/ Preparation Maths Number SystemBy
All counting numbers from 1 to infinity are known as natural numbers, meaning all positive integers and zero.
All whole numbers are integers, whereas all integers cannot be whole-numbers. We can perform various arithmetic operations like addition, subtraction, multiplication, and division on whole numbers.
- Properties
- Importance and Weightage in Class 10
- Illustrated Examples
- Frequently Asked Questions
Properties
- Commutative property
The commutative property of whole numbers states that the result of the addition or multiplication of two whole numbers is the same irrespective of the order in which the operation is performed.
m + n = n + m and m x n = n x m
- Additive identity
When zero is added to a whole number, the result is the number itself.
m + 0 = m
- Multiplicative identity
When 1 is multiplied by a whole number, the result is the number itself.
m x 1 = m
- Associative property
When more than two whole numbers are added or multiplied, they can be grouped in any manner, and the answer will remain unchanged. Irrespective of the grouping, the result remains the same.(m+n) + p = m + (n+p)
(k x l) x m = k x (l x m)
- Distributive property
When an arithmetic operation is performed on a set, it applies the same to all members of the set.
m.(n-p) = m.n - m.p
m.(n+p) = m.n + m.p
Importance and Weightage in Class 10
The topic of whole numbers is thoroughly explained in Class 9 maths and is a part of the Real Numbers chapter in Class 10. Approximate weightage of this topic in the exams is 2-3 marks.
Illustrated Examples
- Which of these are whole numbers?
5, ½, 89, 3, -7, 4i
Solution:
All the natural numbers and zero are whole numbers.So, from the given set of numbers
5, 3 and 89 are whole numbers.
- A shopkeeper supplies 16 litres of milk to a society in the morning and 34 litres of milk in the afternoon. If the milk costs Rs 45 per litre, how much money does the shopkeeper make per day
Solution:
According to the question, milk supplied in a day is 16 litres and 34 litres.
The cost of milk per liter is Rs. 45
Amount due= quantity of milk in the morning x rate per liter + quantity of milk in the afternoon x rate per liter
Amount due = 16 x 45 + 34 x 45
= (16 + 34) x 45= 50 x 45 = Rs. 2250
- Find the value of 71265 × 149 – 71265 × 49.
Solution:
Using reverse distributive property,
= 71265 (149 - 49)
= 71265 x 100 = 7126500
Frequently Asked Questions
Q: What is the relation between a whole number and a natural number?
Q: What kind of number is zero?
Q: Can a negative number be called a whole number?
Q: What is Closure Property?
Q: Is it possible to determine the biggest whole number?
Maths Number System Exam
Student Forum
Anything you would want to ask experts?Answered 6 days ago
Candidates should first understand basic concepts, including divisibility rules, prime factorisation, HCF and LCM, and remainders. They should then solve topic-wise practice questions and previous years' CAT questions to improve accuracy and problem-solving speed.
S
Contributor-Level 7
Answered 6 days ago
There is no fixed number of questions from the Number System in CAT. The number of questions varies across exam slots and years. Candidates should prepare the topic along with other important areas of Quantitative Aptitude.
A
Contributor-Level 7
Answered 6 days ago
Yes, the Number System is an important topic for CAT Quantitative Aptitude. Questions may test concepts such as divisibility, remainders, factors, and properties of integers. Candidates should also practise applying these concepts to different question types.
J
Contributor-Level 7
Answered 6 days ago
The CAT Number System covers topics such as divisibility rules, factors and multiples, prime numbers, HCF and LCM, remainders, unit digits, factorials, integers, rational numbers, and properties of numbers.
Contributor-Level 10
Answered 2 months ago
CLAT does not publish a fixed count for Number System questions. The UG exam stays largely passage-based. This topic supports calculation inside Quantitative Techniques passages. It does not appear as standalone questions.
S
Contributor-Level 10
Answered 2 months ago
Number System questions cover many types. These include basic property checks, combined divisibility conditions, HCF and LCM problems, remainder patterns and multi condition reasoning. They test calculation speed and accuracy.
S
Contributor-Level 10
Answered 2 months ago
Students can improve step by step. Learn divisibility rules. Practise HCF and LCM daily. Work through remainder questions carefully. Regular revision of common traps also builds accuracy and speed.
S
Contributor-Level 10
Answered 2 months ago
There is no single fixed book for this topic. Students often use standard Class 10 level maths books. Combine these with regular practice sets and previous year papers to build accuracy.
S
Contributor-Level 10
Answered 2 months ago
Students should start early. Practice Number System alongside other Quantitative Techniques topics. Strong basics make combined divisibility and multi condition questions easier later.
S
Contributor-Level 10
Answered 2 months ago
Number System is not a separate scored CLAT topic. But the calculation skills help with passage-based Quantitative Techniques questions. Skipping it fully is not wise. Most passages need quick, accurate number work.
S
Contributor-Level 10
Other Class 10th Maths Chapters
Popular Courses After 12th
Exams accepted
CA FoundationExams accepted
ICSI ExamBachelor of Business Administration & Bachelor of Law
Exams accepted
CLAT | LSAT India | AIBEExams accepted
IPMAT | NMIMS - NPAT | SET
Exams accepted
BHU UET | KUK Entrance Exam | JMI Entrance ExamBachelor of Design in Animation (BDes)
Exams accepted
UCEED | NIFT Entrance Exam | NID Entrance ExamBA LLB (Bachelor of Arts + Bachelor of Laws)
Exams accepted
CLAT | AILET | LSAT India
How can I prepare for the CAT Number System?