The Other Side of Zero
What lies to the left of zero? This Class 6 Ganita Prakash chapter extends numbers beyond the counting numbers to introduce negative numbers and integers. Students place them on a number line, compare and order them, add and subtract simple integers, and meet real-life uses like temperature and depth.
Learning objectives
- Understand negative numbers and integers.
- Place integers on a number line.
- Compare and order integers.
- Add and subtract simple integers.
Key concepts
Negative numbers and integers
Numbers less than zero are negative numbers, written with a minus sign such as −3. Together, the positive whole numbers, zero, and the negative whole numbers form the integers: …, −3, −2, −1, 0, 1, 2, 3, …. Zero is an integer that is neither positive nor negative.
Integers on the number line
On a number line, zero sits in the middle, positive integers extend to the right and negative integers to the left, each step the same distance apart. Numbers like 3 and −3 are opposites, lying the same distance from zero on either side.
Comparing and ordering integers
On the number line, a number to the right is always greater than one to the left. So every positive number is greater than zero, zero is greater than every negative number, and among negatives the one closer to zero is greater — for example −2 is greater than −5.
Adding and subtracting integers
Moving right on the number line means adding, and moving left means subtracting, which also covers negative numbers. So 2 + (−5) lands on −3, and −1 − 2 lands on −3. Real-life settings such as temperatures below zero, depths below sea level, and money owed all use these ideas.
Important formulas
Opposite of a number
the opposite of n is −n
On the number line
right = add; left = subtract
Key definitions
- Negative number
- A number less than zero, written with a minus sign.
- Integer
- A positive whole number, zero, or a negative whole number.
- Opposite
- Two numbers the same distance from zero on either side, like 4 and −4.
- Number line
- A line on which numbers are marked at equal steps, with zero in the middle.
Solved examples
Q1. Which is greater, −2 or −7?
Solution: −2 is greater, because it lies to the right of −7 (closer to zero).
Q2. What is the opposite of 6?
Solution: −6, the same distance from zero on the other side.
Q3. Find 3 + (−5).
Solution: Start at 3 and move 5 steps left to reach −2.
Common mistakes to avoid
- Thinking −5 is greater than −2 because 5 is bigger than 2.
- Treating zero as a positive (or negative) number.
- Moving the wrong way on the number line when adding a negative.
- Dropping the minus sign and using the number as positive.
The Other Side of Zero — MCQ Quiz
10 questions with instant feedback. Use number keys 1–4 to answer.
A number less than zero is called:
Practice questions
Short answer
What are integers?
The positive whole numbers, zero, and the negative whole numbers together.
Which is greater, −3 or −8?
−3, because it is closer to zero (to the right) on the number line.
Give a real-life use of negative numbers.
Temperatures below zero, depths below sea level, or money owed.
Long answer
Explain how integers are arranged on a number line and how to compare them.
On a number line, zero is placed in the middle, the positive integers go to the right and the negative integers to the left, with each integer one equal step from the next. To compare two integers, the one lying further to the right is greater. This means every positive number is greater than zero, zero is greater than every negative number, and among two negatives the one nearer to zero is greater — for instance −2 is greater than −5, even though 5 is a bigger digit than 2.
Using the number line, explain how to work out 4 + (−6) and −2 − 3.
Adding moves right and subtracting moves left, and this works with negatives too. For 4 + (−6), start at 4 and move 6 steps to the left, landing on −2, so 4 + (−6) = −2. For −2 − 3, start at −2 and move 3 steps further left, landing on −5, so −2 − 3 = −5. Picturing the moves on the number line keeps the direction clear and prevents losing the minus sign.
HOTS (Higher Order Thinking)
The temperature was −3°C and then fell by 4°C. What is the new temperature?
Falling means moving left: −3 − 4 = −7°C.
Name all the integers that lie between −3 and 2.
−2, −1, 0 and 1.
Quick revision
Revision notes
- Negative numbers are less than zero (e.g., −3); integers are …−2, −1, 0, 1, 2…
- Number line: negatives left, positives right, zero in the middle.
- Right of another number = greater; closer to zero among negatives = greater.
- Add → move right; subtract → move left.
Key takeaways
- Integers extend numbers to 'the other side of zero'.
- Among negatives, closer to zero means greater.
- Negative numbers describe temperature, depth and debt.
Frequently asked questions
What is an integer?
A positive whole number, zero, or a negative whole number.
Is −2 greater or less than −5?
Greater, because it is closer to zero on the number line.
How do I add a negative number on the number line?
Move that many steps to the left from your starting number.