Anand Classes provides the best SSC exam preparation study material, covering important mathematics topics like Natural Numbers, Whole Numbers, Integers, and Fractions with detailed explanations, examples, and solved questions. These concepts form the foundation for SSC CGL, SSC CHSL, SSC MTS, SSC GD, and other competitive exams where number system questions are frequently asked. Our SSC Maths notes are designed to help aspirants understand the basics clearly and practice effectively with exam-oriented questions. Click the print button to download study material and notes.
REAL NUMBERS – SSC Exam Notes
The study of numbers begins with natural numbers, whole numbers, and integers. However, understanding only these types of numbers is not sufficient for a complete study of mathematics.
In SSC Mathematics and other competitive exams, a deeper knowledge of numbers is required. This chapter covers real numbers, including rational numbers and irrational numbers, along with their laws and properties.
Types of Numbers
1. Natural Numbers (N)
- All counting numbers are called natural numbers.
- Represented by N.
- Example: N = {1, 2, 3, 4,…}
2. Whole Numbers (W)
- All counting numbers together with 0 form the set of whole numbers.
- Represented by W.
- Example: W = {0, 1, 2, 3,…}
3. Integers (Z or I)
- All natural numbers, 0, and negatives of counting numbers form the set of integers.
- Represented by Z (or I).
- Example: Z={…,−3, −2, −1, 0, 1, 2, 3,…}
Observation:
- Set of natural numbers (N) ⊂ Integers (Z).
- Set of whole numbers (W) ⊂ Integers (Z).
Properties of Integers
- The opposite of an integer m is –m, equidistant from zero on a number line.
- Product of two positive integers = positive integer.
- Product of two negative integers = positive integer.
- Product of a positive integer and a negative integer = negative integer.
Successor and Predecessor of Integers
- Successor: Number obtained by adding 1.
Example: Successor of –10 = –10 + 1 = –9. - Predecessor: Number obtained by subtracting 1.
Example: Predecessor of –7 = –7 – 1 = –8.
Fractions
- A number of the form a/b, where a, b ∈ Z and b ≠ 0, is called a fraction.
FAQs on Types of Numbers – SSC Exam Preparation
Q1. What are Natural Numbers?
Answer:
- All counting numbers are called natural numbers.
- Represented by N.
- Example: N={1, 2, 3, 4,…}
- Natural numbers do not include 0 or negative numbers.
👉 Useful for SSC Math preparation, download SSC notes and SSC study material PDF for practice.
Q2. What are Whole Numbers?
Answer:
- Whole numbers are all natural numbers together with 0.
- Represented by W.
- Example: W={0, 1, 2, 3,…}
- Whole numbers start from 0. So, 0 is the smallest whole number.
👉 Important for SSC CGL Maths, download SSC math notes preparation material PDF for revision.
Q3. What are Integers?
Answer:
- Integers include all natural numbers, 0, and negatives of natural numbers.
- Represented by Z (or I).
- Example: Z={…,−3, −2, −1, 0, 1, 2, 3,…}
- Observations:
- Natural Numbers (N) ⊂ Integers (Z)
- Whole Numbers (W) ⊂ Integers (Z)
👉 For SSC exams like CGL, CHSL, GD Constable, practice integers from SSC maths notes PDF and SSC exam study material.
Q4. What are the important properties of Integers?
Answer:
- The opposite of an integer m is –m, both are equidistant from 0.
- Product of two positive integers = positive integer.
- Product of two negative integers = positive integer.
- Product of a positive integer and a negative integer = negative integer.
👉 These properties are frequently asked in SSC Maths Questions. Download SSC preparation notes and SSC study material PDF for practice.
Q5. What is the Successor and Predecessor of an Integer?
Answer:
- Successor: Obtained by adding 1.
- Example: Successor of –10 = –10 + 1 = –9.
- Predecessor: Obtained by subtracting 1.
- Example: Predecessor of –7 = –7 – 1 = –8.
- Every integer has both a successor and a predecessor.
👉 Learn these concepts for SSC exam math preparation. Download SSC notes PDF and SSC maths study material for practice.
Q6. What is a Fraction?
Answer:
- A number of the form a/b, where a, b ∈ Z and b ≠ 0, is called a fraction.
- Examples: $frac{2}{3}, quad frac{-5}{8}, quad frac{7}{4}$
- Fractions can be proper, improper, or mixed numbers.
👉 Fractions are important in SSC CGL, CHSL, MTS exams. Download SSC math notes preparation PDF and SSC study material for better practice.
✅ Quick SSC Exam Tip:
- Smallest Natural Number = 1
- Smallest Whole Number = 0
- Smallest Integer = No smallest integer (goes to –∞)
👉 Revise these from SSC Maths Notes PDF and SSC study material for exam preparation.
SSC Exam MCQs on Types of Numbers
Q1. Which of the following is the set of Natural Numbers (N)?
(A) {0, 1, 2, 3, …}
(B) {1, 2, 3, 4, …}
(C) {…, –2, –1, 0, 1, 2, 3, …}
(D) {–1, 0, 1}
✅ Answer: (B) {1, 2, 3, 4, …}
Explanation: Natural numbers are counting numbers starting from 1. Zero and negative numbers are not included.
👉 Important for SSC CGL Math. Download SSC maths notes PDF for practice.
Q2. What is the smallest Whole Number (W)?
(A) –1
(B) 0
(C) 1
(D) None of these
✅ Answer: (B) 0
Explanation: Whole numbers include all natural numbers along with 0. So, 0 is the smallest whole number.
👉 Frequently asked in SSC CHSL maths questions. Download SSC study material PDF for revision.
Q3. Which of the following is true about Integers (Z)?
(A) Z = {1, 2, 3, …}
(B) Z = {0, 1, 2, 3, …}
(C) Z = {…, –2, –1, 0, 1, 2, 3, …}
(D) Z = {–1, 0, 1}
✅ Answer: (C) Z = {…, –2, –1, 0, 1, 2, 3, …}
Explanation: Integers consist of negative numbers, zero, and positive numbers.
👉 Practice from SSC exam maths notes PDF for better preparation.
Q4. What is the successor of –15?
(A) –16
(B) –14
(C) –15
(D) 15
✅ Answer: (B) –14
Explanation: Successor of an integer = integer + 1. So, –15 + 1 = –14.
👉 Repeated concept in SSC GD and SSC CGL math section. Download SSC math notes preparation PDF.
Q5. If the product of two integers is positive, then which of the following is true?
(A) Both are positive
(B) Both are negative
(C) One is positive and one is negative
(D) Both (A) and (B)
✅ Answer: (D) Both (A) and (B)
Explanation:
- Positive × Positive = Positive
- Negative × Negative = Positive
👉 Concept-based question often asked in SSC CGL and SSC CHSL maths. Revise from SSC study material PDF.
Q6. Which of the following is NOT a fraction?
(A) 2/3
(B) –5/7
(C) 0/4
(D) 4/0
✅ Answer: (D) 4/0
Explanation: In a fraction a/b, denominator (b) ≠ 0. Hence, 4/0 is not a valid fraction.
👉 Important for SSC MTS & CGL maths preparation. Download SSC maths notes PDF for practice.
Q7. Which of the following relations is correct?
(A) N ⊂ Z
(B) W ⊂ Z
(C) Both (A) and (B)
(D) None of these
✅ Answer: (C) Both (A) and (B)
Explanation:
- Natural numbers (N) are included in Integers (Z).
- Whole numbers (W) are also included in Integers (Z).
👉 Frequently tested in SSC Maths exam questions. Practice more from SSC notes PDF and SSC exam study material.
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