O Level MathematicsC1.6 The four operations (incl. negative numbers and order of operations).

🔢 Mastering the Big 4! Conquer Negative Numbers & Order of Ops

Edudent Academy
28 Nov 25

Whether you are adding pocket-money, subtracting debts, multiplying scores, or dividing pizza slices, the **four operations** are everywhere. For O-Level success, you must also juggle negative numbers and follow the *order of operations* so your answers match the examiner’s marking scheme.

The Core Idea: BIDMAS with Signed Numbers

Remember **BIDMAS** (Brackets, Indices, Division & Multiplication, Addition & Subtraction). Work from left to right within the same rank. When negatives appear, treat the sign in front of a number as part of that number. For example, in 3−(−5)3-(-5) the second minus is part of −5-5, so the expression is really 3+5=83 + 5 = 8.

Worked Example: Mixing All Four Operations

  • Problem: Evaluate
      4−3×(−2)2+18−3  \; 4 - 3 \times ( -2 )^2 + \dfrac{18}{-3} \;
    .
  • Step 1 (B, I):
    (−2)2=4(-2)^2 = 4
    so the expression becomes
    4−3×4+18−34 - 3 \times 4 + \dfrac{18}{-3}
    .
  • Step 2 (D & M, left→right): First multiply
    3×4=123 \times 4 = 12
    , giving
    4−12+18−34 - 12 + \dfrac{18}{-3}
    . Next divide
    18−3=−6\dfrac{18}{-3} = -6
    to get
    4−12−64 - 12 - 6
    .
  • Step 3 (A & S, left→right):
    4−12=−84 - 12 = -8
    then
    −8−6=−14-8 - 6 = -14
    .
  • Answer:
    −14\boxed{-14}

Practice combining the **operations**, keep BIDMAS in mind, and watch those negative signs. With regular drill, you will breeze through any O-Level question of this type!