About Integers
Integers include positive numbers, negative numbers, and zero.
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They can be added or subtracted using simple rules.
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They are used widely in daily life to show loss/gain, up/down, and temperature.
- All Level
- Last updated 15-May-2025
- english
Course description
What You’ll Learn
This chapter helps you understand:
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What integers are
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How to represent integers on a number line
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The concept of opposites in numbers
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How to add and subtract integers
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Rules for operations with positive and negative numbers
Key Concepts
1. What are Integers?
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Integers are a set of numbers that include:
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Positive numbers (1, 2, 3, ...)
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Negative numbers (−1, −2, −3, ...)
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Zero (0)
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???? Examples of integers:
... −4, −3, −2, −1, 0, 1, 2, 3, 4, ...
2. Representation on a Number Line
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Integers are placed on a horizontal line called the number line.
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Zero (0) is in the middle.
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Positive numbers go to the right of zero.
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Negative numbers go to the left of zero.
Tip: The farther right a number is, the greater its value.
3. Comparing Integers
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On the number line:
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Numbers to the right are greater
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Numbers to the left are smaller
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Examples:
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3 > -2
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-5 < -3
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0 > -1
4. Ordering Integers
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To arrange integers in ascending order, write them from the smallest to the largest.
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For descending order, write them from the largest to the smallest.
Example:
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Ascending: −5, −3, 0, 2, 4
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Descending: 4, 2, 0, −3, −5
5. Adding Integers
| Case | Rule | Example |
|---|---|---|
| Same signs (both +ve or both −ve) | Add the numbers, keep the same sign | (−2) + (−3) = −5 |
| Different signs (+ve and −ve) | Subtract smaller from bigger, take bigger’s sign | (5) + (−3) = 2 |
Examples:
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(−7) + (−2) = −9
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(4) + (−6) = −2
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(−8) + (5) = −3
6. Subtracting Integers
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Change the subtraction to addition of the opposite.
Rule:
a − b = a + (−b)
Examples:
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7 − (−3) = 7 + 3 = 10
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(−5) − (−2) = (−5) + 2 = −3
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(−6) − 4 = (−6) + (−4) = −10
Important Rules for Operations
| Operation | Rule Example |
|---|---|
| (+) + (+) = + | 3 + 2 = 5 |
| (−) + (−) = − | (−3) + (−2) = −5 |
| (+) + (−) = Depends | 6 + (−4) = 2, since 6 > 4 |
| (−) + (+) = Depends | (−5) + 7 = 2, since 7 > 5 |
| a − b = a + (−b) | 3 − (−2) = 3 + 2 = 5 |
Real-Life Examples of Integers
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Temperatures (e.g., −2°C is below 0°C)
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Elevations (e.g., sea level is 0, mountains are positive, valleys are negative)
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Bank balances (positive means deposit, negative means debt)
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Game scores (gains and losses)
Practice Questions
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Represent the following integers on a number line: −3, 0, 4, −1, 2
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Find the sum: (−5) + (−7)
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Find the value of: 6 − (−3)
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Arrange in ascending order: −1, −6, 2, 0, −3
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Subtract: (−8) − (4)
This course includes
- Lectures 10
- Duration 4h 50m
- Skills All Level
- Language english
- Certificate yes
Sample
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