2.2 Expressions and Operators
Java Expressions, Operators, and Integer Division
Unit 2: Variables, Decisions, and Input · Lesson 2.2 · about 30 minutes · no coding experience needed
Adding one to a score sounds like the easiest thing in this course. It contains the single most confusing line a beginner meets, and a division rule that will silently give you the wrong answer for as long as you do not know it.
What you will be able to do
- Predict the result of integer division and the remainder operator
- Read and write `score = score + 1` and explain why it is not a contradiction
- Use the compound assignment shorthand
Words you will need
- Expression
- In plain words Anything that works out to a value.
- More precisely A combination of values, variables and operators that evaluates to a single value.
- Operator
- In plain words A symbol that does something to values.
- More precisely Plus, minus, times, divide, and remainder: + - * / %
- Integer division
- In plain words Whole-number division. The remainder is thrown away.
- More precisely Division where both operands are integers; the fractional part is truncated.
Build it step by step
Every step below leaves a scenario that compiles and runs. If you stop halfway you will have something that works, not something broken. Follow along in Greenfoot rather than reading straight through.
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Step 1
On your screen An editor showing arithmetic expressions with their results in comments.
int a = 7 + 2; // 9 int b = 7 - 2; // 5 int c = 7 * 2; // 14Nothing surprising yet. `*` is multiply, because there is no times sign on a keyboard. The right side is worked out first, and the answer goes in the box.
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Step 2
On your screen The result of integer division shown as 3, with the remainder highlighted as discarded.
int d = 7 / 2; // 3, NOT 3.5 int e = 7 % 2; // 1, the remainder double f = 7.0 / 2; // 3.5Here is the one that catches everyone.
`7 / 2` is 3. Not 3.5, not 4. When BOTH sides are whole numbers Java does whole-number division and throws the remainder away. It does not round; it truncates.
`%` gives you that discarded remainder. 7 % 2 is 1.
To get 3.5, at least one side has to be a decimal: `7.0 / 2`.
This is not a quirk you can avoid. It will produce wrong numbers in a working program with no error message at all.
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Step 3
On your screen A score variable being incremented, with the old and new values annotated.
int score = 10; score = score + 1; // score is now 11As math, `score = score + 1` is nonsense. As Java it is an instruction, and the order is what makes it work:
1. Work out the RIGHT side using the current value: 10 + 1 is 11. 2. Put that result into the box on the LEFT.
Read `=` as "becomes", never as "equals", and the line stops being strange.
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Step 4
On your screen Compound assignment operators shown alongside their longhand equivalents.
score += 1; // same as score = score + 1 score -= 5; // same as score = score - 5 score++; // same as score = score + 1Shorthand for the same thing. You will see all three in real code, so you need to read them, and `score++` is the one you will meet most.
They are conveniences, not new ideas. If a line confuses you, expand it back to the long form in your head.
Mistakes almost everyone makes here
These are the wrong ideas students actually build at this point. Read them even if you think you understand, because a wrong idea you have not noticed is the expensive kind.
Common wrong idea 7 / 2 is 3.5, or rounds to 4.
What is actually true It is 3. Integer division truncates, and never rounds.
Why it matters This is the highest-value fact in the lesson. It produces wrong answers with no error, which is the worst kind of bug for a beginner to face.
Common wrong idea `score = score + 1` is a contradiction and cannot be true.
What is actually true `=` means "becomes", not "equals". Right side first, then store.
Why it matters Students who read = as equals get stuck permanently on the single most common line in game code.
Common wrong idea Storing 3.5 in an int rounds it to 4.
What is actually true Java refuses it outright, and if you force it you get 3.
Why it matters Expecting rounding hides a whole class of off-by-one bugs.
Check your understanding
Answer these before moving on. They are graded instantly and you can retry.
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1. What is the value of `9 / 2` in Java, when both are ints?
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2. What is `9 % 2`?
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3. int score = 4; score = score + 3; What is score?
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4. Which expression gives 4.5?
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5. `lives--;` does the same as which line?
Fill in the code
A coin is collected. Add one to the score, then work out how many complete rows of 10 coins the player has, and how many are left over.
score = score 1;
int fullRows = score 10;
int leftOver = score 10;Stuck? Open a hint for each blank
- Blank 1: One more than it was.
- Blank 2: How many complete tens fit in. Whole-number division does this for you.
- Blank 3: What is left after taking out the complete tens.
Lesson quiz
This one counts toward your progress. Take it when the section above makes sense.
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1. int x = 15 / 4; What is x?
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2. Which is the best way to test whether an int n is even?
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3. int a = 3; a += 4; a++; What is a?
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4. Why is `score = score + 1;` not a contradiction?
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5. A game divides 7 coins evenly between 2 players using `int each = 7 / 2;`. What goes wrong?
The short version
- Integer division TRUNCATES. 7 / 2 is 3.
- % gives the remainder, and is how you test for even or wrap a value around.
- Read `=` as "becomes". Right side first, then store.
- += and ++ are shorthand for the same thing.
If you get stuck
These pages cover the problems that come up most often in this lesson. Opening one is not cheating and it is not counted against you.
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