Operations on Numbers

Objective

The objective of this lesson is to introduce students to various operations performed on numbers, including addition, subtraction, multiplication, and division. Additionally, students will learn about the properties associated with these operations.

I. Addition

- Addition is the process of combining two or more numbers to find their total sum.

- Symbol: "+"

- Example: 5 + 3 = 8

- Properties:

  1. Commutative Property: The order of numbers can be changed without affecting the result. For any two numbers a and b, a + b = b + a.

  2. Associative Property: The grouping of numbers can be changed without affecting the result. For any three numbers a, b, and c, (a + b) + c = a + (b + c).

  3. Identity Property: The sum of any number and zero is the number itself.

For any number a, a + 0 = a.

II. Subtraction

- Subtraction is the process of finding the difference between two numbers.

- Symbol: "-"

- Example: 8 - 3 = 5

- Properties:

  1. Subtraction is not commutative: The order matters. For any two numbers a and b, a - b ≠ b - a.

  2. Subtraction is not associative: The grouping matters. For any three numbers a, b, and c, (a - b) - c ≠ a - (b - c).

III. Multiplication

- Multiplication is the process of repeated addition or scaling.

- Symbol: "×" or "*"

- Example: 4 × 3 = 12

- Properties:

  1. Commutative Property: The order of numbers can be changed without affecting the result. For any two numbers a and b, a × b = b × a.

  2. Associative Property: The grouping of numbers can be changed without affecting the result. For any three numbers a, b, and c, (a × b) × c = a × (b × c).

  3. Identity Property: The product of any number and one is the number itself. For any number a, a × 1 = a.

  4. Zero Property: The product of any number and zero is zero. For any number a, a × 0 = 0.

IV. Division

- Division is the process of distributing a quantity into equal parts or finding how many times one number is contained in another.

- Symbol: "÷" or "/"

- Example: 12 ÷ 3 = 4

- Properties:

  1. Division is not commutative: The order matters. For any two numbers a and b, a ÷ b ≠ b ÷ a.

  2. Division is not associative: The grouping matters. For any three numbers a, b, and c, (a ÷ b) ÷ c ≠ a ÷ (b ÷ c).

  3. Identity Property: The quotient of any number and itself is one. For any number a (except zero), a ÷ a = 1.

  4. Zero cannot be divided: Division by zero is undefined. For any number a, a ÷ 0 is undefined.