The real number system defines the operations of addition, subtraction, multiplication, and division for real numbers. Addition involves finding the sum of two numbers, multiplication finds the product, subtraction finds the difference by adding the opposite number, and division finds the quotient but is undefined if the number being divided by is zero.

1. Real Number System
Math 11 – College Algebra

2. Real Number System

3. Addition Operation
• If a and b are real numbers
a + b
denotes the sum of a and b

4. Multiplication Operation
• If a and b are real numbers,
a x b
denotes the product of a and b.

5. Subtraction and Division ???
• If a and b are real numbers,
a – b = d if and only if a = b + d
d denotes the difference of a and b
5 – 2 = 3 because 5 = 3+2

6. Subtraction and Division ???
• If a and b are real numbers, and b is
not equal to 0, then
a ÷ b = q if and only if a = b x q
q denotes the quotient of a and b.
50 ÷ 5 = 10 because 50 = 5 x 10

7. Why must b not equal to zero?
a ÷ b = q if and only if a = b x q
5 ÷ 0 = q 5 = 0 x q
Division by zero is not
defined.