Schooling · Class 6 · Mathematics · The Other Side of Zero · Chapter on a page
CBSE Class 6 · Mathematics · NCERT Ganita Prakash
The Other Side of Zero: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- Negative numbers
- Positive numbers
- Zero
- Integers
- number line
- A number further to the right on the…
- Opposite numbers
- Formulas and facts
- 5 > 0
- −7 < 0
- Any positive number is greater than…
- Among negative numbers, the one…
- 5 + (−5) = 0
- 7 + (−3) = 7 − 3 = 4
- 4 − (−2) = 4 + 2 = 6
- Watch out for
- Thinking −10 is greater than −2…
- Saying 0 is a positive number
- Forgetting the minus sign when the…
- Confusing subtraction with "make…
- Writing integers without the minus…
What this chapter is about
Until now, you have worked with numbers like 1, 2, 3 and so on. These are counting numbers and whole numbers. But what happens when you go below zero? Think of a thermometer on a cold winter night in the hills. The temperature can drop below 0°C. Or think of a building with floors below the ground level, like a basement.
Key ideas
- Negative numbers are numbers less than zero. We write them with a minus sign in front, like −1, −2, −3.
- Positive numbers are numbers greater than zero. We can write them as +1, +2, +3 or simply 1, 2, 3.
- Zero is neither positive nor negative. It sits right in the middle.
- Integers include all positive whole numbers, all their negatives, and zero. Examples: ..., −3, −2, −1, 0, 1, 2, 3, ...
- On a number line, negative numbers are to the left of zero and positive numbers are to the right.
- A number further to the right on the number line is always greater. So 2 > −5, and −1 > −4.
- Opposite numbers are the same distance from zero but on opposite sides. For example, 3 and −3 are opposites.
- Adding a positive number means moving right on the number line. Adding a negative number means moving left.
Formulas and facts to remember
- Any positive number is greater than zero: 5 > 0.
- Any negative number is less than zero: −7 < 0.
- Any positive number is greater than any negative number: 3 > −10.
- Among negative numbers, the one closer to zero is greater: −2 > −8.
- The sum of a number and its opposite is zero: 5 + (−5) = 0.
- Adding a negative number is like subtracting: 7 + (−3) = 7 − 3 = 4.
- Subtracting a negative number is like adding: 4 − (−2) = 4 + 2 = 6.
Common mistakes
- Thinking −10 is greater than −2 because 10 is bigger than 2 → Remember, among negatives, the number closer to zero is greater.
- Saying 0 is a positive number → Zero is neither positive nor negative.
- Forgetting the minus sign when the answer is negative → Always check which side of zero you land on.
- Confusing subtraction with "make negative" → Subtracting a negative actually adds; use a number line to check.
- Writing integers without the minus sign when copying → −7 is very different from 7; be careful.
Quick revision
- Integers = ..., −3, −2, −1, 0, 1, 2, 3, ...
- On a number line, left is less, right is more.
- Every positive number beats every negative number.
- −1 > −100 because −1 is closer to zero.
- A number plus its opposite equals zero.
- Adding a negative means moving left; subtracting a negative means moving right.