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Mathematics

Number and Numeration

Key Points

  • BODMAS/BIDMAS: Brackets, Orders, Division, Multiplication, Addition, Subtraction
  • LCM: Least Common Multiple — smallest number divisible by all given numbers
  • HCF: Highest Common Factor — largest number that divides all given numbers
  • Fractions: proper, improper, mixed numbers
  • Indices: aⁿ × aᵐ = aⁿ⁺ᵐ; aⁿ ÷ aᵐ = aⁿ⁻ᵐ; (aⁿ)ᵐ = aⁿᵐ

Detailed Notes

Number and Numeration covers the fundamental properties of numbers. Master BODMAS for order of operations. For LCM, use prime factorisation. For HCF, find common prime factors. Understand number bases (binary, octal, hexadecimal) and how to convert between them. Practice standard form (scientific notation): a × 10ⁿ where 1 ≤ a < 10.

Key Formulas & Facts

BODMAS Order
Brackets → Orders → Division → Multiplication → Addition → Subtraction
Index Law (Multiply)
aⁿ × aᵐ = aⁿ⁺ᵐ
Index Law (Divide)
aⁿ ÷ aᵐ = aⁿ⁻ᵐ
Index Law (Power)
(aⁿ)ᵐ = aⁿᵐ
Next
Algebra