What Are the Four Basic Number Properties in Maths?
Understanding More On Number Properties is essential for every student tackling arithmetic, algebra, or competitive exams like JEE and NEET. Properties such as commutative, associative, distributive, and identity not only make calculations easier but also form the foundation for more advanced maths topics. At Vedantu, we help students grasp these number properties clearly, supporting exam success and deeper mathematical thinking.
What Are Number Properties?
Number properties are key rules about how numbers behave with different operations. The primary properties you will encounter are the commutative property, associative property, distributive property, and identity property. These properties apply to both addition and multiplication, and knowing them helps simplify problems, check answers, and avoid mistakes in exams.
Summary Table: Properties of Numbers
| Property | Definition | Operation | Example |
|---|---|---|---|
| Commutative | The order of numbers can be changed without changing the result. | Addition, Multiplication | 3 + 5 = 5 + 3 4 × 6 = 6 × 4 |
| Associative | The way numbers are grouped does not affect the outcome. | Addition, Multiplication | (2 + 3) + 4 = 2 + (3 + 4) (5 × 2) × 10 = 5 × (2 × 10) |
| Distributive | Multiplication can be applied to each part inside a bracket before adding or subtracting. | Multiplication over Addition/Subtraction | 2 × (3 + 6) = (2 × 3) + (2 × 6) |
| Identity | Adding 0 or multiplying by 1 does not change the number. | Addition (0), Multiplication (1) | 9 + 0 = 9 7 × 1 = 7 |
Applying Each Number Property: Stepwise Examples
- Commutative (Addition):
6 + 2 = 8; 2 + 6 = 8. The sum is the same no matter the order. - Commutative (Multiplication):
4 × 3 = 12; 3 × 4 = 12. - Associative (Addition):
(1 + 5) + 2 = 6 + 2 = 8; 1 + (5 + 2) = 1 + 7 = 8. Grouping does not change the sum. - Associative (Multiplication):
(2 × 5) × 4 = 10 × 4 = 40; 2 × (5 × 4) = 2 × 20 = 40. - Distributive:
3 × (7 + 2) = 3 × 9 = 27; or (3 × 7) + (3 × 2) = 21 + 6 = 27. - Identity (Addition):
15 + 0 = 15. - Identity (Multiplication):
9 × 1 = 9.
Key Formulae: Number Properties
- Commutative: a + b = b + a; a × b = b × a
- Associative: (a + b) + c = a + (b + c); (a × b) × c = a × (b × c)
- Distributive: a × (b + c) = a × b + a × c
- Identity: a + 0 = a; a × 1 = a
Practice Problems
- 1. Does 5 + (3 + 6) = (5 + 3) + 6? Which property is illustrated?
- 2. Solve using distributive property: 4 × (8 + 12)
- 3. Is 7 × 0 = 0 an example of identity property?
- 4. What is the value of 0 + 27? State the property.
- 5. Without calculating directly, prove that 3 × 25 = 25 × 3.
- 6. Simplify: (2 × 4) × 5 and 2 × (4 × 5). Are results equal?
- 7. Find a number which, when multiplied by 1, gives 96 back.
- 8. Write an example showing distributive property with subtraction.
Common Mistakes to Avoid
- Confusing the associative property (grouping) with commutative property (order).
- Applying commutative or associative properties to subtraction or division (these do not always apply).
- Forgetting distributive property connects multiplication with addition or subtraction, not with division.
- Assuming the identity property applies to zero in multiplication (a × 0 = 0 – this is zero property, not identity).
Real-World Applications
Number properties are used daily in mental maths, budgeting, coding, and solving equations. For example, when splitting a bill (distributive property), rearranging shopping items for easier calculation (commutative), or verifying calculations quickly using identity property. In competitive exams like JEE and NEET, recognizing and applying these properties can make complex problems simpler and faster to solve.
Importance for Class 6/7/8 Syllabus and Exams
- Properties of whole numbers, natural numbers, and integers form the basis of most arithmetical operations in whole numbers.
- Class 6/7 students must master these to solve NCERT and CBSE exam questions confidently.
- Algebraic expressions and mental math strategies often rely on distributive and commutative properties.
At Vedantu, we emphasize clear, stepwise learning of More On Number Properties, equipping you for school exams and real-life problem solving. For deeper understanding, explore related topics such as Properties of Whole Numbers or practice using our downloadable worksheets on number properties.
To sum up, mastering number properties gives you powerful tools for simplifying problems, checking your work, and laying a solid foundation for higher mathematics. Practice regularly, use tables and examples, and soon these properties will become second nature in every maths problem you solve.
FAQs on Number Properties Explained with Examples
1. What are number properties?
Number properties are fundamental rules in mathematics that govern how numbers behave under operations like addition and multiplication. They help simplify calculations and solve problems more efficiently. Key properties include commutative, associative, distributive, and identity properties.
2. What are the 4 main properties of math?
The four main number properties are: commutative (order doesn't matter), associative (grouping doesn't matter), distributive (combining multiplication and addition), and identity (adding zero or multiplying by one doesn't change the number).
3. Can you give examples for each property?
Yes! Here are examples for each property:
- Commutative (Addition): 3 + 5 = 5 + 3
- Commutative (Multiplication): 4 × 6 = 6 × 4
- Associative (Addition): (2 + 3) + 4 = 2 + (3 + 4)
- Associative (Multiplication): (5 × 2) × 3 = 5 × (2 × 3)
- Distributive: 2 × (3 + 5) = (2 × 3) + (2 × 5)
- Identity (Addition): 7 + 0 = 7
- Identity (Multiplication): 9 × 1 = 9
4. Are these properties the same for multiplication and addition?
Many properties apply to both addition and multiplication, like the commutative and associative properties. However, the distributive property uniquely links multiplication and addition.
5. What are the more properties of numbers?
Beyond the four main properties, other number properties include the closure property (the result of an operation remains within the same set of numbers), and the inverse property (every number has an additive or multiplicative inverse).
6. What are number properties? Why are number properties important?
Number properties are rules governing arithmetic operations (addition, subtraction, multiplication, division). They're crucial for simplifying calculations, understanding mathematical relationships, and building a strong foundation for algebra.
7. What are the 7 properties of whole numbers?
While there isn't a universally defined list of '7 properties,' key properties for whole numbers include closure under addition and multiplication, commutative and associative properties for both operations, distributive property, and identity elements (0 for addition, 1 for multiplication).
8. How do I use distributive property?
The distributive property states a(b + c) = ab + ac. To use it, multiply the term outside the parentheses by each term inside, then add the results. For example: 3(x + 2) = 3x + 6
9. What is commutative property?
The commutative property states that the order of numbers in addition or multiplication does not affect the result. For example, 5 + 3 = 3 + 5 and 4 × 2 = 2 × 4.
10. How do number properties help in maths?
Number properties significantly simplify calculations, allowing for mental math strategies, efficient problem-solving, and a deeper understanding of mathematical relationships. They are essential for algebra and beyond.
11. What are the properties of whole numbers with examples class 6?
Class 6 typically covers the commutative, associative, distributive, and identity properties. Examples include: 2 + 3 = 3 + 2 (commutative), (1 + 2) + 3 = 1 + (2 + 3) (associative), and 2(3 + 4) = 2(3) + 2(4) (distributive).
12. Properties of numbers with examples?
Key properties of numbers include: Commutative Property (a + b = b + a; a × b = b × a), Associative Property ((a + b) + c = a + (b + c); (a × b) × c = a × (b × c)), Distributive Property (a × (b + c) = a × b + a × c), and Identity Property (a + 0 = a; a × 1 = a).
