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Numbers are among the most important concepts in mathematics. Without our notice, we apply numbers in our daily lives. For activities like setting alarms, budgeting, managing time, and increasing productivity at work numbers are used.
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Numbers are the common tools used for counting or measuring the quantity of events, objects or individuals. It is a fundamental tool used for mathematical operations. Numbers are also used for collecting and labelling data.
There are different kinds of numbers like
Initially, numbers were represented by basic symbols. Over time, humans created unique symbols to represent them.
So now, let’s discuss some mathematical operations like addition, multiplication, and division. Numbers have certain rules to make it easier.
1. Commutative Property : This property tells us the order of numbers does not matter. The result is the same regardless of the order. We apply commutative property in addition and multiplication.
Example:
Addition: 2 + 3 = 3 + 2 = 5
Multiplication: 4 × 5 = 5 × 4 = 20
2. Associative Property:This property shows us that the way numbers are grouped does not affect the result.
It is applied in addition and multiplication.
Example of 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: Multiplying a number with a sum or difference gives the same result as doing each multiplication separately. Distributive property is about simplifying a complex expressions to make calculations easy.
A factor can be distributed to each member of a group of numbers that have been subtracted or added.
The factor is distributed and multiplied separately by each term in the group.
Example of distributive property of addition:
2 × (3 + 4) = (2 × 3) + (2 × 4) = 14.
4. Identity Property: The identity property tells us that a few operations leave numbers unchanged.
In addition, adding 0 to a number does not change it.
In multiplication, multiplying 1 does not change the number.
Example for identity property:
Addition: 5 + 0 = 5 and Multiplication: 8 × 1 = 8
5. Inverse Property: In the inverse property, the effect of an operation is reversed:
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: Closure property is when we perform a certain operation on two numbers, which will result in a number within the same set.
For instance, we get a whole number if we add two whole numbers together. However, when 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 grouped into different. Depending on how we use them and their characteristics. Let’s get to know more about numbers:
1. Natural Numbers:
Natural numbers are used for counting, starting from 1 and continuing infinitely.
These numbers are represented by the letter ‘N’.
For example: N = {1,2,3,4,5,...}
2. Whole Numbers :
The whole numbers consist of all natural numbers and 0
They are represented by the letter ‘W’.
For example W = {0, 1, 2, 3, 4, 5,...}
3. Integers:
Integers are numbers that can either be positive, negative, or zero.
They do not include fractions or decimals.
For example: -2, -1, 0, 1, 2,...
4. Rational Numbers:
A number that can be written as a fraction.
It is represented in the p/q form, where q is not equal to 0 and both p, q are integers.
For example: 1/2, -3, 57/100.
5. Irrational Numbers:
Irrational numbers cannot be written as fractions.
They cannot be represented in the form p/q, where p and q are integers.
For example: π, √2.
6. Real Numbers:
All the rational and irrational numbers form a group of real numbers. For example, 2,-5, √3, 0.5.
7. Complex Numbers:
Complex numbers are divided into parts: real and imaginary. Here, a + bi, where i = √(-1).
Numbers are everywhere in our daily lives! They help us count, measure, and solve problems in school and in real 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
For co-prime numbers, two numbers that share no common factors other than 1.
Example: 8 and 15 are co-prime because the common factor between them is 1. But 15 and 9 are not co-prime numbers, they have 3 as a common factor.
6. Perfect Numbers
A perfect number is a positive integer which is equal to the sum of its factors or positive divisor excluding the number itself
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
GCF (also known as HCF) is the greatest common factor two numbers share. Example: GCF of 12 and 18 is 6 because it divides both. LCM is the least common multiple that two numbers share. Example: LCM of 4 and 6 is 12.
10. Prime Factorization
The breaking down of numbers into their factors. Example: prime factors of 18 are 2 × 3 × 3.
11. Algebraic and Transcendental Numbers
Understanding numbers can be made simpler using a few tricks. Like 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 one's 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.