Operators: Arithmetic, Comparison, and Boolean

This lesson covers the three types of operators you need to know for OCR J277 Section 2.3: arithmetic operators, comparison operators, and Boolean operators (AND, OR, NOT). Operators are the building blocks of expressions and conditions in programming.

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Arithmetic Operators

Arithmetic operators perform mathematical calculations on numerical values.

Operator	OCR Pseudocode	Python	Description	Example	Result
Addition	+	+	Adds two values	7 + 3	10
Subtraction	-	-	Subtracts right from left	7 - 3	4
Multiplication	*	*	Multiplies two values	7 * 3	21
Division	/	/	Divides left by right (real division)	7 / 2	3.5
Integer division	DIV	//	Divides and rounds down to whole number	7 DIV 2	3
Modulus	MOD	%	Returns the remainder after division	7 MOD 2	1
Exponentiation	^	**	Raises to a power	2 ^ 3	8

Understanding DIV and MOD

DIV and MOD are the most commonly tested arithmetic operators in the OCR exam.

DIV gives the whole number part of a division:

• 17 DIV 5 = 3 (because 5 goes into 17 three whole times)
• 10 DIV 3 = 3

MOD gives the remainder:

• 17 MOD 5 = 2 (because 17 = 5 × 3 remainder 2)
• 10 MOD 3 = 1

Common uses of MOD:

• Checking if a number is even: number MOD 2 == 0
• Checking if a number is divisible by another: number MOD n == 0
• Extracting the last digit: 1234 MOD 10 = 4

OCR Exam Tip: DIV and MOD appear in almost every Paper 2 exam. Practise until you can calculate them instantly. Remember: DIV = quotient, MOD = remainder. For example, 23 DIV 7 = 3 and 23 MOD 7 = 2 because 23 = 7 × 3 + 2.

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Comparison Operators

Comparison operators compare two values and return a Boolean result (true or false).

Operator	OCR Pseudocode	Python	Description	Example	Result
Equal to	==	==	Checks if values are equal	5 == 5	true
Not equal to	!=	!=	Checks if values are not equal	5 != 3	true
Greater than	>	>	Left is greater than right	5 > 3	true
Less than	<	<	Left is less than right	5 < 3	false
Greater than or equal to	>=	>=	Left is greater than or equal to right	5 >= 5	true
Less than or equal to	<=	<=	Left is less than or equal to right	3 <= 5	true

OCR Exam Tip: A very common mistake is confusing = (assignment) with == (comparison). x = 5 sets x to 5. x == 5 checks if x is equal to 5. In pseudocode, OCR uses == for comparison and = for assignment.

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Boolean Operators (AND, OR, NOT)

Boolean operators combine or modify Boolean values. They are essential for building complex conditions in selection and iteration statements.

AND

Returns true only if both conditions are true.

A	B	A AND B
true	true	true
true	false	false
false	true	false
false	false	false

OR

Returns true if at least one condition is true.

A	B	A OR B
true	true	true
true	false	true
false	true	true
false	false	false

NOT

Reverses (inverts) a Boolean value.

A	NOT A
true	false
false	true

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Combining Operators in Practice

OCR Pseudocode:

age = int(input("Enter age: "))
hasTichet = true

if age >= 18 AND hasTicket == true then
    print("Entry allowed")
elseif age < 18 OR hasTicket == false then
    print("Entry denied")
endif

Python:

age = int(input("Enter age: "))
has_ticket = True

if age >= 18 and has_ticket:
    print("Entry allowed")
elif age < 18 or not has_ticket:
    print("Entry denied")

The flow of an entry decision built from comparison and Boolean operators can be drawn as an IF/ELSE flowchart:

flowchart TD
    A([Start]) --> B[Read age, hasTicket]
    B --> C{"age >= 18<br/>AND<br/>hasTicket == true?"}
    C -->|true| D[print 'Entry allowed']
    C -->|false| E{"age < 18<br/>OR<br/>hasTicket == false?"}
    E -->|true| F[print 'Entry denied']
    E -->|false| G[no output]
    D --> H([End])
    F --> H
    G --> H

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Operator Precedence

When multiple operators appear in a single expression, they are evaluated in a specific order:

Priority	Operators
1 (highest)	Parentheses ()
2	Exponentiation ^ / **
3	Multiplication, Division, DIV, MOD
4	Addition, Subtraction
5	Comparison operators (==, !=, <, >, etc.)
6	NOT
7	AND
8 (lowest)	OR

Example: What is 3 + 4 * 2? Answer: 11 (not 14), because multiplication is done before addition.

To override precedence, use parentheses: (3 + 4) * 2 = 14.

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Summary

• Arithmetic operators perform calculations: +, -, *, /, DIV, MOD, ^.
• Comparison operators return Boolean values: ==, !=, <, >, <=, >=.
• Boolean operators combine conditions: AND, OR, NOT.
• Understand operator precedence — use parentheses when in doubt.
• DIV and MOD are the most commonly tested operators.

OCR Exam Tip: In the exam, if you are unsure about precedence, use parentheses to make your intention clear. The examiner will accept (a + b) * c and this avoids any ambiguity. Clarity in your code demonstrates good programming practice.

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Worked Example: Splitting Seconds into Hours, Minutes, Seconds