Class 6 Mathematics · 10 min read · Published 10 October 2026

Integers for Class 6: Negative Numbers, Number Line, Comparison, Addition and Subtraction

By Dishantra Editorial · Reviewed 10 October 2026

What comes before zero? A learner working mainly with whole numbers may be used to 0, 1, 2, 3, 4… But the number line continues in the other direction: … −4, −3, −2, −1, 0, 1, 2, 3, 4 …

Once negative integers are understood as positions on the number line, comparing and calculating with them becomes much easier.

1. What are integers?

Integers include negative whole numbers, zero and positive whole numbers.

Integers do not include fractions or decimals such as 1/2, −2.5 or 3.7. They are the whole-number positions extending in both directions from zero.

2. Where do negative numbers appear?

Negative numbers can represent quantities measured below or on the opposite side of a reference point: temperatures below 0°C, floors below ground level, positions below sea level and some situations involving decreases or losses.

The meaning of zero depends on the situation. In temperature it can be 0°C; in a building it can represent ground level; on a number line it is the reference between negative and positive integers. Negative values describe positions below or opposite that reference.

For example, −3°C means three degrees below zero.

3. Comparing negative integers

Which is greater: −2 or −7? It is tempting to think 7 > 2, therefore −7 > −2. But on a number line, −2 lies farther to the right.

This same number-line rule works across zero as well. Any positive integer lies to the right of zero, and zero lies to the right of every negative integer. So 2 > 0 > −2.

−2 > −7

The rule with meaning is simple: the number farther to the right is greater.

4. Why is −1 greater than −10?

Think about temperature: −1°C is warmer than −10°C. Or think about distance below zero: −1 is one unit below zero while −10 is ten units below zero. Therefore −1 > −10.

5. Opposite integers

Numbers the same distance from zero but on opposite sides are opposites: 5 and −5, 3 and −3, 1 and −1.

Opposites have the same distance from zero, often called the same magnitude, but different signs. Their sum is zero because the two equal movements cancel each other.

6. Adding integers using a number line

Consider −2 + 5. Start at −2. Adding positive 5 means moving 5 units to the right: −2 → −1 → 0 → 1 → 2 → 3. Therefore −2 + 5 = 3.

7. Adding a negative integer

Consider 3 + (−5). Start at 3. Adding −5 means moving five units left: 3 → 2 → 1 → 0 → −1 → −2. Therefore 3 + (−5) = −2.

This is useful because it replaces a memorised sign rule with movement. The sign of the number being added tells us the direction, while its size tells us how many unit steps to move.

8. Adding two negative integers

For −3 + (−4), start at −3 and move another four units left. You land at −7. Both movements take us farther in the negative direction.

−3 + (−4) = −7

9. Subtracting a positive integer

Subtraction can also be shown as movement. For 2 − 5, start at 2 and move five units left: 2 → 1 → 0 → −1 → −2 → −3.

Subtraction is not restricted to answers that stay above zero. If the movement passes through zero, keep moving the required number of steps; the landing point may be negative.

2 − 5 = −3

Likewise, starting at a negative integer works the same way: −2 − 3 = −5. You start at −2 and move three units left.

10. Subtracting a negative integer

Consider 3 − (−2). One way to understand this is that subtracting a number means adding its opposite. The opposite of −2 is +2, so:

For another example, −4 − (−3) = −4 + 3 = −1. Thinking in terms of adding the opposite works whether the starting integer is positive or negative.

3 − (−2) = 3 + 2 = 5

The shortcut “subtracting a negative becomes addition” is useful after the idea of opposites is understood.

11. Temperature example

At 6 a.m., the temperature is −4°C. By afternoon it rises by 7°C. Start at −4 and move seven units to the right. The movement crosses zero and lands at 3°C.

A second way to check is to think about the total change: rising 4 degrees takes −4°C to 0°C, and the remaining 3-degree rise takes it to 3°C.

12. Common integer mistakes

• Thinking −8 > −3 because 8 > 3. Correctly, −3 > −8 because −3 is farther right.
• Thinking zero is positive. Zero is neither positive nor negative.
• Ignoring the sign: 5 and −5 are different numbers.
• Memorising sign rules without understanding direction and opposites. A number line can reconstruct the reasoning when a rule is forgotten.

13. Quick check

14. Integer decision map

The key idea

Negative numbers become easier when they are understood as positions relative to zero. Instead of beginning with “What sign rule do I need?”, ask: Where am I starting? Which direction am I moving? How far am I moving? Where do I land?

Once that mental model is secure, symbolic rules become easier to understand and remember.