Whole Numbers and Integers: Class 6 Study Guide
Numbers can go below zero. Integers help us talk about temperature, depth, profit and loss.
Whole numbers are 0, 1, 2, 3… Numbers to the left of zero on a number line are negative. Together, positive numbers, zero and negative numbers are called integers: …, −3, −2, −1, 0, 1, 2, 3, …
Negative numbers appear in many real situations: a temperature of −4 °C in Leh in winter, a depth of 20 m below sea level (−20 m), or a loss of ₹50 (−50). Every integer has an opposite the same distance from zero: the opposite of 5 is −5.
The number line
Numbers increase as you move to the right. So −2 > −5, because −2 is further right. The greater the number after the minus sign, the smaller the negative number. Zero is neither positive nor negative.
Adding and subtracting integers
To add a positive number, move right on the number line. To add a negative number, move left. Subtracting a number is the same as adding its opposite: 3 − (−2) = 3 + 2 = 5. When signs are the same, add and keep the sign: (−4) + (−3) = −7. When signs differ, subtract the smaller from the larger and keep the sign of the larger: (−7) + 4 = −3.
| Sum | Working | Answer |
|---|---|---|
| 5 + (−8) | 8 − 5 = 3, sign of 8 | −3 |
| (−6) + (−2) | 6 + 2 = 8, negative | −8 |
| (−3) − (−5) | (−3) + 5 | 2 |
| 4 − 9 | 4 + (−9) | −5 |
Problems from real life
A town's temperature is 3 °C at 6 pm and falls by 7 °C overnight: 3 − 7 = −4 °C. A diver at −12 m rises 5 m: −12 + 5 = −7 m. A shop makes a profit of ₹200 on Monday and a loss of ₹350 on Tuesday: 200 + (−350) = −150, a net loss of ₹150.
Gain is positive; loss is negative.
Combine the values.
Move right or left.
Include units.
Worked examples and common mistakes
Example: Order −8, 3, −1 and 0: −8, −1, 0, 3. Common mistakes: thinking −9 > −2 because 9 > 2, forgetting that subtracting a negative adds, and dropping the sign in the answer. Always draw a quick number line.
Check your understanding: model answers
1. −7. 2. 4. 3. 8.
✨ Key Takeaways
- Integers include negatives, zero and positives.
- On a number line, numbers increase to the right.
- Subtracting a number = adding its opposite.
- Negative numbers describe losses and temperatures below zero.
💬 Questions for Discussion & Reflection
- Which is smaller: −7 or −3?
- Find (−5) + 9.
- Find 2 − (−6).
Print graph paper for number lines →