Biểu thức Toán học

Doing arithmetic in a program

• Programs often do arithmetic 算术.
• An arithmetic expression 算术表达式 combines numbers with operators: $+$, $-$, $\times$, $\div$.
• The result is usually stored in a variable for later, e.g. $\text{area} \leftarrow \text{length} \times \text{width}$.
• To get the right answer, you must apply the operators in the right order.

Order of operations

• A computer follows the order of operations 运算顺序 — the same rules as maths.
• Do multiplication and division before addition and subtraction.
• Work left to right for operators of equal rank; do anything in brackets first.
• So $2 + 3 \times 4 = 14$ (not 20); writing $(2 + 3) \times 4$ forces the addition first, giving 20.

MOD gives the remainder 余数; multiplication comes before addition

The modulus operator

• The modulus 取模 operator (MOD) returns the remainder of integer division.
• For example $17 \bmod 5 = 2$, because $17 \div 5$ is 3 with 2 left over.
• Modulus is handy for tests: a number is even when $n \bmod 2 = 0$.
• It comes up constantly — cycling through positions, checking divisibility, and more.

Integer vs decimal

• Think about integer 整数 versus decimal results.
• Adding two integers gives an integer, but division can give a decimal: $7 \div 2 = 3.5$.
• Some languages treat $7 \div 2$ as integer division and give $3$ — know which you get.