3176 Learners
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.
Share Post:
Trustpilot | Rated 4.7
1,292 reviews
Numbers can be represented in two ways: numerically and in words. For example, 45 in words is "forty-five", while in numbers it is "45". A number system organizes numbers logically using symbol or digits, and a numeral system defines a collection of numbers within an arithmetic or algebraic structure. By combining the digits 0 to 9, we can create 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 are 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, it is called a 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 - Rational and irrational numbers together make real numbers. For example, 2, -5, √3, 0.5.
7. Complex Numbers - Complex numbers consist of 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:
Numbers can be grouped based on their types and usage. Let us see what are all the types of numbers.
1. Cardinal and Ordinal Numbers - The numbers that indicate quantity are called cardinal numbers. For example, 1, 2, 3, 4... The numbers that show position or order are called ordinal numbers. For example, 1st, 2nd, 3rd…
2. Even and Odd Numbers - Even numbers are divisible by 2. For example, 2, 4, 6. While odd numbers are not divisible by 2. For example, 1, 3, 5.
3. Consecutive Numbers - Numbers that follow one another consecutively. For example, 1, 2, 3 or 5, 6, 7.
4. Prime and Composite Numbers - Prime numbers have only two divisors. For example, 2, 3, 5. Composite numbers have more than two divisors. For example, 4, 6, 8.
5. Co-Prime Numbers - Co-prime numbers are pairs of numbers with no common factors except 1. For 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 - Numbers equal to the sum of their proper divisors. For example, 6 has the divisors 1, 2, and 3, and by adding them we get 6.
7. Fractions and Decimals - Fraction show parts of a whole. For example, 12. While decimals express numbers in base 10. For example, 0.5.
8. Factors and Multiples - Factors divide a number exactly. For example, factors of 12 are 1, 2, 3, 4, 6, and 12. Multiples are products of a number. For example, multiples of 3 are 3, 6, 9, 12 etc.
9. GCF and LCM - GCF is the greatest common divisor. For example, the GCF of 12 and 18 is 6, because it divides both evenly. While LCM is the smallest common multiple. For example, LCM of 5 and 10 is 10. So, 10 can be divided by both 5 and 10 evenly.
10. Prime Factorization - Expressing a number as a product of its prime factors. For example, prime factorization of 18 is 2 × 3 × 3.
11. Algebraic and Transcendental Number - Algebraic numbers satisfy polynomial equations, while transcendental numbers do not. For example, π.
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.
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
When learning about numbers, children may get confused since there are many topics to understand. 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, and similar medical procedures rely on accurate numbers to ensure patient safety and correct results.
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
Since 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, \( \frac{8}{3} \div \frac{2}{3} \)
Multiplying\( \frac{8}{3} \) with the reciprocal of \( \frac{2}{3} \)
That is, \( \frac{8}{3} \times \frac{3}{2} = \frac{24}{6} \)
Simplifying the fraction, \( \frac{24}{6} = 4 \)
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 as 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.