Number Types & Arithmetic
Natural numbers, integers, rationals and irrationals, the four operations, and BODMAS.
Number sense is the base layer of the whole exam. If you can identify number types, handle signs, and follow the correct order of operations, every later topic becomes easier.
CSEC uses computation across all sections, not only in the Computation questions. A geometry answer, statistics answer, or consumer arithmetic answer can still be wrong because of a sign error or BODMAS mistake. Use estimation to check whether your final value is reasonable.
Before you calculate anything, you need to know what kind of number you're dealing with.
Natural Numbers
These are the numbers you learned to count with as a child.
Natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...
Notice: Natural numbers start at 1. Zero is NOT included.
How many students are in a class? A natural number answer: 25 students.
Whole Numbers
Whole numbers are like natural numbers, BUT they include zero.
Whole numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...
The only difference between whole numbers and natural numbers is that zero exists in whole numbers.
How many apples are left after you eat them all? Zero apples. This is a whole number but NOT a natural number.
Integers
Integers include negative numbers. They are all the whole numbers PLUS their negative versions.
Integers: ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...
Integers go forever in both directions—to negative infinity and positive infinity.
Temperature can be negative: "It's -5°C outside." This is an integer.
Bank account: "You owe the bank 200. This is an integer.
Rational Numbers
A rational number is any number that can be written as a fraction.
Rational numbers include:
- Fractions: , ,
- Decimals that terminate: 0.5, 0.75, 0.25
- Decimals that repeat forever: 0.333... (which is ), 0.666... (which is )
= 0.5 (these are the same number, just written differently)
= 0.75
= 0.333... (the 3 repeats forever)
All of these are rational numbers because they can be written as fractions.
Irrational Numbers
An irrational number cannot be written exactly as a fraction. The decimal never ends and never repeats.
The most famous irrational numbers are:
- Pi: ≈ 3.14159265358979... (never ends, never repeats)
- Square root of 2: ≈ 1.41421356... (never ends, never repeats)
If you use a calculator to find , it shows: 3.141592653589793...
But that's NOT the exact value. The digits go on forever. You can never write the exact decimal form of .
The difference between rational and irrational:
- Rational = can be written as a fraction
- Irrational = cannot be written as a fraction
Basic Arithmetic: The Four Operations
You need to be fluent with addition, subtraction, multiplication, and division. Especially when negative numbers are involved.
Adding and Subtracting with Negatives
Rule 1: Adding a negative is the same as subtracting
Think of it: "I have 5, I owe 3, so I have 2 left."
Rule 2: Subtracting a negative is the same as adding
Think of it: "I have 12, and I DON'T owe 5, so I actually have 17."
Problem 1: Calculate
Start at -7 on a number line. Move 15 steps to the right.
You end up at:
Problem 2: Calculate
This means:
(Subtracting a negative becomes addition)
Multiplying and Dividing with Negatives
The Sign Rules:
| Operation | Result | Example |
|---|---|---|
| Positive × Positive | Positive | |
| Negative × Negative | Positive | |
| Positive × Negative | Negative | |
| Negative × Positive | Negative |
The same rules apply to division.
Problem 1:
Negative times positive = negative
Problem 2:
Negative divided by negative = positive
Problem 3:
Negative divided by positive = negative
A quick way to remember:
- Same signs (both positive or both negative) = positive result
- Different signs (one positive, one negative) = negative result
Order of Operations (BODMAS)
Imagine you have this problem:
Do you get or ?
- If you do first, then
- If you do first, then
The answer is 14. Why? Because there's an order you MUST follow.
BODMAS tells you the order:
- Brackets (parentheses)
- Orders (powers and roots, like or )
- Division and Multiplication (left to right, whichever comes first)
- Addition and Subtraction (left to right, whichever comes first)
Calculate:
Step 1 - Brackets first:
Now we have:
Step 2 - Orders (powers):
Now we have:
Step 3 - Division and Multiplication (left to right):
Now we have:
Step 4 - Addition and Subtraction (left to right):
Answer: 11
In CSEC exams, always follow BODMAS. If you skip this, you'll get the wrong answer even if your arithmetic is correct!