Whole Numbers & Integers — REET Maths Notes
Whole numbers and integers are the most basic building blocks of arithmetic, and questions from them show up in the Number System section of the REET maths paper. This page walks through their definitions, the four core properties (closure, commutative, associative, distributive) and the rules for adding and subtracting integers, all with worked examples, so both your calculation speed and accuracy improve.
- 0 questions in REET 2024
- Class 6 level
- 9 min read
How this topic is asked in REET
The Number System section of the REET maths syllabus includes basic building blocks like whole numbers. No direct question from this specific sub-topic showed up in the REET 2024 paper, so this page is built on standard syllabus facts and the NCERT Class 6 maths textbook. Typically, a question asks you to add or subtract integers, or identify a property (closure/commutative/associative). Sometimes a real-life situation (temperature, height-depth, profit-loss) is given and you're asked to convert it into an integer expression and solve it.
Defining whole numbers and integers
Natural numbers are the numbers used for counting — 1, 2, 3, 4... Adding 0 to natural numbers gives you whole numbers — 0, 1, 2, 3... Adding negative numbers (such as −1, −2, −3...) to whole numbers gives you integers, which include positive numbers, negative numbers and zero, all three.
The easiest way to understand integers is on a number line — place 0 in the middle, write positive integers (1, 2, 3...) increasing to the right, and negative integers (−1, −2, −3...) increasing in magnitude to the left. Whichever number sits further to the right on the number line is the larger one — so −2 is greater than −5, even though both are negative.
Whole numbers are used in everyday life for counting, ordering and showing quantity, while integers are used wherever you need to show a position above or below, or ahead or behind, some reference point — for example, height above sea level (positive) or depth below it (negative), temperature above or below zero, and a deposit (positive) or overdraft (negative) in a bank account. REET also builds questions around these kinds of practical, everyday examples.
Properties of whole numbers
| Property | Addition/Multiplication (+, ×) | Subtraction/Division (−, ÷) |
|---|---|---|
| Closure property | Whole numbers are closed under addition and multiplication (the result is always a whole number) | Not closed under subtraction or division (e.g. 5 − 8 = −3, which is not a whole number) |
| Commutative property | a + b = b + a and a × b = b × a | Does not hold for subtraction or division (5 − 3 ≠ 3 − 5) |
| Associative property | (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c) | Does not hold for subtraction or division |
| Distributive property | a × (b + c) = (a × b) + (a × c) | — |
Here a, b, c can be any whole numbers
Identity elements and consecutive numbers
- Additive identity
- 0 is the additive identity, because adding 0 to any whole number a gives back a (a + 0 = a)
- Multiplicative identity
- 1 is the multiplicative identity, because a × 1 = a
- Successor
- The next number you get by adding 1 to a number — for example, the successor of 25 is 26
- Predecessor
- The previous number you get by subtracting 1 from a number — for example, the predecessor of 25 is 24; note that 0 has no predecessor among whole numbers
Integer addition and subtraction — key rules
| Rule | Example |
|---|---|
| When adding integers with the same sign, add the numbers and keep that same sign | (−4) + (−6) = −10 |
| When adding integers with different signs, subtract the smaller number from the larger and give the sign of the larger number | (−7) + 4 = −3, because 7 > 4 |
| Subtracting an integer is the same as adding its additive inverse | 8 − (−3) = 8 + 3 = 11 |
Sign rules for multiplying and dividing integers
- Same sign
- Positive × positive = positive; negative × negative = positive — for example, (−3) × (−4) = 12
- Different signs
- Positive × negative = negative; negative × positive = negative — for example, (−3) × 4 = −12
- Same rule applies to division
- The same sign rule that applies to multiplication also applies to division (÷) — for example, (−12) ÷ (−3) = 4
- A quick trick to remember
- Count the number of negative signs — an even count of negative signs gives a positive final result, and an odd count gives a negative final result
How to teach this to children
Classroom activity
Draw a large number line on the classroom floor with chalk and let students physically walk it to add and subtract integers — for example, starting at −3 and walking 5 steps to the right, then stating the final position.
Teaching aid
Use coloured counters (red = negative, blue = positive) to teach integer addition — an equal number of red and blue counters 'cancel out', and the counters that remain show the answer.
Common misconception
Students often assume subtraction is commutative like addition, but 5 − 3 and 3 − 5 give different results — clear this up by showing both on a number line.
Assessment idea
Give students everyday examples (rising or falling temperature, deposits and withdrawals in a bank account, height above or depth below sea level) and have them express these as integers, carry out simple addition and subtraction, and also show the working on a number line.
A trick worth remembering
'Add and multiply, you never leave the set; subtract and divide, you might step outside it' — whole numbers always give you back a whole number under addition and multiplication, but subtraction and division can produce a negative number or a fraction. To remember the sign rule for multiplying and dividing integers, just count how many negative signs are involved — an even count gives a positive answer, an odd count gives a negative one.
Practice questions
Question 1
Which of the following is the smallest whole number?
- A1
- B0
- C−1
- Dकोई नहीं
Explanation
0 is the smallest whole number; whole numbers never include any negative number, so nothing smaller than 0 belongs to the set.
Question 2
The value of (−8) + 5 is—
- A−13
- B13
- C−3
- D3
Explanation
When integers have different signs, subtract the smaller value (5) from the larger value (8) and keep the sign of the larger value (−), so the answer is −3.
Question 3
The value of 7 − (−4) is—
- A3
- B−3
- C11
- D−11
Explanation
Subtracting an integer is the same as adding its additive inverse: 7 − (−4) = 7 + 4 = 11.
Question 4
The value of (−6) + (−9) is—
- A15
- B−15
- C3
- D−3
Explanation
When integers share the same sign (both negative here), add the numbers and keep that sign: −6 − 9 = −15.
Question 5
Which of the following properties does not hold for subtraction of whole numbers?
- Aसंवृत गुणधर्म
- Bक्रमविनिमेय गुणधर्म
- Cसाहचर्य गुणधर्म
- Dउपरोक्त सभी
Explanation
Subtraction of whole numbers is neither closed (5 − 8 isn't a whole number), nor commutative (5 − 3 ≠ 3 − 5), nor associative ((5 − 3) − 1 ≠ 5 − (3 − 1)) — so all three properties fail for subtraction.
Question 6
Writing 8 × (5 + 3) as (8×5) + (8×3) is an example of which property?
- Aक्रमविनिमेय
- Bसाहचर्य
- Cवितरण
- Dसंवृत
Explanation
Writing 8 × (5 + 3) as (8×5) + (8×3) is exactly the distributive law of multiplication over addition, a × (b + c) = (a×b) + (a×c).
Question 7
The predecessor and successor of 25 are, respectively—
- A24, 26
- B26, 24
- C24, 25
- D25, 26
Explanation
Predecessor = number − 1 = 24, successor = number + 1 = 26.
Question 8
The temperature rose from −5°C to 3°C. What was the total increase in temperature?
- A2°C
- B8°C
- C−8°C
- D−2°C
Explanation
Rise in temperature = final temperature − initial temperature = 3 − (−5) = 3 + 5 = 8°C.
Question 9
A bank account had a deposit of ₹500. After withdrawing ₹800, the integer representing the account status is—
- A₹1300
- B−₹300
- C₹300
- D−₹1300
Explanation
500 − 800 = −300, meaning the account moves into a negative (overdraft) position of ₹300.
Question 10
A Class 6 teacher wants to use colored counters (red = negative, blue = positive) to teach addition of integers. The correct way to show '(−3) + 5' is—
- A3 लाल और 5 नीले काउंटर रखकर बराबर संख्या में लाल-नीले जोड़े हटाना, शेष बचे काउंटरों से उत्तर बताना
- Bकेवल 8 नीले काउंटर दिखाना
- Cबिना गिनती के सीधे उत्तर बता देना
- Dकाउंटरों का प्रयोग न करना
Explanation
Cancelling out 3 red and 3 blue counters from 3 red and 5 blue counters leaves 2 blue counters, which show the answer +2 — this hands-on (concrete) method makes integer addition easier to grasp.
Frequently asked questions
What's the difference between whole numbers and integers?+
Whole numbers are 0, 1, 2, 3... (no negative numbers), while integers include positive numbers, negative numbers and zero, all three — for example, −3, −2, −1, 0, 1, 2, 3...
What is the smallest whole number?+
0 is the smallest whole number; integers have no smallest number at all, because they keep going infinitely in the negative direction.
Which operations are whole numbers closed under?+
Whole numbers are closed under addition and multiplication (the result is always a whole number), but they are not closed under subtraction or division.
What's the easy rule for subtracting integers?+
Subtracting an integer is the same as adding its additive inverse (flipping its sign) — for example, 8 − (−3) = 8 + 3 = 11.
What happens when you multiply two negative integers?+
Multiplying two negative integers always gives a positive result — for example, (−4) × (−5) = 20; but multiplying one positive and one negative integer gives a negative result.
Read next
Number System
Classifying numbers — the previous topic in the REET maths sequence
Fractions & Decimals
Fractions and decimal numbers — the next topic in the REET maths sequence
REET Syllabus
The complete official syllabus for REET Level 1 and Level 2, in one place
REET 2024 Solved Paper
All solved REET 2024 questions, organised subject-wise
Change Log
- 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked