Study Notes
Integers are whole numbers that can be positive, negative, or zero. Directed numbers are integers with both size and direction, where one direction is positive and the other is negative.
- Directed Numbers — numbers with both size and direction; one direction is positive, and the other is negative. Example: Temperature can be described as degrees above zero (positive) or below zero (negative).
- Order of Operations — rules that state the sequence in which multiple operations in an expression should be solved. Example: In the expression 10 x (9 + 81) - 25, you first solve inside the brackets, then multiply, and finally subtract.
- Product of Prime Numbers — writing a number as a product of all its prime factors. Example: The product of prime numbers for 36 is 2 x 2 x 3 x 3.
- Highest Common Factor (HCF) — the greatest common divisor of two or more positive integers. Example: The HCF of 36 and 48 is 12.
- Lowest Common Multiple (LCM) — the smallest positive integer that can divide the given numbers. Example: The LCM of 6 and 10 is 30.
Exam Tips
Key Definitions to Remember
- Directed Numbers: Numbers with both size and direction.
- Order of Operations: Sequence of solving multiple operations.
- Product of Prime Numbers: Writing a number as a product of its prime factors.
- Highest Common Factor (HCF): Greatest common divisor of integers.
- Lowest Common Multiple (LCM): Smallest positive integer that divides given numbers.
Common Confusions
- Mixing up positive and negative signs in directed numbers.
- Incorrectly applying the order of operations.
- Confusing HCF with LCM.
Typical Exam Questions
- What is the result of 6 - (-3)? Answer: 9
- Find the HCF of 12 and 16. Answer: 4
- What is the LCM of 12 and 18? Answer: 36
What Examiners Usually Test
- Understanding and applying the rules for directed numbers.
- Correctly using the order of operations in calculations.
- Ability to find the HCF and LCM of given numbers.