AQA 7517 · Paper 1 · 4.1.1b

Arithmetic & Relational
Operators

AQA A-Level Computer Science · Section 4.1 Fundamentals of Programming

WHAT YOU'LL LEARN

Arithmetic operators (+ - * / DIV MOD ^) · Relational operators · Operator precedence

EXAM RELEVANCE

Appears in trace tables, program writing & error-finding questions

Arithmetic Operators

AQA 7517 Arithmetic Operators

Operator	Meaning	Example	Result
+	Addition	17 + 5	22
-	Subtraction	17 - 5	12
*	Multiplication	17 * 5	85
/	Real division	17 / 5	3.4
DIV	Integer division (quotient)	17 DIV 5	3
MOD	Modulo (remainder)	17 MOD 5	2
^	Exponentiation (power)	2 ^ 8	256

DIV & MOD

Understanding DIV and MOD

DIV — INTEGER DIVISION

Returns the whole-number quotient, discarding any remainder.

17 DIV 5 = 3 (5 goes into 17 three times)
100 DIV 7 = 14

MOD — MODULO (REMAINDER)

Returns the remainder after integer division.

17 MOD 5 = 2 (17 = 3×5 + 2)
100 MOD 7 = 2 (100 = 14×7 + 2)

Real-world uses of MOD: Testing if a number is even (n MOD 2 = 0), finding last digit (n MOD 10), wrapping array indices, clock arithmetic

Relational Operators

Comparison Operators

Relational operators compare two values and return a Boolean (True/False).

Operator	Meaning	Example	Result
=	Equal to	5 = 5	True
≠	Not equal to	5 ≠ 3	True
<	Less than	3 < 7	True
>	Greater than	9 > 4	True
≤	Less than or equal to	5 ≤ 5	True
≥	Greater than or equal to	6 ≥ 9	False

⚠️ In AQA pseudocode, = is used for both assignment AND comparison (context determines meaning). Python uses == for comparison.

Precedence

Operator Precedence (BIDMAS)

ORDER (HIGHEST → LOWEST)

1. Brackets ( )

2. Exponent ^

3. Multiplication, Division * / DIV MOD

4. Addition, Subtraction + -

WORKED EXAMPLES

2 + 3 * 4 = 14 (not 20)
(2 + 3) * 4 = 20
2 ^ 3 + 1 = 9 (8 + 1)
10 DIV 3 + 1 = 4 (3 + 1)

Trace Table

Following Operator Expressions

AQA PSEUDOCODE

x ← 15
y ← 4
a ← x DIV y
b ← x MOD y
c ← x / y
OUTPUT a, b, c

Variable	Value	Explanation
a	3	15 DIV 4 = 3 (quotient)
b	3	15 MOD 4 = 3 (15 = 3×4 + 3)
c	3.75	15 / 4 = 3.75 (real division)

Real-World Context

Operators in Programs

MOD 2 = 0 — check if a number is even (e.g. for alternating rows, parity checks)

DIV 10 — extract digits (e.g. 153 DIV 10 = 15 removes last digit)

MOD 60 — convert seconds to minutes/seconds (clock arithmetic)

^ — calculate compound interest, exponential growth, bitwise powers of 2

Relational operators used in IF conditions and WHILE loops to control program flow

Example: IF score MOD 2 = 0 THEN OUTPUT "even" ENDIF

Python vs Pseudocode

AQA Pseudocode ↔ Python

Operation	AQA Pseudocode	Python
Addition	a + b	a + b
Multiplication	a * b	a * b
Real division	a / b	a / b
Integer division	a DIV b	a // b
Modulo	a MOD b	a % b
Exponentiation	a ^ b	a ** b
Not equal to	a ≠ b	a != b

AQA Exam Style

Practice Question

AQA 7517 — Paper 1 Style Question

A programmer writes the following pseudocode:

x ← 29
y ← 6
OUTPUT x MOD y
OUTPUT x DIV y
OUTPUT (x + y) ^ 2

State the output produced by each line.

[3 marks]

1 mark

x MOD y → 5 (29 = 4×6 + 5)

1 mark

x DIV y → 4 (6 goes into 29 four times)

1 mark

(x + y) ^ 2 → 1225 (35² = 1225)

Summary

Key Points to Remember

/ (division) returns a REAL result · DIV returns an INTEGER quotient

MOD returns the remainder after integer division — vital for even/odd checks

^ is the AQA power operator — Python uses **

Relational operators always return Boolean True/False

BIDMAS applies — use brackets to override precedence

Watch out: AQA uses ≠ not !=, and DIV not //

Exam trace table questions often test MOD and DIV

🎉 Lesson complete — move to the quiz!

Arithmetic & RelationalOperators

AQA 7517 Arithmetic Operators

Understanding DIV and MOD

Comparison Operators

Operator Precedence (BIDMAS)

Following Operator Expressions

Operators in Programs

AQA Pseudocode ↔ Python

Practice Question

Key Points to Remember

Arithmetic & Relational
Operators