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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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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
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.
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)
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).
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.
Begin your journey into Numbers by exploring key concepts. Understand important number topics in detail by selecting from the list below:
1. Cardinal and Ordinal Numbers
2. Even and Odd Numbers
3. Consecutive Numbers
4. Prime and Composite Numbers
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
For example, 28 the divisors are 1, 2, 4, 7, and 14, and by adding them, we get 28
7. Fractions and Decimals
8. Factors and Multiples
9. GCF and LCM
10. Prime Factorization
11. Algebraic and Transcendental 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.
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
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.
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:
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.
While cooking or baking, the right measurement/quantity of ingredients is very crucial.
Time management in scheduling appointments, catching buses, or setting alarms.
In algorithms, computers use binary numbers Zeros and Ones.
Used in sports for calculating timing and statistics.
Medicine dosage calculations, MRI scans, X-rays, etc.
Find the missing two numbers if the sum of 2 consecutive natural numbers is 37.
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
The two consecutive natural numbers are 18 and 19. The sum of 18 and 19 is 37.
Check whether 15 and 28 are co-prime.
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
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.
Find the quotient of 8/3 ÷ 2/3.
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
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.
Show that 5 + 7 is the same as 7 + 5.
Add in the given order, 5 + 7 = 12.
Swap the order, 7 + 5 = 12.
The commutative property of addition says the order doesn’t matter. So, 5 + 7 and 7 + 5 both give the same result: 12.
Simplify (2 × 3) × 4 and 2 × (3 × 4).
First group: (2 × 3) = 6 → 6 × 4 = 24.
Second group: (3 × 4) = 12 → 2 × 12 = 24.
The associative property says grouping doesn’t change the result in multiplication. So both methods give the same answer: 24.
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 |
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.
: She loves to read number jokes and games.