NCERT Solutions for Class 6th Maths Chapter 10 The Other Side of Zero
Updated on 2026-09-19
About this chapter
There are numbers less than zero. They are written with a ‘–’ sign in front, are called negative numbers , and lie to the left of 0 on the number line. In Bela's Building of Fun they are the floors below the ground. The numbers … –3, –2, –1, 0, 1, 2, 3 … are the integers . Positive integers are 1, 2, 3, …; negative integers are –1, –2, –3, …; and 0 is neither positive nor negative — it is the reference point. Every number has an additive inverse — the number that gives 0 when added to it. The inverse of +4 is –4, the inverse of –543 is 543, and the inverse of 0 is 0. Addition means Starting Position + Movement = Target Position . Subtraction means Target Position – Starting Position = Movement needed . Both come straight from the lift. Subtracting a number is the same as adding its inverse
- Bela’s Building of Fun
- Numbering the floors in the Building of Fun
- Addition to keep track of movement
- Combining button presses is also addition
- Back to zero! · Comparing numbers using floors
- Comparing numbers using floors
- Subtraction to find which button to press
- Adding and subtracting larger numbers (the mine)
- Adding, subtracting, and comparing any numbers
- Back to the number line
Quick revision
| Idea | What it means | Example from the chapter | Quick rule |
|---|---|---|---|
| Positive number | A number written with a ‘+’ in front; a floor above the ground floor | + 5 — the Sports Centre | Lies to the right of 0 on the number line |
| Negative number | A number written with a ‘–’ in front; a floor below the ground | – 3 — the Cinema | Lies to the left of 0 on the number line |
| Zero | Neither positive nor negative; the reference point | Floor 0 — the Welcome Hall | No sign is written in front of 0 |
| Integers | Positive numbers, negative numbers and zero together | … – 3, – 2, – 1, 0, 1, 2, 3 … | They go on for ever in both directions |
| Additive inverse | The number that gives 0 when added | Inverse of + 4 is – 4 | Keep the digits, change the sign |
| Addition | Starting Position + Movement = Target Position | (+ 1) + (+ 2) = + 3 | Press the buttons one after the other |
| Subtraction | Target Position – Starting Position = Movement needed | (+ 5) – (+ 2) = + 3 | a – b = a + (inverse of b) |
| Subtracting a negative | Same as adding the matching positive number | 7 – (– 7) = 7 + 7 = 14 | Two minus signs together become a plus |
| Zero pair | One positive token with one negative token | (+ 1) + (– 1) = 0 | Cancel the pairs, read what is left |
| Comparing | Smaller numbers lie to the left on the number line | – 4 < – 3 < 0 < + 3 | Every negative < 0 < every positive |
| Credit and debit | Money coming in (+) and money going out (–) | + ₹200 credit, – ₹150 debit | Balance = total of all credits and debits |
| Height and temperature | Above sea level / above 0 °C is +, below is – | – 2 °C at night in Leh | 0 is only a starting mark, not ‘nothing’ |
Exercises
- In-text Questions — Bela’s Building of Fun Page 243
- Numbering the floors in the Building of Fun — In-text Questions Page 244
- Addition to keep track of movement — In-text Question Page 245
- Addition to keep track of movement — Figure it Out Page 245
- Combining button presses is also addition — Figure it Out Page 246
- Back to zero! · Comparing numbers using floors — In-text Questions Page 246 & 247
- Comparing numbers using floors — Figure it Out Page 247
- Subtraction to find which button to press — In-text Question Page 248
- Subtraction to find which button to press — Figure it Out Page 249
- Adding and subtracting larger numbers (the mine) — Figure it Out Page 251
- Adding, subtracting, and comparing any numbers — In-text Question Page 251
- Back to the number line — In-text Questions Page 252 & 253
- Back to the number line — Figure it Out Page 253 & 254
- Using the unmarked number line to add and subtract — In-text Question Page 255
- Figure it Out — The Token Model Page 257
- Using tokens for subtraction — In-text Question Page 257
- Using tokens for subtraction — Figure it Out Page 258
- Using tokens for subtraction — Figure it Out Page 259
- In-text Questions — Integers in Other Places Page 259 & 260
- Credits and debits — Figure it Out Page 260
- Geographical cross sections — Figure it Out Page 261
- Temperature — In-text Questions Page 262
- Temperature — Figure it Out Page 262
- Figure it Out — Explorations with Integers Page 263 & 264
- An amazing grid of numbers! — Figure it Out Page 265
- Practice with integers — Figure it Out Page 265 & 266
- Figure it Out — A Pinch of History Page 268