GCSE · Computer Science · AQA · Spec 8525

Subtraction (arithmetic operator)

14 °C at 9 am, 9 °C by 3 pm. Did the temperature change by -5 or by 5? In code, it depends on which number you write first.

Computer Science · Algorithms

Trace table — dry run the code

A weather app stores two temperature readings and works out the change. Before each Next, predict what the line will store. Line 4 is the one to watch.

1earlier ← 14

2later ← 9

3change ← later - earlier

4swapped ← earlier - later

5later ← later - 2

6OUTPUT change

earlier

later

change

swapped

Output

Press Start to run the first line.

Ready when you are — step through one line at a time.

Predict, then check

Two minus signs in one line. Which subtraction happens first?

A program runs this line: left ← 20 - 5 - 3. What number is stored in left?

Which idea is yours?

A line that subtracts from itself

A game stores how many lives a player has left. Every time the player is hit, this line runs: lives ← lives - 1

Which is closest to what you think this line does?

It's an equation, and it can never be true. Nothing is equal to itself minus 1.It works out lives - 1, but lives itself stays the same.It sets lives to -1.It takes the value lives holds now, subtracts 1, and stores the answer back in lives.

How sure are you?

I'm sureI think soI'm guessing

It's an equation, and it can never be true. Nothing is equal to itself minus 1.

This is a common misconception

In maths you'd be right. But ← is not an equals sign. It's an instruction: work out the right-hand side, then store the answer in the variable on the left. Lots of languages write this line as lives = lives - 1, and that's why it looks like a broken equation. Read it as 'lives becomes lives - 1'.

It works out lives - 1, but lives itself stays the same.

This is a common misconception

The answer isn't thrown away. The arrow stores it back in lives. If lives was 3 before the line ran, it's 2 afterwards.

It sets lives to -1.

This is a common misconception

That line would be lives ← -1. Here the right-hand side uses the value lives holds right now. If that's 3, then 3 - 1 = 2, so lives becomes 2, not -1.

It takes the value lives holds now, subtracts 1, and stores the answer back in lives.

This matches the evidence

Exactly. The right-hand side is worked out first, using the current value. Then the answer replaces it. Each time the line runs, lives goes down by 1.

Read an update line in two moves: first do the subtraction using the variable's current value, then store the answer back in that same variable.

Your turn to write it

Finish the tuck-shop program

A tuck-shop program sells one snack. Amounts are in pence. Choose the missing lines so it stores the change owed and takes the snack off the stock count.

price ← 120
paid ← 200
missing step

Which line is step 3?

change ← price - paidchange ← paid - pricepaid - pricepaid ← paid - price

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

The same two numbers can give a rise or a fall. It all depends on which one you write first.

What you need to know

The subtraction operator (-) takes the second operand away from the first: a - b.
Order matters. a - b and b - a have the same size but opposite signs, e.g. 9 - 14 = -5 and 14 - 9 = 5.
A chain such as 20 - 5 - 3 is worked left to right (answer 12). Brackets are worked first: 20 - (5 - 3) = 18.
The result must be stored (assigned to a variable) if the program needs it later.
x ← x - 1 updates x: the current value is used, then the answer replaces it.

The big picture

The subtraction operator (-) takes the second value away from the first. The values either side of it are called operands, and their order matters: 9 - 14 is -5, but 14 - 9 is 5. The answer has the same size and the opposite sign. A chain like 20 - 5 - 3 is worked left to right, and brackets change that order. The result only survives if it is stored, and a line like later ← later - 2 updates a variable using its own current value.

Key points

1Subtraction in code works on stored values and gives a result the program can store or output.

2Swapping the operands flips the sign of the answer, so pick the order that gives the meaning you want.

3A negative result is a normal answer. Its sign tells you the direction, such as a fall rather than a rise.

4Several subtractions in one line are worked left to right unless brackets say otherwise.

5A stored result doesn't change by itself. If a value used in the subtraction changes later, the result stays the same until the subtraction runs again.

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Worked example

Problem

A car park program starts with spaces ← 150. Then these lines run in order: spaces ← spaces - 40, then spaces ← spaces - 25, then taken ← 150 - spaces. What values are stored in spaces and taken at the end?

⚠ Watch out

Writing the operands the wrong way round, e.g. earlier - later when you meant later - earlier. The answer has the right size and the wrong sign, so it's easy to miss. Decide what the answer should mean first, then choose the order.

🧠

Memory hook

First minus second, exactly as written. Swap them and the sign flips.

✓

Check yourself

These lines run in order: a ← 10, b ← 25, a ← a - b. What does a hold now? (Answer: -15. 10 - 25 = -15, and that replaces the 10.)

Flashcards

(7)

What does the subtraction operator (-) do in a program?

It takes the second operand away from the first and gives a result the program can store or output.

Does a - b give the same answer as b - a?

No. Same size, opposite sign. For example 3 - 8 = -5, but 8 - 3 = 5.

How is 30 - 10 - 4 worked out?

Left to right: 30 - 10 = 20, then 20 - 4 = 16.

What do the brackets do in 30 - (10 - 4)?

The bracket is worked out first: 10 - 4 = 6, then 30 - 6 = 24.

What does score ← score - 5 do?

It takes the current value of score, subtracts 5, and stores the answer back in score, replacing the old value.

Why should the result of a subtraction be assigned to a variable?

So the program keeps it. For example, change ← paid - price stores the difference in change, ready for later lines to use.

What does a negative result from later - earlier tell you?

That the value went down: the later reading is smaller than the earlier one.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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Trace table — dry run the code

A line that subtracts from itself

Finish the tuck-shop program

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