What Happens When Numbers Go Below Zero?
Learn how to use negative numbers in real-life situations, represent them on a number line, and compare and order integers confidently.
What are negative numbers and where do we see them in real life?
Negative numbers are numbers that are less than zero, and they are written with a minus sign (−) in front of them. We use negative numbers to show values below a certain reference point, like zero. In CBSE Class 6 Mathematics Chapter 10, you will learn how negative numbers help us describe situations such as temperatures below freezing, money owed, depths below sea level, and years before the Common Era (BCE). For example, if the temperature in Shimla drops to 4 degrees below zero, we write it as −4°C. If a lift goes 2 floors below the ground floor, we call it floor −2. If you have spent ₹50 more than you have, your balance is −₹50. Always remember, negative numbers are not just for maths—they help us describe many things in daily life. A common mistake is to forget the minus sign when talking about values below zero, which changes the meaning completely.
How do you show positive and negative numbers on a number line?
On a number line, zero is placed at the centre, positive numbers are marked to the right, and negative numbers are marked to the left. Each point on the number line represents an integer. To show a number, start at zero and move right for positive numbers or left for negative numbers. For example, to show −3, start at zero and move three steps left; for +4, move four steps right. If you are asked which integer is at a certain position, count the steps from zero in the correct direction. In real life, if you are in a building and go up 2 floors from the ground floor (0), you are on floor +2. If you go down 3 floors, you are on floor −3. Students often think negative numbers are 'smaller' in size, but on the number line, being further left means being less than a number to the right, even if the digits are larger.
How can you compare and arrange integers using the number line?
To compare integers, look at their positions on the number line: the integer to the right is always greater than the one to the left. This means all positive numbers are greater than zero, and zero is greater than any negative number. When arranging integers in ascending order (smallest to largest), write them from left to right as they appear on the number line. For example, the order of −5, 0, −2, 3 is −5, −2, 0, 3. In descending order, you go from right to left: 3, 0, −2, −5. For another example, if you compare −7 and −3, since −3 is to the right of −7, −3 is greater than −7. A common confusion is thinking that −7 is greater than −3 because 7 is bigger than 3, but the minus sign means it is actually less.
What is the additive inverse of an integer and how does it work?
The additive inverse of an integer is the number that, when added to the original integer, gives zero. For any integer a, its additive inverse is −a. For example, the additive inverse of 5 is −5, and the additive inverse of −8 is 8. If you add an integer and its additive inverse, you get 0: 7 + (−7) = 0 or (−12) + 12 = 0. In real life, if you owe ₹20 (−20) and then pay back ₹20 (+20), your balance is zero. A common mistake is to think the additive inverse means just changing the sign, but you must always check that their sum is zero to be sure.
Exam tip
The mistake most students make with negative numbers on the number line
Many students forget that negative numbers are to the left of zero and positive numbers are to the right. For example, some may place −4 to the right of −2 because 4 is more than 2, but on the number line, −4 is to the left of −2. The correct way is: the more negative the number, the further left it is. Always check the direction before marking or comparing integers.
Did you know
Why do we use negative numbers for temperature and money?
Negative numbers let us describe situations where values fall below a reference point, like zero. In weather reports, temperatures below zero are shown as negative numbers to signal freezing conditions. In banking, a negative balance means you owe money. This helps everyone understand whether something is above or below a standard level.
Key takeaways
What to remember about negative numbers and integers
- Negative numbers represent values below zero, such as debts, temperatures, and depths.
- On a number line, zero is in the centre, positives are to the right, and negatives to the left.
- To compare and order integers, look at their positions: further right means greater value.
- The additive inverse of an integer is the number that adds to it to make zero.
You will remember these ideas much better if you try arranging and comparing some integers yourself right now.
- On a number line, zero is in the centre, positives are to the right, and negatives to the left.
- To compare and order integers, look at their positions: further right means greater value.
- The additive inverse of an integer is the number that adds to it to make zero.
You will remember these ideas much better if you try arranging and comparing some integers yourself right now.