Addition, Subtraction, Multiplication
Chapter
1 video
INTRODUCTION
Addition, subtraction, and multiplication are basic arithmetic operations that allow for the processing of numerical and algebraic expressions. These operations are the foundation of all further mathematical concepts.
ADDITION
Addition is an operation in which we combine two or more numbers into a single total value (sum).
RULES OF ADDITION:
- COMMUTATIVITY: a + b = b + a
- ASSOCIATIVITY: (a + b) + c = a + (b + c)
- EXISTENCE OF AN IDENTITY ELEMENT (NEUTRAL ELEMENT): a + 0 = a (0 is the additive identity)
Examples:
- 5 + 3 = 8
- (-4) + 7 = 3
SUBTRACTION
Subtraction is the inverse operation of addition, where we determine the difference between two numbers.
RULES OF SUBTRACTION:
- a – b ≠ b – a (subtraction is generally not commutative)
- a – 0 = a (subtracting the additive identity)
- 9 – 4 = 5
- (-3) – (-7) = -3 + 7 = 4
MULTIPLICATION
Multiplication is an operation of repeated addition of the same number.
RULES OF MULTIPLICATION:
- COMMUTATIVITY: a × b = b × a
- ASSOCIATIVITY: (a × b) × c = a × (b × c)
- DISTRIBUTIVITY OVER ADDITION: a × (b + c) = (a × b) + (a × c)
- EXISTENCE OF AN IDENTITY ELEMENT (NEUTRAL ELEMENT): a × 1 = a (1 is the multiplicative identity)
- PRODUCT WITH 0: a × 0 = 0
- 4 × 3 = 12
- (-2) × 5 = -10
IMPORTANCE OF THESE OPERATIONS
Addition, subtraction, and multiplication are key operations in solving equations, computational problems, and analyzing numerical relationships.
CONCLUSION
Addition, subtraction, and multiplication allow for the basic processing of numbers and are the foundation of all further mathematical operations. Their rules ensure consistency in calculations.
Factoring Expressions 1
Explanation