Arithmetic operators
Integer division — THIS IS CRITICAL
java
int result = 7 / 2; // result = 3 (not 3.5!)
int result2 = 1 / 3; // result2 = 0 (not 0.333...)
int result3 = -7 / 2; // result3 = -3 (truncates toward zero)
java
double result = 7.0 / 2; // result = 3.5
double result2 = 7 / 2.0; // result2 = 3.5
double result3 = (double) 7 / 2; // result3 = 3.5 (casting)
The modulo operator (%)
java
10 % 3 // → 1 (10 ÷ 3 = 3 remainder 1)
15 % 5 // → 0 (15 ÷ 5 = 3 remainder 0)
7 % 10 // → 7 (7 ÷ 10 = 0 remainder 7)
Common uses of %
Operator precedence
java
int result = 2 + 3 * 4; // 2 + 12 = 14 (NOT 20)
int result2 = (2 + 3) * 4; // 5 * 4 = 20 (parentheses change order)
int result3 = 10 - 4 / 2; // 10 - 2 = 8
int result4 = 10 % 3 + 2; // 1 + 2 = 3
The assignment operator (=)
java
int x = 5; // x is now 5
x = x + 1; // x is now 6 (take old x, add 1, store back in x)
String concatenation with +
java
String first = "Hello";
String last = "World";
System.out.println(first + " " + last); // "Hello World"
Mixing Strings and numbers
java
System.out.println("Score: " + 95); // "Score: 95"
System.out.println("2 + 3 = " + 2 + 3); // "2 + 3 = 23" (!)
System.out.println("2 + 3 = " + (2 + 3)); // "2 + 3 = 5"
java
int age = 17;
System.out.println("I am " + age + " years old."); // "I am 17 years old."
Tracing code step by step
java
int a = 10;
int b = 3;
int c = a / b; // c = 3 (integer division)
int d = a % b; // d = 1 (remainder)
double e = a / b; // e = 3.0 (int division happens FIRST, then stored as double)
double f = (double) a / b; // f = 3.333... (cast forces real division)
AP Exam Tips
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Common Mistakes
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