but the result in the subtraction and division is not always a natural number.

Let’s understand the operations on natural numbers:

Sum of First n Natural Numbers

Sum of first n natural numbers is given by

S = n(n+1)/2

where n is the number of terms taken into consideration.

Mean of First n Natural Numbers

As mean is defined as the ratio of the sum of observations to the number of total observations.

Mean Formula for the first n terms of natural number :

Mean = S/n = (n+1)/2

• S is Sum of all Observations
• n is Number of Terms Taken into Consideration

Sum of Square of First n Natural Numbers

Sum of square of first n natural numbers is given as follows:

S = n(n + 1)(2n + 1)/6

• n is Number Taken into Consideration

Related Articles,

Number System Counting Numbers Is 0 a Natural Number Whole Numbers Real Numbers Rational Numbers Another Name for Natural Numbers

Examples of Natural Numbers

Let’s solve some example problems on Natural Numbers.

Example 1: Identify the natural numbers among the given numbers:

23, 98, 0, -98, 12.7, 11/7, 3.

Since negative numbers, 0, decimals, and fractions are not a part of natural numbers. Therefore, 0, -98, 12.7, and 11/7 are not natural numbers. Thus, natural numbers are 23, 98, and 3.

Example 2: Prove distributive law of multiplication over addition with an example.

Distributive law of multiplication over addition states: a(b + c) = ab + ac For example, 4(10 + 20), here 4, 10, and 20 are all natural numbers and hence must follow distributive law 4(10 + 20) = 4 × 10 + 4 × 20 4 × 30 = 40 + 80 120 = 120 Hence, proved.

Example 3: Prove distributive law of multiplication over subtraction with an example.

Distributive law of multiplication over addition states: a(b – c) = ab – ac. For example, 7(3 – 6), here 7, 3, and 6 are all natural numbers and hence must follow the distributive law. Therefore, 7(3 – 6) = 7 × 3 – 7 × 6 7 × -3 = 21 + 42 -21 = -21 Hence, proved.

Example 4: List first 10 natural numbers.

1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are the first ten natural numbers.

Practice Questions on Natural Numbers

Various practice question on Natural Numbers are,

Q1: What is Smallest Natural Number?

Q2: What is Biggest Natural Number?

Q3: Simplify, 17(13 – 16)

Q4: Simplify, 11(9 – 2)

Natural Numbers- FAQs

What is natural number definition in math.

Number used for counting such as 1, 2, 3, 4, 5, . . . so on to infinity, are called natural numbers and any element from this collection is a natural number.

Is 0 a Natural Number?

No, 0 is not a part of natural numbers. 0 is a part of whole numbers, and this is the major difference between whole numbers and natural numbers.

Which is Smallest Natural Number?

Smallest natural number is 1. Natural numbers begin at 1 and go up to infinity. Therefore, the smallest natural number is 1.

How many Natural Numbers are there?

There are infinite natural numbers.

Are Natural Numbers Whole Numbers?

Yes, as set of natural number is subset of the whole number or we can say whole number are natural number with 0. Thus all the natral number are whole number.

Every Whole Number is a Natural Number. True or False?

False. Every whole number is not a natural number as 0 is involved in whole numbers but not in natural numbers. Therefore, the assertion is wrong.

How many Natural Numbers are there between 1 and 100?

As natural number are 1, 2, 3, 4, 5, . . . so on, Thus, there are exactly 100 natural number till number 100, but as we don’t have to include the 1 and 100. Thus, there are 100 – 2 = 98, natural number in between 1 and 100.

What is Sum of First n Natural Numbers?

Formula for the sum of first n natural numbers is: S = n (n + 1)/2

What is Sum of First 10 Natural Numbers?

1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are the first ten natural numbers. Therefore, the sum of the first 10 natural numbers will be 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55.

Please Login to comment...

Similar reads.

• Math-Concepts
• Natural Numbers
• School Learning
• How to Use Bard for Creative Writing
• How To Get A Free Domain Name [2024]
• 10 Best Crypto Portfolio Tracker Apps in 2024
• 10 Best Free Blockchain Learning apps for Android in 2024
• Top 10 R Project Ideas for Beginners in 2024

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

Two Kinds of Real Numbers

Rational Numbers

Irrational Numbers

• Students will understand:�all numbers, rational and irrational, have a location on a number line.�

Explore the real number system and its appropriate usage in real-world situations.�a. Recognize the differences between rational and irrational numbers.

b. Understand that all real numbers have a decimal expansion. Numbers:�c. Model the hierarchy of the real number system, including natural, whole, integer,�● Exploring Irrational Numbers�rational, and irrational numbers.�● Approximating Irrational Numbers

Essential Question for Topic �

What other types of numbers are there? Why do you need them?

Focus Question for Lesson

• What does being able to express numbers in equivalent forms allow you to do?

Key Vocabulary

• rational number, repeating decimal, terminating decimal, irrational number

The Real Number System

The real numbers is the set of numbers containing all of the rational numbers and all of the irrational numbers. The real numbers are “all the numbers” on the number line.

The natural (or counting ) numbers are 1, 2, 3, 4, 5, etc.

The whole numbers are the natural numbers together with 0

The integers are the set of real numbers consisting of the natural numbers, their additive inverses and zero.

{..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...}

The rational numbers are those numbers which can be expressed as a ratio between two integers. For example, the fractions 1/3 and –1111/8 are both rational numbers. All the integers are included in the rational numbers,

All decimals which terminate are rational numbers (since 8.27 can be written as 827/100.) Decimals which have a repeating pattern after some point are also rationals:

An irrational number is a number that cannot be written as a ratio (or fraction). In decimal form, it never ends or repeats.

• A rational number is a real number that can be written as a ratio of two integers.
• A rational number written in decimal form is terminating or repeating.

Examples of Rational Numbers

• An irrational number is a number that cannot be written as a ratio(fraction) of two integers.
• Irrational numbers written as decimals are non-terminating and non-repeating.

Examples of Irrational Numbers

• Square roots of non-perfect “squares”

Rational or Irrational?

Expressing Rational Numbers with Decimal Expansions

Converting Fractions to Decimals

You can convert all  fractions .You can convert all fractions to  decimals .To convert fractions to decimals you just divide the top by the bottom — divide the  numerator by the  denominator .

• http://www.virtualnerd.com/pre-algebra/rational-numbers/definitions-basics/convert-decimals-fractions/fraction-to-repeating-decimal-conversion
• http://www.brainpop.com/math/numbersandoperations/convertingfractionstodecimals/

Compare rational numbers

• Decimal numbers are compared in the same way as other numbers: by comparing the different place values from left to right. We use the symbols <, > and = to compare decimals as shown below.

When comparing two decimals, it is helpful to write one below the other.�

Compare each pair of decimals using the symbols <, > or =.

• 1. 4.1__ 4.01 8. 5.042__5.402
• 2. 3.05__3.5 9. 27.18__2.718
• 3. 1.3__1.30 10. 0.38__0.380
• 4. 0.17__0.9
• 5. 0.17__0.09
• 6. 0.31__0.201
• 7. 3.487__3.9

• Science Notes Posts
• Contact Science Notes
• Todd Helmenstine Biography
• Anne Helmenstine Biography
• Free Printable Periodic Tables (PDF and PNG)
• Periodic Table Wallpapers
• Interactive Periodic Table
• Periodic Table Posters
• How to Grow Crystals
• Chemistry Projects
• Fire and Flames Projects
• Holiday Science
• Chemistry Problems With Answers
• Physics Problems
• Unit Conversion Example Problems
• Chemistry Worksheets
• Biology Worksheets
• Periodic Table Worksheets
• Physical Science Worksheets
• Science Lab Worksheets
• My Amazon Books

Natural Numbers – Definition, Examples, Properties

Natural numbers, often symbolized as ℕ, form the foundation of our numeric system and are the basic counting numbers that we use in everyday life. By definition, natural numbers start from one (1) and extend indefinitely in the positive direction, i.e., 1, 2, 3, 4, 5, 6, and so on.

Zero is not typically included in the set of natural numbers; however, in some mathematical contexts, it is part of this set. It’s crucial to note that the natural numbers do not include fractions, decimals, irrational, or negative numbers.

Importance of Natural Numbers

Natural numbers are important. They form the basis for counting and measuring. We used them every day for understanding quantities, performing basic arithmetic operations, and ultimately understanding the universe. They are the first numbers children learn and find use in daily life in counting objects, measuring distances, and denoting time.

Moreover, natural numbers have deep significance in advanced mathematics and computer science. They provide the basis for defining more complex number sets, like integers, rational numbers, and real numbers. They form the bedrock for nearly all mathematical theories and computations.

Examples of Natural Numbers and Non-Natural Numbers

The smallest natural number is 1. Any positive count starting from 1 represents a natural number. For example, the first ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Other examples of natural numbers are 42, 955, and 124889. Odd natural numbers include 3, 7, and 145. Examples of even natural numbers are, 2, 6, 36, and 152.

Numbers that are not natural include fractions (like 1/2, 3/4), decimals (0.5, 3.14), negative numbers (-1, -7), and irrational numbers (like pi or the square root of 2). Also, 0 is not (usually) a natural number.

Natural Numbers Vs. Whole Numbers and Integers

People sometimes confuse natural numbers with whole numbers and integers, but there are key distinctions between these classes of numbers.

Whole Numbers : The set of whole numbers (usually denoted as ℤ⁺) is very similar to the set of natural numbers, with one crucial difference: it includes zero. So while natural numbers start from 1 and extend in the positive direction, whole numbers start from 0 and extend positively: {0, 1, 2, 3, 4, …}.

Integers : The set of integers (represented as ℤ) includes all natural numbers, their negatives, and zero. So while natural numbers are always positive, integers can be negative, zero, or positive: {…, -3, -2, -1, 0, 1, 2, 3, ….}.

Mathematical Properties of Natural Numbers

Natural numbers have several fundamental properties that make them invaluable in mathematical operations:

• Closure Property : Natural numbers are closed under addition and multiplication, which means that the sum or product of any two natural numbers is always a natural number.
• Associative Property : For any three natural numbers, the grouping doesn’t affect the outcome of addition or multiplication. For example, (2 + 3) + 4 = 2 + (3 + 4) and (2 x 3) x 4 = 2 x (3 x 4).
• Commutative Property : The order of natural numbers does not change the result of addition or multiplication. For example, 2 + 3 = 3 + 2 and 2 x 3 = 3 x 2.
• Distributive Property : Multiplication distributes over addition in the set of natural numbers. For example, 2 x (3 + 4) = (2 x 3) + (2 x 4).
• Identity Property : Adding zero to a natural number or multiplying a natural number by one leaves it unchanged. For example, 5 + 0 = 5 and 5 x 1 = 5.
• Well-Ordering Principle : Every non-empty set of natural numbers has a least element.

However, natural numbers lack certain properties that integers and rational numbers have, such as the ability to subtract larger numbers from smaller ones, or to divide one number by another and always obtain a number within the same set.

In summary, natural numbers are fundamental to understanding quantity and forming the basis of our number system. Though basic in nature, they establish a foundation for more complex mathematical concepts and systems.

• Eves, Howard (1990). An Introduction to the History of Mathematics (6th ed.). Thomson. ISBN 978-0-03-029558-4.
• Fletcher, Harold; Howell, Arnold A. (2014). Mathematics With Understanding . Elsevier. ISBN 978-1-4832-8079-0.
• Ifrah, Georges (2000). The Universal History of Numbers . Wiley. ISBN 0-471-37568-3.
• Levy, Azriel (1979). Basic Set Theory . Springer-Verlag Berlin Heidelberg. ISBN 978-3-662-02310-5.
• Szczepanski, Amy F.; Kositsky, Andrew P. (2008). The Complete Idiot’s Guide to Pre-algebra . Penguin Group. ISBN 978-1-59257-772-9.

Related Posts

• My presentations

Auth with social network:

Download presentation

We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!

Presentation is loading. Please wait.

Properties of Natural Numbers

Published by Dayna Wiggins Modified over 5 years ago

Similar presentations

Presentation on theme: "Properties of Natural Numbers"— Presentation transcript:

Properties of Real Numbers

Adding First, you need to know… Associative Property of Addition When: (a + b) + c = a + (b + c) Commutative Property of Addition When: a + b= b + a.

Properties of Real Numbers. Closure Property Commutative Property.

EXAMPLE 3 Identify properties of real numbers

PROPERTIES REVIEW!. MULTIPLICATION PROPERTY OF EQUALITY.

Quiz Review Properties and Integers Operations with Decimals Addition Subtraction Multiplication Division.

Operations with Rational Numbers. When simplifying expressions with rational numbers, you must follow the order of operations while remembering your rules.

Objective The student will be able to: recognize and use the commutative and associative properties and the properties of equality.

Find the sum or difference. Then simplify if possible.

3 x 55 = 55 x 3 Commutative Property of Multiplication.

Properties of Real Numbers 1.Objective: To apply the properties of operations. 2.Commutative Properties 3.Associative Properties 4.Identity Properties.

Properties are special qualities of something. Addition and multiplication have special qualities that help you solve problems mentally = MENTAL MATH!!

The properties of real numbers help us simplify math expressions and help us better understand the concepts of algebra.

Properties of Numbers. Additive Identity Adding “0” to a number gives you the same initial number. Example = = 99.

Properties Associative, Commutative and Distributive.

Commutative Property of Addition By: Zach Jamison Period 5.

By: Tameicka James Addition Subtraction Division Multiplication

Multiplication and Division Properties. Multiplication Properties Commutative Property Associative Property Identity Property Zero Property Distributive.

Real Numbers Chapter 1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-1.

About project

© 2024 SlidePlayer.com Inc. All rights reserved.

Properties of Natural Numbers: Definitions, Examples, Facts

What are the properties of natural numbers, closure property of natural numbers, associative property of natural numbers, solved examples on properties of natural numbers, practice problems on properties of natural numbers, frequently asked questions on properties of natural numbers.

Properties of natural numbers in mathematics are certain rules that can be applied or the characteristics of natural numbers that can be used when we perform arithmetic operations on them.

The four basic properties of natural numbers are:

• Closure Property 
• Associative Property
• Commutative Property 
• Distributive Property

Natural numbers are 1, 2, 3, 4, 5, 6, and go on till infinity. They are also called counting numbers as they are used to count objects. Natural numbers do not include 0 or negative numbers. The alphabet ℕ is used as a symbol to refer to natural numbers. 

The basic operation of addition, subtraction, multiplication, and division give rise to four main properties of natural numbers. 

The image shown above simply gives a quick overview of each property. Let’s understand each property in detail with examples.

• Closure property of addition

When you add two natural numbers, the result will always be a natural number. 

Examples of closure property of addition: $2 + 2 = 4, 3 + 4 = 7, 5 + 5 = 10$

In each case, the result of the addition of natural numbers is a natural number. 

• Closure property of multiplication

When you multiply two natural numbers, the result will always be a natural number. 

Examples of closure property of multiplication: $2 \times 2 = 4, 3 \times 2 = 6, 5 \times5 = 25$ 

In each case, the result of the multiplication of natural numbers is a natural number. 

Thus, we say that the natural numbers are closed under addition and multiplication.

However, in the case of division and subtraction, this property does not hold true. Subtracting or dividing two natural numbers will not always give us a natural number. 

Examples: $4 \;-\; 6 = \;-\;2,\; 5 \;-\; 3 = 2,\; 6 \;-\; 9 = \;-\;3$ 

The second case resulted in a natural number but the first and third ones did not.  

Examples of division: $10 \div 3 = 3.33,\; 9 \div 3 = 3,\; 15 \div 4 = 3.75$ 

The first and third cases did not result in natural numbers.

Related Worksheets

• Associative property of addition 

The sum of natural numbers remains unchanged even if the grouping of numbers is changed. 

It is expressed in the form of an equation as $a + (b + c) = (a + b) + c$

Examples of associative property of addition: $2 + (5 + 6) = 13$ and $(2 + 5) + 6 = 13$

• Associative property of multiplication  

The product of natural numbers remains unchanged even if the grouping of numbers is changed. It is expressed in the form of an equation as $a \times (b \times c) = (a \times b) \times c$

Examples of associative property of multiplication: $2 \times (3 \times 4) = 24$ and $(2 \times 3) \times 4 = 24$

Let us now look at the nature of subtraction and division with respect to this property. 

Associative property does not hold true for subtraction and division.

$a \;-\; (b \;-\; c) \neq (a \;-\; b) \;-\; c$ 

$a \div (b \div c) \neq (a \div b) \div c$

Examples of subtraction: $4 \;-\;(10 \;-\; 2) = \;-\; 4$ and $(4 \;-\; 10) \;-\; 2 = \;-\; 8$ 

Examples of division: $5 \div (6 \div 3) = 2.5$ and $(5 \div 6) \div 3 = 0.27$

Commutative Property of Natural Numbers

• Commutative property of addition 

If we change the order of natural numbers during addition, the result does not change. 

It is expressed in the form of an equation as $(a + b) = (b + a)$

Examples of commutative property of addition: $6 + 5 = 11$ and $5 + 6 = 11$

• Commutative property of multiplication

If we change the order of natural numbers during multiplication, the result does not change. 

It can be expressed in the form of an equation as $(a \times b) = (b \times a)$

Examples of commutative property of multiplication: $2 \times 4 = 8$ and $4 \times 2 = 8$

The commutative property does not apply to subtraction and division of natural numbers. 

$a \;-\; b \neq b \;-\; a$

$a \div b \neq b \div a$

Examples for subtraction: $5 \;-\; 3 = 2$ and $3 \;-\; 5 = \;-\; 2$

Examples for division: $6 \div 3 = 2$ and $3 \div 6 = 0.5$

Distributive Property of Natural Numbers

According to the distributive property of multiplication over addition, if we multiply the total of two addends by a number or multiply each addend individually and then add them, the result will be the same. 

Distributive property of multiplication over addition: $a(b + c) = (a \times b) + (a \times c)$

Example: $2 \times (5 + 3) = 16$

       $(2 \times5) + (2 \times 3) = 16$

This property also holds true in the case of multiplication over subtraction. 

Distributive property of multiplication over subtraction: $a(b \;-\; c) = (a \times b) \;-\; (a \times c)$

Example: $2 \times (5 \;–\; 3) = 4$

               $(2 \times 5) \;–\; (2 \times 3) = 4$

Facts about Properties of Natural Numbers

• There are an infinite number of natural numbers. There is no largest natural number. Natural numbers go on forever. The smallest natural number is 1. 
• By simply adding 1 to a given natural number, you will get the next natural number.
•  For the natural number 1, there is no “predecessor” or a previous natural number.

 ($1 = 0 + 1$, but we know that 0 is not a natural number).

• Natural numbers are also called counting numbers as they are used to count objects.
• The properties of natural numbers do not hold true in the case of division and 

subtraction.

• Negative numbers, fractions, and decimals are neither natural numbers nor whole numbers.
• Even natural numbers $= E = \left\{2, 4, 6, 8, 10, …\right\}$

Odd natural numbers $= O = \left\{1, 3, 5, 7, 9, 11, …\right\}$

In this article, we explored natural numbers and its properties. These properties make the natural number set unique. In this process, we also understand that division and subtraction of natural numbers is not guaranteed to be a natural number, but that there are incidences where the result is a natural number. Now let’s apply this knowledge to solve some examples.

1. Which of the following numbers are natural numbers? 

$2, 18, \;-\;5, 25.5, 1, \;-\;20$ . 

Solution: 

Natural numbers are given by 1, 2, 3, 4, 5, … and so on.

The numbers 2, 18, and 1 are natural numbers.

The numbers $\;-\;5$ and $\;-\;20$  are not natural numbers because they are negative.

25.5 is not a natural number because it is a decimal.

2. State whether each of the given statements is True or False.

• There is always a natural number between any two consecutive natural numbers.
• Subtraction of two natural numbers is always a natural number.
• Natural numbers do not include 0.

Solution:  

• The statement is false. Between two consecutive natural numbers, there is no natural number. 

For example, between 1 and 2, no natural number exists as 1.1, 1.2, 1.3, 1.7, 1.9, etc. are decimal numbers.

• The statement is false. The natural numbers are not closed under subtraction. It means that the subtraction of two natural numbers may or may not be a natural number.
• True. 0 is not a natural number. It is a whole number.

3. Solve the expression 2 (20 + 15) using the distributive property of multiplication over addition.

According to distributive property,  

          $a(b + c) = (a \times b) + (a \times c)$

     $2 (20 + 15) = (2 \times 20) + (2 \times 15)$

                       $= 40 + 30$

                       $= 70$

Thus,  $2 (20 + 15) = 70$

4. Identify the properties of the natural numbers based on the expressions given below

a) $2 + (5 + 6) = (2 + 5) + 6$

b) $(10 + 15) = (15 + 10)$

c) $4 \times (6 \times 8) = (4 \times 6) 8$

This is an example of the associative property of addition. 

This is an example of the commutative property of addition.

c) $4 \times (6 \times 8) = (4 \times 6) \times 8$ 

This is an example of the associative property of multiplication.

Attend this quiz & Test your knowledge.

The smallest natural number is _______.

The natural numbers do not follow the closure property under _______., the sum and product of two natural numbers is always a natural number. this property is called ______., if a, b and c are natural numbers then $(a + b) + c = a + (b + c)$. this property is called ______., which of the following is an example of the commutative property of multiplication.

Is $-1$ a natural number?

The set of natural numbers in mathematics is the set {1, 2, 3, …}. Since – 1 is a negative number, it is not a natural number.

Are natural numbers whole numbers?

All natural numbers are whole numbers. Whole numbers include natural numbers and 0.

Is 0 a natural number ?

Natural numbers are a subset of real numbers that only include positive integers like 1, 2, 3, 4, 5, 6, and so on, while excluding negative numbers, zero, decimals, and fractions. They do not comprise negative numbers or zero.

What are cardinal numbers ?

Cardinal numbers are the numbers used for the purpose of counting. Cardinal numbers are natural numbers or positive integers. The smallest cardinal number is 1. Examples of cardinal numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, and so on. The smallest cardinal number is 1.

Is associative property true for subtraction and division of natural numbers ?

The associative property holds true in case of addition and multiplication of natural numbers.  

But for subtraction and division of natural numbers, the associative property does not hold true.

For example,  $5 \;-\; (3 \;-\; 2 ) = 4$  and  $(5 \;-\; 3) \;-\; 2 = 0$

$30 \div (10 \div 5 ) = 15$ and $(30 \div 10) \div 5 = \frac{3}{5}$

Is a square of a natural number also a natural number?

A square of a natural number is a natural number multiplied by itself. Since natural numbers follow the closure property, the square of a natural number is also a natural number. For example, $5^2 = 5 \times 5 = 25$, and  $25$ is a natural number.

Is the square root of a natural number always a natural number?

The square root of a natural number may or may not be a natural number. 

For example, the square root of 9 is 3, square root of 16 is 4, which are natural numbers, but the square root of 6 is approximately 2.449, which is not a natural number.

RELATED POSTS

• Operations on Rational Numbers – Methods, Steps, Facts, Examples
• Difference Between Line and Line Segment – Definition, Examples
• Associative Property – Definition, Examples, FAQs, Practice Problems
• Improper Fractions – Definition, Conversion, Examples, FAQs
• Times Tables – Definition with Examples

Math & ELA | PreK To Grade 5

Kids see fun., you see real learning outcomes..

Make study-time fun with 14,000+ games & activities, 450+ lesson plans, and more—free forever.

Parents, Try for Free Teachers, Use for Free

• skip to main content
• skip to search
• Scoilnet Maps
• I Am An Artist
• FÍS Film Project
• Irish Flag Website
• CensusAtSchool
• Science Hooks
• ThinkB4UClick
• Look At History
• Go To Primary
• Go To Post-Primary
• Post-Primary

Natural Numbers

Ease your first year maths class into learning about numbers and the number system using the following structured presentation. The PPT presentation comes alongside supporting worksheets. Students will discover the meaning of key mathematical terminology such as odd, even, prime numbers, highest common factor, multiples, and composite numbers. Download PPT presentation

Prior Knowledge Checklist

Odd and Even Numbers

Highest Common Factor

Multiples and LCM

Prime Numbers

Mix & Match Activity

Reflection 

Keyword Sheet

Videos by Khan Academy . Advice students to look at the videos prior to lesson or after the lesson to reflect on the lesson content.

You might also be interested in...

The PDST Maths team has developed some interactive animations for the number strand using a online tool called GeoGebra. Teachers can use interactive GeoGebra files to help students visualise; - the subtracting and additions of integers on a number line - the comparison of different fractions or decimals to one another - the comparison of different percentages and how they compare to each other.

Did you know that your Internet Explorer is out of date

To get the best possible experience using our website we recommend that you upgrade to a newer version or other web browser.

Upgrade your browser now

Registering for a Scoilnet Account – your first step to contributing and sharing

What you need....

To register for a Scoilnet Account you will need to have a Teaching Council number and a roll number for your school in Ireland.

If you already have a Scoilnet Account then you can sign in here .

The benefits...

A Scoilnet account will allow you to upload your resources or weblinks to Scoilnet as well as enabling you to share and add resources to a favourites listing. Users who have a Scoilnet Account will also be able to fully access Scoilnet Maps and Census@School from home.

Add this resource to your Learning Path

You need to login before you can add this resource to a Learning Path

Become a math whiz with AI Tutoring, Practice Questions & more.

Number Systems

There are a variety of number systems, a handful of which are used on a regular basis for basic mathematics in intermediate and high school. These include natural numbers , integers , rational numbers , irrational numbers , real numbers , and more. Continue reading to learn more about the properties of each of these types of numbers.

• Natural numbers

The natural (or counting) numbers are the part of the number system that includes all the positive integers from 1 through infinity. They are used for the purpose of counting. Natural numbers do not include 0, fractions , decimals , or negative numbers.

The set of natural numbers is usually represented by the letter "N".

N = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 … }

Natural numbers include all whole numbers except for the number 0. In other words, all natural numbers are whole numbers, but not all whole numbers are natural numbers.

There are four properties that natural numbers fit into:

• Closure property – the sum or product of any two natural numbers is a natural number. This does not hold true for subtraction or division .
• Commutative property – the order in which you add or multiply natural numbers does not affect the result. This does not hold true for subtraction or division.
• Associative property – the way natural numbers are grouped in addition or multiplication does not affect the result. This does not hold true for subtraction or division.
• Distributive property – multiplication of natural numbers is always distributive over addition.

The integers are a set of numbers consisting of the natural numbers, their additive inverses, and zero. In other words, they include all positive numbers, negative numbers, and 0. They can never be a fraction or decimal. All natural numbers are integers that start from 1 and end at infinity. All whole numbers are integers that start from 0 and end at infinity.

The set of integers is usually represented by the letter "Z". It can also be represented by the letter "J".

Z = { … -3 , -2 , -1 , 0 , 1 , 2 , 3 , 4 … }

The sum, product, and difference of any two integers is always an integer. The same is not true for division.

There are four types of numbers that fall under the integer category.

• Whole numbers
• Odd and even integers
• Prime and composite numbers

There are rules for integers based on the four basic operations:

Addition rule – If the sign of both integers is the same, the result will have the same sign. Two positives equal a positive and two negatives equal a negative.

- 14 + ( - 12 ) = - 26

If the two numbers being added have a different sign, it will lead to a subtraction and the result will have the sign of the larger (in absolute value) integer.

- 2 + 10 = 8

- 10 + 2 = 8

Subtraction rule – Keep the sign of the first number the same, change the operator from subtraction to addition, and change the sign of the second number. Once you have applied this rule, follow the rules for adding integers.

Multiplication division rule – If the signs are the same, multiply or divide, and the answer is always positive.

5 ∗ 5 = 25

-5 ∗ ( - 5 ) = 25

If the signs are different, multiply or divide, and the answer is always negative.

-5 ∗ 5 = -25

25 - 5 = - 5

There are five properties that integers fit into. The first four are the same as natural numbers. The last one is the identity property.

The additive identity property states that any integer added to 0 will give the same number. So 0 is called the additive identity. For any integer x,

x + 0 = x = 0 + x

The multiplicative identity states that when an integer is multiplied by 1, it will give the integer itself as the product. So 1 is called the multiplicative identity. For any integer x,

x ∗ 1 = x = 1 ∗ x

If any integer is multiplied by 0, the product will be 0.

x ∗ 0 = 0 = 0 ∗ x

If any integer is multiplied by -1, the product will be the opposite of the number.

x ∗ - 1 = - x = -1 ∗ x

Rational numbers

Rational numbers can be expressed as a ratio between two integers. For example, the fractions 1 3 and -1211 19 are both rational numbers.

The rational numbers include all the integers because any integer z can be expressed as the ratio z 1 .

All decimals that terminate are also rational numbers because, for example, 8.27 can be expressed as 827 100 . Decimals that have a repeating pattern at some point are also rational. For example, 0.0833333 … = 1 12 .

Some of the important properties of the rational numbers are as follows:

• The results are always a rational number if you add, subtract, or multiply any two rational numbers.
• A rational number remains the same if you divide or multiply both the numerator and denominator with the same factor.
• If you add 0 to a rational number, the result will be the number itself.
• Rational numbers are closed under addition, subtraction, and multiplication.

Irrational numbers

An irrational number is one that cannot be written as a ratio, or fraction of integers. In decimal form, it never ends or repeats. The ancient Greeks discovered that not all numbers are rational. There are equations that cannot be solved by using ratios of integers.

One of the first such equations to be studied was 2 = x 2 . What number times itself equals 2?

2 is about 1.414 because 1.414 2 = 1.999396 , which is close to 2. But you'll never reach 2 exactly by squaring a fraction (or terminating decimal ). The square root of 2 is an irrational number, meaning its decimal equivalent goes on forever, with no repeating pattern.

2 = 1.41421356237309 …

Another famous irrational number is the golden ratio , a number that has great importance in biology.

1 + 5 2 = 1.61803398874989 …

Another famous irrational number is pi , the ratio of the circumference of a circle to its diameter.

π = 3.14159265358979 …

And another famous irrational number is e , the most important number in calculus.

e = 2.718281828455904 …

Irrational numbers can be further divided into algebraic numbers, which are the solutions of some polynomial equations (such as 2 and the golden ratio), and transcendental numbers , which are not the solutions of any polynomial equation. π and e are both transcendental.

Real numbers

The real numbers are the set of numbers that contain all of the rational numbers and all of the irrational numbers. The real numbers are "all the numbers" on the number line. There are infinitely many real numbers, just as there are infinitely many numbers in each of the other sets of numbers. But it can be proved that the infinity of the real numbers is a bigger infinity!

The smaller, or countable, infinity of the integers and rationals is sometimes called ℵ ⁡ 0 (aleph-naught), and the uncountable infinity of the reals is called ℵ ⁡ 1 or aleph-one.

There are actually even bigger infinities, but you would want to take a set theory class to learn about those.

Complex numbers

The complex numbers are the set { a + b i | a and b are real numbers}, where i is the imaginary unit - 1 .

The complex numbers include the set of real numbers. The real numbers, in the complex system, are written as a + 0 i = a where a is a real number.

This set is sometimes written as C for short. The set of complex numbers is important because for any polynomial p ( x ) with real number coefficients, all the solutions of p ( x ) = 0 will be in C.

..and beyond

There are even bigger sets of numbers that are used by mathematicians. For example, the hyper-real numbers or the quaternions, discovered by William H. Hamilton in 1845, form a number system with three different imaginary units!

Topics related to the Number Systems

Base (Number Systems)

Product of Powers Property

Flashcards covering the Number Systems

8th Grade Math Flashcards

Common Core: 8th Grade Math Flashcards

Practice tests covering the Number Systems

MAP 8th Grade Math Practice Tests

8th Grade Math Practice Tests

Get help learning about number systems

From natural numbers to real numbers to the imaginary numbers of quaternions, the concepts learned in number systems can be challenging for students to remember and use practically. Getting help from a private tutor is an effective and efficient way to help clear up any misunderstandings your student may have when it comes to math concepts including number systems.

Working with a math tutor helps your student in many different ways. A private tutor will move at your student's pace, taking the time your student needs to make sure they understand each concept thoroughly before moving on to the next concept. They are right there to answer questions as your student thinks of them so they don't waste time completing equations the wrong way. Contact the Educational Directors at Varsity Tutors to see how tutoring can help your student today.

• ACCUPLACER ESL Tutors
• German 4 Tutors
• BCABA - Board Certified Assistant Behavior Analyst Test Prep
• Georgia Bar Exam Courses & Classes
• IB World Religions SL Tutors
• MOS - Microsoft Office Specialist Courses & Classes
• GATE/ TAG Test Prep
• SAT Subject Test in World History Tutors
• TASC Reading and Writing Tutors
• ISAT Tutors
• Ohio Bar Exam Courses & Classes
• Pre-AP Biology Tutors
• Classics Tutors
• ABIM Exam - American Board of Internal Medicine Courses & Classes
• Series 99 Test Prep
• South Carolina Bar Exam Test Prep
• Adult ESL Tutors
• OAT Survey of Natural Sciences Tutors
• GCSE History Tutors
• Series 14 Test Prep
• Las Vegas Tutoring
• Madison Tutoring
• Kansas City Tutoring
• Milwaukee Tutoring
• Washington DC Tutoring
• New York City Tutoring
• Chicago Tutoring
• Salt Lake City Tutoring
• Spokane Tutoring
• Ann Arbor Tutoring
• GRE Tutors in Washington DC
• Spanish Tutors in Houston
• English Tutors in Seattle
• SSAT Tutors in Denver
• SSAT Tutors in Washington DC
• English Tutors in Phoenix
• French Tutors in Chicago
• Calculus Tutors in Miami
• ACT Tutors in New York City
• Physics Tutors in San Francisco-Bay Area

THE NATURAL NUMBERS

Apr 06, 2019

220 likes | 430 Views

THE NATURAL NUMBERS. N 0, 1, 2, 3, 4. . . REMEMBER. 0 zero 1 2 3 4 5 one two three four five 6 7 8 9 10 six seven eight nine ten. 11 12 13 14 15

Share Presentation

• m a hundred
• operations hierarchy
• wikispaces com
• subtraction operations
• natural number set

Presentation Transcript

THE NATURAL NUMBERS N 0, 1, 2, 3, 4. . .

REMEMBER 0 zero 1 2 3 4 5 one two three four five 6 7 8 9 10 six seven eight nine ten

11 12 13 14 15 Eleven Twelve Thirteen Fourteen Fifteen 16 17 18 19 20 Sixteen Seventeen Eighteen Nineteen Twenty 21 22 23 . . . Twenty-one Twenty-two Twenty-three . . .

30 Thirty 40 Forty 50 Fifty 60 Sixty 70 Seventy 80 Eighty 90 Ninety 100 A Hundred 1 000 A Thousand 1 000 000 A Million 1 000 000 000 A Billion

Operations • 5 + 3 Five plus three • 8 – 3 Eight minus three • 6 x 2 Six times two • 15 / 3 Fifteen divided by three

Comparisons • 7 > 5 Seven is greater than five • 5 < 7 Five is less than seven • 3 = 3 Three is equal to three

1.- EVOLUTION OF NUMBERS • The numbers appeared due to the necessity of counting. • Primitive societies created symbols to express quantities like how many animals they had hunted. They made marks on bones and on stones. • The Egyptians used these symbols: ONE TEN A HUNDRED A THOUSAND

What quantity is written on the stone?

. Are you sure that you are right? Yes, you are. The quantity is 1,435

As you know, The Romans used this letters: I V X L One Five Ten Fifty C D M A Hundred Five Hundred A Thousand

What quantities are written? a) MVI b) CXLII

What quantities are written? a) MVI 1 006 b) CXLII 142

a) M = 1000 V = 5 I = 1 MVI = 1006 b) C = 100 X = 10 L = 50 I I = 2 CXLII = 142 Note: Remember to subtract when the smaller number is on the left.

1.- THE NATURAL NUMBER SET The Natural Number Set is represented with the letter N N = { 0, 1, 2, 3, ... } Operations • Addition 2314 + 25 = ?

Remember when writing: * Unities under unities * Ten unities under ten unities * Hundred under hundred

2. Subtraction: Remember when writing: * Unities under unities * Ten unities under ten unities * Hundred under hundred

3. Multiplication: Remember when writing: * Unities under unities * Ten unities under ten unities * Hundred under hundred

4. Division: Remember: Dividend = 726 Divisor = 23 Quotient = 31 Remainder = 3 Dividend = Divisor x Quotient + Remainder 726 = 23 x 31 + 3

Operations hierarchy 1st. First, solve the parenthesis 2nd. After that, solve the multiplication and division operations. 3rd. Finally, solve the addition and the subtraction operations.

Example: 32 – 3 * ( 7 + 6 : 3) = 32 - 3 * ( 7 + 2) = 32 – 3 * 9 = 32 – 27 = 5

3.- On the internet • http://bilingualproject.wikispaces.com/Resources • http://www.youtube.com/watch?v=kZKOPKIHsrc&feature=related • http://www.mathgoodies.com/lessons

• More by User

By the Numbers

By the Numbers. The Illinois Mental Health System. Prevalence of Mental Illnesses. 1% of the population has schizophrenia—130,000 people in Illinois 1 to2% of the population has bipolar affective disorder—130,000 to 260,000 people in Illinois

398 views • 11 slides

By the Numbers. In May NAHU received more than 825 press hits. So far in 2014, NAHU has received 4,200 press hits. In 2013, NAHU received more than 11,000 press hits. In 2012, NAHU received more than 7,500 press hits. In 2011, NAHU received more than 4,400 press hits .

133 views • 0 slides

Natural numbers are counting numbers.

= {1, 2, 3, 4, 5…}. Natural Numbers. Natural numbers are counting numbers. = {0, 1, 2, 3, 4, 5…}. Whole Numbers. Whole numbers are natural numbers and zero. N is a subset of W. = {...−3, −2, −1, 0, 1, 2, 3…}. Integers. Integers are whole numbers and opposites of naturals.

661 views • 39 slides

The Numbers

Jasper City Schools: A Look at the Numbers Dr. Martha LaCroix Jasper City Schools Administrative Retreat – 7.7.14. The Numbers. AdvancED Assist Surveys. Assessments. Vision 2015. Stakeholder Surveys – AdvancED ASSIST Portal. ASSIST Staff Survey Respondents.

288 views • 16 slides

Snapshots of Brooklyn Public Library’s Downloadable Collections and of an IFLA Sponsored eBook Survey. Tomorrow’s Library in a World of Digits:  Publishers and Librarians Share Concerns, Ideas and Opinions for New Mutually Beneficial Models BookExpo America May 27, 2010

328 views • 19 slides

The Numbers:

144 views • 8 slides

Numbers, Numbers, Numbers…

Numbers, Numbers, Numbers…. On Over-Education and Pressure to Learn/Perform in South Korea. Between 1999 and 2005, South Korea ranked #1 among 30 OECD member nations in expenditure on all education.

438 views • 11 slides

THE NUMBERS

THE NUMBERS. The Mummers’ Dance. Loreena McKennitt. 10 6 1.000 km. Typical sight from a satellite. 10 7 10.000 km. The north hemisphere of Earth, and part of South America. 10 8 100.000 km. The Earth starts looking small. 10 10 10 Millions de km.

301 views • 20 slides

Diabetes: The Numbers

Diabetes: The Numbers. With Michigan Data. Adapted from the National Diabetes Education Program. What is Diabetes?. Diabetes is a group of diseases characterized by high levels of blood glucose (blood sugar) Diabetes can lead to serious health problems and premature death.

498 views • 25 slides

Natural Numbers

Natural Numbers. or, &quot;All you ever need is compounds, variants, and recursion&quot;. Today's Lecture. We've seen types like: [any] -&gt; natural [num] -&gt; num [num] -&gt; [num] [X], [X] -&gt; [X] Let's check out this guy: flatten : [[X]] -&gt; [X] And look at &quot;lists without baggage&quot;

277 views • 13 slides

THE NATURAL NUMBERS. N 0, 1, 2, 3, 4. 1.- EVOLUTION OF NUMBERS. The numbers appeared due to the necessity of counting. Primitive societies created symbols to express quantities like how many animals they had hunted. They made marks on bones and on stones.

283 views • 16 slides

The Real Numbers

The Real Numbers. 1.1. Sets. A set is a collection of objects, symbols, or numbers called elements. is a set containing the first three counting numbers. 1, 2, and 3 are elements of the set. Example 1. Example 2. is a set containing the the vowel letters in English language.

888 views • 19 slides

even. natural numbers. odd. significant figures. consecutive. rounding. number line. distributive. associative. Natural Numbers. place value. commutative. square root. numerals. highest common factor (HCF). factor. squares. lowest common multiple (LCM). prime number. divisor.

840 views • 1 slides

By the numbers…

30,000 students 8,000 square miles $30 million budget 270 staff members Serving: 40 Districts 11 Non-Public Schools 2 prisons, 2 juvenile facilities, 1 behavior school. By the numbers…. Perspectives…Des Moines Public Schools. 30,000 students 80 square miles $450 million budget

286 views • 18 slides

THE NATURAL NUMBERS. N 0, 1, 2, 3, 4. REMEMBER. 0 zero 1 2 3 4 5 one two three four five 6 7 8 9 10 six seven eight nine ten. 11 12 13 14 15

291 views • 21 slides

The Numbers. 11 Souls Saved Over 300 Bibles Distributed 4 Villages Evangelized Over 15 Villages Reached. The Main Story. Daily VBS Eyeglasses and Toothbrushes Church Services. The Side Story. Contact New Churches A New Plan Jungle Seminary. The New Need. Research and Planning

172 views • 11 slides

Using Definite Knowledge: Axiomatizing the Natural Numbers

Using Definite Knowledge: Axiomatizing the Natural Numbers. Notes for Ch.3 of Poole et al. CSCE 580 Marco Valtorta. Constants, function, intended interpretation. The domain: the natural numbers and a special symbol S Two constants: one and zero One function one --- denotes the number 1

257 views • 14 slides

256 views • 25 slides

Rounding Natural Numbers and Multiplying 3-Digit Numbers by 2-Digit Numbers

Rounding Natural Numbers and Multiplying 3-Digit Numbers by 2-Digit Numbers. Learning Goals. Students will learn to round natural numbers so that they can approximate the result of given equations.

183 views • 13 slides

• Preferences

Natural, Integer and Rational numbers - PowerPoint PPT Presentation

Natural, Integer and Rational numbers

There is no natural number whose successor is 0. ... order if we agree not to distinguish between two sequences a and b if ab and ba. ... – powerpoint ppt presentation.

• The natural numbers are best given by the axioms of Giuseppe Peano (1858 - 1932) given in 1889.
• There is a natural number 0.
• Every natural number a has a successor, denoted by a 1.
• There is no natural number whose successor is 0.
• Distinct natural numbers have distinct successors if a ? b, then a 1 ? b 1.
• If a property is possessed by 0 and also by the successor of every natural number it is possessed by, then it is possessed by all natural numbers.
• Richard Dedekind (1831-1916) proved that any model of above axioms is isomorphic to the natural numbers. In particular one obtains a particular model N from the Zermelo-Fraenkel axioms.
• The set of natural number carries two operations addition and mulitplication.
• Adding the inverse operation of addition namely subtraction, one obtains the integers Z.
• Adding the inverse operation to multiplication to Z one arrives at the rational numbers Q.
• Real numbers are commonly associated to the points on a line. Another way to think of them is as the limit of rational numbers or nested intervals. Both observations lead to definitions of the reals starting from the rationals. The important property here is that the sequence of nested intervals need not converge in Q.
• Axioms for the real numbers
• The set R is a field, i.e., addition, subtraction, multiplication and division are defined and have the usual properties.
• The field R is ordered, i.e., there is a linear order such that, for all real numbers x, y and z
• if x y then x z y z
• if x 0 and y 0 then xy 0.
• The order is Dedekind-complete, i.e., every non-empty subset S of R with an upper bound in R has a least upper bound (also called supremum) in R.
• Dedekind defined the real numbers via so-called cuts
• A Dedekind cut is a subset a of the rational numbers Q that satisfies these properties
• a is not empty.
• Q \ a is not empty.
• a contains no greatest element
• For x,y in Q if x in a and y lt x , then y is in a as well.
• Real numbers can then be defined as the set of Dedekind cuts.
• Cantor defined the real numbers through Cauchy sequences.
• A Cauchy sequence of rationals is a sequence rn in Q indexed by the natural numbers N, such that for any rational e there is a natural number N s.t.
• rm-rnlte for all m, n gtN
• Cauchy sequences (xn) and (yn) can be added, multiplied and compared as follows
• (xn) (yn) (xn yn)
• (xn) (yn) if and only if for every e gt 0, there exists an integer N such that xn yn - e for all n gt N.
• Two Cauchy sequences (xn) and (yn) are called equivalent if such that for any rational e there is a natural number N s.t.
• xn-ynlte for all n gtN
• The real numbers are now defined to be equivalence classes of rational Cauchy sequences.
• The real numbers are then complete, i.e. all Cauchy sequences of real numbers converge.
• Lastly one can use the decimal expansion, which essentially selects a representative for each class, with the proviso that some reals have two decimal expansions which are equivalent, e.g. 1.0000 0.99999 .
• In order to make sense of infinitesimals one should think of them as sequences of real numbers (xn).
• we can also add and multiply sequences (a0, a1, a2, ...) (b0, b1, b2, ...) (a0 b0, a1 b1, a2 b2, ...) and analogously for multiplication.
• Hyperreals are defined as equivalence classes of sequences of reals.
• Two sequences will be equivalent is there difference has infinitely many zeros.
• It turns out, this is not enough, though to get multiplication and an order. In technical detail the slightly larger equivalence is given by an so-called ultrafilter U on the natural numbers which does not contain any finite sets. Such an U exists by the axiom of choice. One can think of U as singling out those sets of indices that "matter when comparing two sets We write (a0, a1, a2, ...) (b0, b1, b2, ...) if and only if the set of natural numbers n an bn is in U. This is a total preorder and it turns into a total order if we agree not to distinguish between two sequences a and b if ab and ba.
• R is then given by sequences in R modulo the above equivalence.
• R has addition, subtraction multiplication, and divison.
• The real numbers are the subset given by the constant sequences (r,r,r..)
• R contains the finite numbers, Fr in R rltr for some r in R
• An infinite number is e.g. given by the sequence (1,2,3,4,.)
• R contains the infinitesimal numbers. Infinitesimals r in R rltr for all r in R
• An infinitesimal is given by the sequence (1,1/2,1/2,1/3, )
• Each finite hyperreal r has a unique standard part st(r) which is defined to be the unique number s.t. r-st(r) is infinitesimal.
• Given a function f R?R, it has a unique extension f to R given by f (a0, a1, a2, ...) (f(a0),f(a1),f(a2), ...)
• Also one writes xy if x-y is infinitesimal
• In this notation f is continuous if f(xh)) f(x) for all infinitesimals h.
• Fix an infinitesimal dx then
• df(x) f(xdx)-f(x)
• df(x)/dx (f(xdx)-f(x))/dx is always defined in R, if it is finite for all reals x and all infinitesimals dx then f is differentiable and df(x)/dxf(x).

PowerShow.com is a leading presentation sharing website. It has millions of presentations already uploaded and available with 1,000s more being uploaded by its users every day. Whatever your area of interest, here you’ll be able to find and view presentations you’ll love and possibly download. And, best of all, it is completely free and easy to use.

You might even have a presentation you’d like to share with others. If so, just upload it to PowerShow.com. We’ll convert it to an HTML5 slideshow that includes all the media types you’ve already added: audio, video, music, pictures, animations and transition effects. Then you can share it with your target audience as well as PowerShow.com’s millions of monthly visitors. And, again, it’s all free.

About the Developers

PowerShow.com is brought to you by  CrystalGraphics , the award-winning developer and market-leading publisher of rich-media enhancement products for presentations. Our product offerings include millions of PowerPoint templates, diagrams, animated 3D characters and more.

• International
• Schools directory
• Resources Jobs Schools directory News Search

Types of Numbers - PowerPoint

Subject: Mathematics

Age range: 14 - 16

Resource type: Worksheet/Activity

Last updated

• Share through email
• Share through twitter
• Share through linkedin
• Share through facebook
• Share through pinterest

Tes classic free licence

Your rating is required to reflect your happiness.

It's good to leave some feedback.

Something went wrong, please try again later.

This resource hasn't been reviewed yet

To ensure quality for our reviews, only customers who have downloaded this resource can review it

Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

Not quite what you were looking for? Search by keyword to find the right resource: