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.
This chapter introduces you to negative numbers — numbers that are less than zero. You will learn what numbers like −1, −2, −3 mean and where we see them in daily life. Together with positive numbers (numbers greater than zero) and zero itself, these form integers.
After studying this chapter, you will be able to mark integers on a number line, compare them, and understand which integer is greater or smaller. You will also learn to add and subtract integers using simple ideas like moving left or right on a number line.
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 negative whole numbers, 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.
Worked examples
Example 1: Marking integers on a number line
Draw a number line and mark −3, 0 and 2.
Step 1: Draw a straight line and mark a point for 0 in the middle.
Step 2: Mark equal spaces to the right for 1, 2, 3, etc.
Step 3: Mark equal spaces to the left for −1, −2, −3, etc.
Step 4: Circle −3 (three steps left of 0), 0, and 2 (two steps right of 0).
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Example 2: Comparing integers
Which is greater: −4 or −1?
Step 1: Picture a number line. −4 is four steps left of zero. −1 is only one step left.
Step 2: The number closer to zero is greater among negative numbers.
Answer: −1 > −4.
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Example 3: Adding integers
Find 3 + (−5).
Step 1: Start at 3 on the number line.
Step 2: Adding −5 means move 5 steps to the left.
Step 3: 3 → 2 → 1 → 0 → −1 → −2.
Answer: 3 + (−5) = −2.
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.