Integers
The set …, −2, −1, 0, 1, 2, … closed under addition, subtraction and multiplication.
Key idea
The set …, −2, −1, 0, 1, 2, … closed under addition, subtraction and multiplication.
In depth
The integers are the whole numbers and their negatives: ..., −2, −1, 0, 1, 2, ... They are closed under addition, subtraction and multiplication, but not division, since 1 ÷ 2 is not an integer.
Worked example
−3 and 7 are integers; 7 − 10 = −3 stays inside the integers.
Formula
Real-world uses
- Tracking gains and losses in games and finance
- Representing debts and credits in accounts
Common mistake
Calling fractions or decimals integers. Only whole units count.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Integers?
The set …, −2, −1, 0, 1, 2, … closed under addition, subtraction and multiplication. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Integers?
The key formula is ℤ.
Where is Integers used in real life?
Real-world examples: Tracking gains and losses in games and finance; Representing debts and credits in accounts.
What should I learn before Integers?
Make sure you are comfortable with Negative Numbers, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Integers?
Calling fractions or decimals integers. Only whole units count.
How can I practise Integers?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Integers?
Move on to Adding Integers next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.