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Numbers

Have you ever counted your candies, checked the time on a clock, or looked at your birthday date? All of these use numbers. Numbers help us count, measure, and describe things around us.

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Professor Greenline from BrightChamps

What are the Numbers in Math?

Numbers can be expressed in both numerical and word form. Like 45 is written as forty-five in words, and “45” is known as numerals. A number system denotes numbers logically using symbols or digits. The numeral system represents a set of numbers using an algebraic or arithmetic structure. Using the digits from 0 to 9, we can form an infinite number of numbers.

In math, there are different types of numbers like

  • Composite numbers
  • Prime numbers
  • Rational numbers
  • Irrational numbers
  • Odd numbers
  • Even numbers
  • Integers
  • Complex numbers, and more.

 

Professor Greenline from BrightChamps

History of Numbers

 

Numbers have not always looked the way they do today. Long ago, early humans used simple marks and symbols to keep count of things around them. As time passed, people created new ways to count and calculate more easily.

 

  • Early humans used symbols and tally marks (////) to count things, but it was hard for large numbers.

 

  • As civilization grew, people created different symbols to represent bigger quantities. Romans used I, V, X, L, C, D, M but had no zero.

 

  • Around the 7th century, India perfected the decimal system (base ten). 

 

  • This system used only ten digits (0-9) to show any number. Aryabhata explained the concept of zero and place value. For example, even Pythagoras once said, 'Everything in this world is made of numbers, even music'.

 

  • Arab merchants and scholars spread it to Europe, and today we call it the Hindu-Arabic numeral system, which is still used everywhere.

     
  • Scientists believe counting systems first emerged in ancient societies like Egypt, Mesopotamia, and India.

     
  • Different numeral systems were developed across the world, and as people traveled, these systems spread across continents. The Indian numeral system spread to the Middle East and Europe, becoming the base of the modern decimal system.

     
  • The Brahmi script (around 3rd century BCE, during Emperor Ashoka's time) is the earliest known numeral system of India. Brahmi numerals had symbols for 1-9 and special symbols for 10, 100, and 1000. They are considered the ancestors of modern numerals (0-9) used worldwide.

     
  • Later, numbers were written in Devanagari script, which is used for Sanskrit.
Professor Greenline from BrightChamps

Properties of Numbers

Numbers follow specific special rules, called properties, that help us solve problems easily and understand math better. These properties demonstrate how numbers behave when we add, multiply, or combine them in various ways.

1. Commutative Property:  If you change the order of two numbers and the answer stays the same, that operation is commutative.
Example:
Addition: 2 + 3 = 3 + 2 = 5
Multiplication: 4 × 5 = 5 × 4 = 20

2. Associative Property: If you group numbers differently but still get the same result, the operation is associative.
Example
Associative property of addition and multiplication: 
Addition:  (1 + 2) + 3 = 1 + (2 + 3) = 6
Multiplication: (2 × 3) × 4 = 2 × (3 × 4) = 24

3. Distributive Property: When one number is multiplied by a group of numbers inside brackets, you can "distribute" it to each number inside.
Example
Distributive property of addition: 
2 × (3 + 4) = (2 × 3) + (2 × 4) = 14.

4. Identity Property: An identity is a special number that doesn't change the value when used in an operation.
Example 
Addition: 5 + 0 = 5 and Multiplication: 8 × 1 = 8

5. Inverse Property: An inverse is a number that cancels out another number to bring you back to the identity.
Additive inverse: Adding a number to its additive inverse results in 0. Example: 6 + (-6) = 0.
Multiplicative inverse: Multiplying a number by its reciprocal gives one.
Example: 5 × (1/5) = 1

6. Closure Property: When you operate (like addition or multiplication) on two numbers from a set, the answer always stays in the same set. That operation is closure.
For instance, we get a whole number if we add two whole numbers together. However, subtracting two natural numbers may not give a natural number. 
Example: 
Integers: 5 + 2 = 7 (an integer)
Whole numbers: 4 × 3 = 12 (a whole number)

 

properties of numbers

Professor Greenline from BrightChamps

Classification of Numbers

Numbers can be classified in different ways based on how we use them and their unique features. Let's explore the different kinds of numbers.


1. Natural Numbers:
These are the basic counting numbers that start from 1 and go on without end.
They are represented by the letter 'N'. 
For example: N = {1,2,3,4,5,...}


2. Whole Numbers :
Whole numbers include all natural numbers along with 0.
They are represented by the letter 'W'. 
For example, W = {0, 1, 2, 3, 4, 5,...}


3. Integers:
Any positive, negative, or zero whole numbers are called integers. For example: -2, -1, 0, 1, 2,...


4. Rational Numbers: 
If a number is written as p/q is called rational number, where q is not zero and both p and q are integers.
For example: 1/2, -3, 57/100. 


5. Irrational Numbers:
These numbers can never be expressed as fractions. For example: π, √2.


6. Real Numbers:
All rational and irrational numbers together make real numbers. For example, 2, -5, √3, 0.5.


7. Complex Numbers:
Complex numbers consist a real part and an imaginary part and are written in the form a + bi, where i = √(-1).

 

classification of numbers

Professor Greenline from BrightChamps

Importance of Numbers for Students

Numbers are significant for students because they play a crucial role in our daily lives. A good understanding of numbers makes learning math easier and more useful in daily life.
 

  • A number is one of the building blocks of mathematics. Understanding numbers and how they relate to each other helps children learn more advanced math concepts later.

     
  • Learning numbers helps children think better. It teaches them to follow sequences and solve problems, which improves their thinking capacity and helps them make connections.

     
  • Learning numbers is also part of language development. When children learn numbers, they practice saying them. This helps improve their vocabulary and makes them better communicators.

     
  • Knowing numbers well helps children do better in school. Children who grasp numbers early can learn not only math, but also other subjects more easily.

     
  • Numbers play a crucial role in learning about money. Being good with numbers helps people understand and manage their finances, such as budgeting, saving, and making informed investments.

     
  • Counting helps kids see that numbers stand for real things when they connect numbers to objects around them.

 

  • Children need to understand that numbers represent quantities and can be used to compare different amounts.


Begin your journey into Numbers by exploring key concepts. Understand important number topics in detail by selecting from the list below:

 

Multiples Factors
Prime Numbers LCM (Least Common Multiple)
Greatest Common Factor Counting In Words
Number Names Divisibility Rules
Even Numbers Odd Numbers
Number Systems Perfect Cubes
Sum Addition
Subtraction of Numbers Binary Number System
Place Value Rounding Numbers
Mixed Numbers Factorial
Quotient Division
Common Factors Whole Numbers
Composite Numbers  
Professor Greenline from BrightChamps

Types of Numbers

1. Cardinal and Ordinal Numbers

  • Cardinal numbers tell us ‘how many’. E.g., 1,2,3…
  • Ordinal numbers show the position or rank. E.g., 1st, 2nd, 3rd….

2. Even and Odd Numbers

  • Even numbers can be evenly divided by 2. e.g., 2, 4, 6.
  • Odd numbers cannot be divided by 2, e.g., 1, 3, 5.

3. Consecutive Numbers

  • Numbers that follow each other in order. E.g., 1, 2, 3 or 5, 6, 7

4. Prime and Composite Numbers

  • Prime numbers have only two divisors: 1 and the number itself. E.g., 2, 3, 5
  • Composite numbers have more than two divisors. E.g., 4, 6, 8

5. Co-Prime Numbers

Example: 8 and 15 are co-prime because the common factor between them is 1. However, 15 and 9 are not co-prime numbers, as they share 3 as a common factor.
6. Perfect Numbers

  • A perfect number is equal to the sum of its factors.

For example, 28 the divisors are 1, 2, 4, 7, and 14, and by adding them, we get 28
7. Fractions and Decimals

  • Fractions are numbers that show a part of the whole. Example: 12
  • The decimals show the numbers in base 10. Example: 0.5.

8. Factors and Multiples

  • Factors divide a number without leaving a remainder. Example: Factors of 12 are 1, 2, 3, 4, 6, and 12.
  • Multiples are the result of multiplying a number by an integer. Example: Multiples of 3 are 3, 6, 9, 12, etc.

9. GCF and LCM

  • GCF (also known as HCF) is the most significant number that divides two numbers evenly. Example: The GCF of 12 and 18 is 6, because it divides both evenly.
  • LCM is the smallest multiple of two or more number. Example: LCM of 5 and 10 is 10. So, 10 can be divided by both 5 and 10 evenly.

10. Prime Factorization

  • Prime factorization is the process of writing a number down into its prime factors. Example: Prime factors of 18 are 2 × 3 × 3.

11. Algebraic and Transcendental Numbers

  • Algebraic numbers solve polynomial equations. Example: 2
  • Transcendental numbers do not solve any polynomial equation. Example: π
Professor Greenline from BrightChamps

Tips and Tricks to Learn Numbers

Understanding numbers can be made simpler using a few tricks. Like a game, the more we practice, the easier it gets. Here are a few tips and tricks that can make understanding numbers easier.

  • Think about how you use numbers every day. For example, if your alarm is set for 6:48 am, you can break it down to see how many minutes you have left to sleep.
  • Use the distributive property: Big numbers may sometimes seem intimidating, so break them down into smaller numbers.

Why not try dividing them into parts?
For example: 48 + 36
Group the numbers according to their place values
40 + 8 = 48;
36 = 30 + 6
Now add the numbers in the tens place and ones place,
40 + 30 = 70;
8 + 6 = 14;
70 + 14 = 84

  • Rounding numbers for estimations makes calculations easier. For example, to add 487 + 293, round off to 490 + 290 = 780.
  • Use the rule of divisibility: when the last digit is even, it is divisible by 2; when the last digit is 0 or 5, it is divisible by 5, respectively. The sum of digits is divisible by 3; then the number is a multiple of 3

 

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in Numbers

While we learn about numbers, children are likely to get confused, considering there are separate topics that we learn about. Given below are a few mistakes that children make and how to avoid them.

Mistake 1

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Misunderstanding Place Values (ones, tens, hundreds)
 

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 Learning place values in numbers is very important. Sometimes students are confused about the place values of numbers. For 205, they read it as two hundred and five and wrote it as twenty-five. To avoid this, students can break numbers into place values. And then easily write it according to the place values.
 

Mistake 2

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Confusing Roman Numerals.
 

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Kids get confused or misread the Roman numbers. For example, VI(6) as 4, IX(9) as 11. To avoid such errors, kids should be aware of when to apply the addition rule and subtraction rule
 

Mistake 3

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Errors in Division
 

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In division, we cannot divide a number with 0. For example, we cannot divide an object among 0 people, so we cannot divide any number with 0.  Students should understand that division is used to find how many times a number is in another. 
 

Mistake 4

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 Misunderstanding the Concept of Negative Numbers
 

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Errors are common among kids when performing operations with negative numbers. For example: -4 + 5 = 9 (incorrect) instead of 1 (correct)

-4 × -5 = -20 (incorrect) instead of 20 (correct)

6 - (-3) = 3 (incorrect) instead of 9 (correct).

So students should learn the basic rules and practice regularly using numbers lines. 

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Professor Greenline from BrightChamps

Real-World Applications of Numbers

Numbers are an important part of our daily lives. They are used for simple and complex tasks. Here are a few real-world applications of numbers:
 

1. Budgeting and accounting:

budgeting and accounting

1. Budgeting and accounting:

Ever wondered how you manage your pocket money, plan a trip, or save up for something you want to buy? That's numbers at work, balancing income, and other goals we want to reach.

2. Precision in the Kitchen:

precision in the kitchen

2. Precision in the Kitchen:

While cooking or baking, the right measurement/quantity of ingredients is very crucial.

3. Mastering the Clock:

mastering the clock

3. Mastering the Clock:

Time management in scheduling appointments, catching buses, or setting alarms.

4. Technology and computing:

technology and computing

4. Technology and computing:

In algorithms, computers use binary numbers Zeros and Ones.

5. Sports:

sports

5. Sports:

Used in sports for calculating timing and statistics.

6. Medicine:

medicine

6. Medicine:

Medicine dosage calculations, MRI scans, X-rays, etc.

Max from BrightChamps Saying "Hey"
Hey!

Examples of Numbers

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Find the missing two numbers if the sum of 2 consecutive natural numbers is 37.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

Let the two consecutive natural numbers be x and x+1.

x + (x+1) = 37


2x + 1 = 37


2x = 36


x = 18


Therefore, x + 1 = 19
 

Explanation

The two consecutive natural numbers are 18 and 19. The sum of 18 and 19 is 37.

Max from BrightChamps Praising Clear Math Explanations
Well explained 👍
Max, the Girl Character from BrightChamps

Problem 2

Check whether 15 and 28 are co-prime.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

To Check if 15 and 28 are co-prime, 


The prime factors of 15 = 3 × 5


The prime factors of 28 = 2 × 2 × 7


Hence, there are no common factors other than, 1, 15 and 28 are co-prime
 

Explanation

Co-prime numbers have only 1 common factor between them, that is 1. Here, 15 and 28 have only 1 in common. Therefore, they are co-prime numbers.
 

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Max, the Girl Character from BrightChamps

Problem 3

Find the quotient of 8/3 ÷ 2/3.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

To divide, 8/3 ÷   2/3 


Multiplying 8/3 with the reciprocal of 2/3


That is, (8/3) × (3/2) = 24/6


Simplifying the fraction, 24/6 = 4

Explanation

 To divide a fraction, we multiply the first fraction with the reciprocal of the second fraction. When we divide the given fractions, we get the quotient to be 4.
 

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Max, the Girl Character from BrightChamps

Problem 4

Show that 5 + 7 is the same as 7 + 5.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

Add in the given order, 5 + 7 = 12.


Swap the order, 7 + 5 = 12.
 

Explanation

The commutative property of addition says the order doesn’t matter. So, 5 + 7 and 7 + 5 both give the same result: 12.
 

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Max, the Girl Character from BrightChamps

Problem 5

Simplify (2 × 3) × 4 and 2 × (3 × 4).

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"
Okay, lets begin

First group: (2 × 3) = 6 → 6 × 4 = 24.


Second group: (3 × 4) = 12 → 2 × 12 = 24.
 

Explanation

The associative property says grouping doesn’t change the result in multiplication. So both methods give the same answer: 24.
 

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Well explained 👍
Ray Thinking Deeply About Math Problems

FAQs on Numbers

1.Define natural numbers.

Natural numbers begin with 1 and continuing infinitely. These numbers are represented by the letter 'N'. N = {1,2,3,4,5,...}
 

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2.What are odd numbers?

The numbers that cannot be divided by 2 such as 1, 3, 5.
 

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3.What does Z mean in math?

The letter Z is the symbol used to represent integers. Integers are both positive and negative numbers combined.
 

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4.What is a rational number?

A number that is the p/q form, where q is not equal to 0. Example: 1/2,-3,0.57/100.

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5.What are prime numbers?

The numbers that are divisible by 1 and the number alone are called prime numbers. E.g., 2,3,5

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6.What are the types of numbers?

Numbers are of different types like natural, whole, integers, rational, irrational, real, and complex numbers.

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7.What are the properties of a number

Numbers follow rules like commutative, associative, distributive, identity, and inverse properties.

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8.What is the difference between a number an integer

A number is any value used for counting, measuring, or labeling. Whereas, an integer is a number that can be positive, negative, or zero but has no fractions or decimals.

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9.What is a number system?

A number system is a method to represent and write numbers using symbols. For example, Hindu-Arabic, Roman and Decimal systems.

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10.What is the smallest number?

The smallest whole number is 0. However, since integers go on forever in the negative direction, there is no smallest integer.

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11.How can children in United Arab Emirates use numbers in everyday life to understand Numbers?

Numbers appear everywhere—from counting money to measuring ingredients. Kids in United Arab Emirates see how Numbers helps solve real problems, making numbers meaningful beyond the classroom.

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12.What are some fun ways kids in United Arab Emirates can practice Numbers with numbers?

Games like board games, sports scoring, or even cooking help children in United Arab Emirates use numbers naturally. These activities make practicing Numbers enjoyable and connected to their world.

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13.What role do numbers and Numbers play in helping children in United Arab Emirates develop problem-solving skills?

Working with numbers through Numbers sharpens reasoning and critical thinking, preparing kids in United Arab Emirates for challenges inside and outside the classroom.

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14.How can families in United Arab Emirates create number-rich environments to improve Numbers skills?

Families can include counting chores, measuring recipes, or budgeting allowances, helping children connect numbers and Numbers with everyday activities.

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Professor Greenline from BrightChamps

Explore More Math Topics

From Numbers to Geometry and beyond, you can explore all the important Math topics by selecting from the list below:
 

Multiplication Tables Geometry
Algebra Calculus
Measurement Trigonometry
Commercial Math Data
Math Formulas Math Questions
Math Calculators Math Worksheets
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Math Teacher Image

Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

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