Arithmetic, Relational and Logical Operators in Java with Short-Circuit Evaluation (ICSE Class 9)

Understand Arithmetic, Relational and Logical Operators with Short-Circuit Evaluation

Arithmetic, Relational and Logical Operators with Short-Circuit Evaluation: key facts

Integer division and remainder

• •int / int gives int (fraction dropped)
• •a % b has the sign of a
• •23 % 7 = 2, -23 % 7 = -2

Make one operand decimal for a decimal answer.

Logical operators

• •&& true only if both true
• •|| true if at least one true
• •! reverses
• •&& before ||

Brackets override.

Short-circuit

A && B: B skipped if A is false | A || B: B skipped if A is true

Side effects in B may not happen.

Range test

low <= n && n <= high | never low <= n <= high

Two comparisons joined by &&.

How to answer Arithmetic, Relational and Logical Operators with Short-Circuit Evaluation questions

1. 1Write the value of every variable first.
2. 2Bracket the expression by precedence: ! then * / % then + - then relational then && then ||.
3. 3Evaluate each bracket; for int with int, apply integer division; for string joining, work left to right.
4. 4In && and ||, stop as soon as the answer is fixed and mark the skipped part as not evaluated.
5. 5Write the final output exactly, with the spaces from the string literals.

Arithmetic, Relational and Logical Operators with Short-Circuit Evaluation in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Tricks to remember Arithmetic, Relational and Logical Operators with Short-Circuit Evaluation

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Mod takes the left sign

  The sign of a % b follows a, never b.

  Use it when: Negative remainders.

• AND is strict, OR is lenient

  && needs everything true; || needs just one true.

  Use it when: Logical operators.

• Stops at the answer

  && stops at the first false; || stops at the first true.

  Use it when: Short-circuit questions.

Arithmetic, Relational and Logical Operators with Short-Circuit Evaluation: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

int a = 17, b = 5;
System.out.println(a / b + " " + a % b + " " + (double) a / b + " " + (a / b) * b + a % b);

int x = 12, y = 7;
boolean r1 = x > y && x % 2 == 0;
boolean r2 = !(x < y) || y / 0 == 1;
boolean r3 = x % y > 5;
System.out.println(r1 + " " + r2 + " " + r3);

int age = 15, marks = 58;
boolean ok = (age >= 14 && age <= 16) && (marks >= 60 || age == 15);
System.out.println(ok);

int p = 4, q = 9;
boolean t = (p > 5) && (++q > 9);
boolean u = (p < 5) || (++q > 9);
boolean v = (p > 5) || (++q > 9);
System.out.println(t + " " + u + " " + v + " " + q);

Where students lose marks in Arithmetic, Relational and Logical Operators with Short-Circuit Evaluation

The slips examiners see most often, and what to write instead.

• ✗Mistake: Giving a decimal for int division

  Both operands are int.

  Wrong working

  17 / 5 = 3.4

  Right working

  17 / 5 = 3 and 17 / 5.0 = 3.4

  ✓Do this: Look at the types before dividing.

  Usually costs: 1 mark

• ✗Mistake: Wrong sign of the remainder

  The sign of the divisor is used by mistake.

  Wrong working

  -23 % 7 = 5

  Right working

  -23 % 7 = -2

  ✓Do this: The sign follows the left operand.

  Usually costs: 1 mark

• ✗Mistake: Chaining comparisons

  Mathematics notation is copied.

  Wrong working

  100 <= n <= 999

  Right working

  n >= 100 && n <= 999

  ✓Do this: Join two comparisons with &&.

  Usually costs: 1 to 2 marks

Practice questions on Arithmetic, Relational and Logical Operators with Short-Circuit Evaluation

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQBoard level

   The value of 7 + 8 / 2 * 3 is:
   (a) 19 (b) 21 (c) 10 (d) 12

   Hint

   / and * are done left to right before +.

   Answer

   (a) 19 (8 / 2 = 4, 4 * 3 = 12, 7 + 12 = 19)

2. Q2 · 2 marks · Very short answerBoard level

   Evaluate: (i) 23 % 7 (ii) -23 % 7 (iii) 23 % -7

   Hint

   The sign follows the left operand.

   Answer

   (i) 2 (ii) -2 (iii) 2

3. Q3 · 2 marks · Short answerHarder board level

   Find the output:

   int m = 5;
   System.out.println(m / 2 + m % 2 * 3 + 1.5);

   Hint

   Do / and % * first, left to right.

   Answer

   6.5 (m / 2 = 2; m % 2 * 3 = 1 * 3 = 3; 2 + 3 = 5; 5 + 1.5 = 6.5)

4. Q4 · 3 marks · Short answerHarder board level

   Write Java conditions for: (i) n is a three-digit number; (ii) x is divisible by both 4 and 6; (iii) ch is a lower-case letter.

   Hint

   Join two comparisons with &&.

   Answer

   (i) n >= 100 && n <= 999 (ii) x % 4 == 0 && x % 6 == 0 (iii) ch >= 'a' && ch <= 'z'

5. Q5 · 1 mark · Assertion-reasonHOTS / competency

   Assertion (A): In (a != 0) && (b / a > 2), a division by zero error does not occur when a is 0.
   Reason (R): The && operator does not evaluate its right operand when the left operand is false.
   (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

   Hint

   What does a != 0 give when a is 0?

   Answer

   (a) a != 0 is false, so b / a is never evaluated and R explains A.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.How many operands has a binary operator?Show answer

   Two.

2. 2.What is 29 / 6 for ints?Show answer

   4

3. 3.What does 29 % 6 give?Show answer

   5

4. 4.Which operator is the only ternary one?Show answer

   ?:

5. 5.When is B skipped in A || B?Show answer

   When A is true.

6. 6.What type of value do relational operators give?Show answer

   boolean

Arithmetic, Relational and Logical Operators with Short-Circuit Evaluation: frequently asked questions