5.1 Whole Numbers, Operations & Order of Operations
Key Takeaways
- Whole numbers are 0, 1, 2, 3, …; arithmetic on the entrance paper is general civil-service math, not firefighting hydraulics or pump formulas.
- Master the four operations and place value first—most multi-step word problems fail at a single careless add, subtract, multiply, or divide step.
- Order of operations (BODMAS/PEMDAS) decides which part of an expression you evaluate first: brackets, then powers/roots if present, then multiply/divide left to right, then add/subtract left to right.
- Left-to-right rule for equal-priority operations is a common trap: 24 ÷ 4 × 2 is 12, not 3; 10 − 3 + 2 is 9, not 5.
- Everyday Trinidad & Tobago contexts—budgets in TT dollars, fuel litres, class sizes, and shared costs—train the same skills the SCD Mathematics subject tests.
5.1 Whole Numbers, Operations & Order of Operations
Quick Answer: Whole-number success on civil-service Mathematics means place value, the four operations, and order of operations (BODMAS/PEMDAS)—brackets first, then powers if shown, then multiply/divide left to right, then add/subtract left to right. Practise with ordinary money, fuel, and head-count problems; do not study hose pressure, pump math, or fireground formulas for this entrance paper.
Mathematics is one of the three subjects named in the Service Commissions Department’s published entrance-examination notices (General Knowledge, English Language and Mathematics). The paper is a competitive multiple-choice filter. This chapter teaches general arithmetic foundations—the same number skills used for household budgets, market purchases, and shared bills across Trinidad & Tobago—not technical firefighting calculations taught later at Fire Service School.
What whole numbers are (and why place value matters)
Whole numbers are 0, 1, 2, 3, 4, … (non-negative integers). Entrance items may also involve positive integers written in words or as large totals (for example, national population figures or annual budgets in the millions), but the operations remain ordinary addition, subtraction, multiplication, and division.
Place value is the value of a digit based on its position:
| Place | Example digit in 487,526 | Value |
|---|---|---|
| Ones | 6 | 6 |
| Tens | 2 | 20 |
| Hundreds | 5 | 500 |
| Thousands | 7 | 7,000 |
| Ten thousands | 8 | 80,000 |
| Hundred thousands | 4 | 400,000 |
Example — reading a total correctly. A school fair raised $48,256. The digit 8 is in the thousands place → 8,000, not 80 or 80,000. Misreading place value turns an easy item into a wrong option that “looks close.”
When you compare two whole numbers, start from the left (largest place). 9,870 is less than 10,050 even though 9,870 “starts with 9,” because 10,050 has a ten-thousands digit of 1 while 9,870 has 0 in that place when both are aligned.
The four operations: clean definitions
| Operation | Meaning | Keywords in word problems |
|---|---|---|
| Addition (+) | Combine groups; total | sum, total, altogether, in all, combined |
| Subtraction (−) | Difference; how many left | difference, remaining, fewer, less than, how many more |
| Multiplication (×) | Equal groups; repeated addition | each, per, product, times, of (when groups are equal) |
| Division (÷) | Split into equal parts; how many groups | share equally, per person, average when equal split is implied, quotient |
Addition example. Three community centres collect 245, 318, and 167 food hampers. Total: 245 + 318 = 563; 563 + 167 = 730 hampers.
Subtraction example. A maxi-taxi route has 96 seats booked out of 120. Empty seats: 120 − 96 = 24.
Multiplication example. A stationery pack costs $35. Twelve packs: 12 × 35. Think 12 × 30 = 360 and 12 × 5 = 60 → 420. Answer: $420.
Division example. A mini-mart bill of $288 is split equally among 6 friends: 288 ÷ 6 = $48 each.
Remainders and “exact” multiple-choice answers
Division does not always land on a whole number. On MCQs you may need the quotient and remainder, the rounded result if the stem says so, or recognition that an option assumes an exact split when the numbers do not divide evenly.
Example. Share 50 exercise books among 6 classes as evenly as possible. 50 ÷ 6 = 8 remainder 2 → some classes get 8, two classes get 9 if extras are distributed one each—or the item may ask only for the whole-number quotient 8 books per class with 2 left over. Read the stem carefully.
Order of operations: BODMAS and PEMDAS
When an expression mixes operations, you do not always work left to right across every symbol. You follow a fixed priority so every correct solver gets the same value.
BODMAS (common in Caribbean classrooms): Brackets, Orders (powers/roots), Division and Multiplication (left to right), Addition and Subtraction (left to right).
PEMDAS (same idea, different letters): Parentheses, Exponents, Multiply/Divide left to right, Add/Subtract left to right.
Critical rule: Division and multiplication share one priority level. You do not always do all multiplications before all divisions. Work left to right among × and ÷. The same applies to + and −.
Worked example A — mixed multiply and add
Evaluate: 12 + 4 × 5
- Multiplication before addition: 4 × 5 = 20
- Then 12 + 20 = 32
Trap option: (12 + 4) × 5 = 80 — that would require brackets that are not there.
Worked example B — left-to-right division and multiplication
Evaluate: 24 ÷ 4 × 2
- Left to right: 24 ÷ 4 = 6
- Then 6 × 2 = 12
Trap: doing 4 × 2 first → 24 ÷ 8 = 3. That is wrong without brackets: 24 ÷ (4 × 2).
Worked example C — brackets force priority
Evaluate: (18 − 6) ÷ 3 + 5 × 2
- Brackets: 18 − 6 = 12 → expression becomes 12 ÷ 3 + 5 × 2
- Division and multiplication left to right: 12 ÷ 3 = 4; 5 × 2 = 10 → 4 + 10
- Addition: 4 + 10 = 14
Worked example D — everyday budget with order of operations
A household plans: pay $80 for internet, buy 3 grocery bags at $45 each, and receive a $20 discount coupon applied once at the end of the expression as written: 80 + 3 × 45 − 20
- Multiply: 3 × 45 = 135
- 80 + 135 = 215
- 215 − 20 = $195
If someone adds first as (80 + 3) × 45 − 20, they invent a different problem.
Worked example E — fuel and travel (civilian)
A driver buys 4 bottles of water at $6 each and 2 packs of snacks at $15 each after already paying $200 for petrol: 200 + 4 × 6 + 2 × 15
- 4 × 6 = 24; 2 × 15 = 30
- 200 + 24 + 30 = $254
Properties that speed mental math (and catch traps)
- Commutative property (add/multiply): 7 + 9 = 9 + 7; 6 × 4 = 4 × 6. Order can be swapped for convenience.
- Associative property (add/multiply): (2 + 3) + 8 = 2 + (3 + 8). Group freely when only + or only × appears.
- Distributive property: a(b + c) = ab + ac. Useful for 7 × 23 = 7 × 20 + 7 × 3 = 140 + 21 = 161.
- Zero and one: Adding 0 leaves a number unchanged; multiplying by 1 leaves it unchanged; multiplying by 0 gives 0; division by 0 is undefined (never choose an option that divides by zero).
Distributive mental check. 15 × 98 = 15 × (100 − 2) = 1,500 − 30 = 1,470. If an option is 1,500, someone forgot to subtract the 15 × 2.
Multi-step whole-number word problems
Translate words into a number sentence, then apply order of operations.
Example — shared class trip cost. Forty students each pay $75 for a field trip. The school adds a fixed bus hire of $600. Total money collected from students: 40 × 75 = 3,000. Total available with bus already paid from another fund is a different story—read what is asked.
If the question is: “Students pay $75 each and the class must also cover a $600 deposit from the same pool. What is the total the class needs before any other donations?” → 40 × 75 + 600 = 3,000 + 600 = $3,600.
Example — inventory. A shop starts with 240 bottles of water. Morning sales: 85. Afternoon delivery: 50. Closing stock: 240 − 85 + 50 = 205. Order matters for the story, but with only + and − left to right after the numbers are sequenced by the narrative, you get 155 + 50 = 205.
Common trap table (whole numbers & order of operations)
| Trap | What candidates do | Correct approach |
|---|---|---|
| Left-to-right everything | 12 + 4 × 5 → 16 × 5 = 80 | Multiply first → 32 |
| Always multiply before divide | 24 ÷ 4 × 2 → 24 ÷ 8 = 3 | Left to right → 12 |
| Always subtract before add | 10 − 3 + 2 → 10 − 5 = 5 | Left to right → 9 |
| Ignoring brackets | Treat (a + b) × c like a + b × c | Brackets first |
| Place-value misread | 4,080 as “four thousand eighty” vs four thousand eight | Align places; count zeros |
| Wrong operation from keyword | “How many more” → multiply | Difference → subtract |
| Invented technical formula | Applying pump or pressure formulas | Use only ordinary arithmetic |
Exam-day habits for arithmetic MCQs
- Underline the question (total? difference? each? remaining?).
- Write a short expression before calculating—especially when × and + both appear.
- Mark BODMAS steps in the margin (① brackets ② ×÷ ③ +−).
- Estimate: 19 × 21 is about 20 × 20 = 400; if your exact work gives 8,000, you misplaced a zero.
- Check reverse: if 288 ÷ 6 = 48, then 48 × 6 should return 288.
Remember: published item counts, time limits, pass scores, and subject weights for this entrance examination are not fixed in public sources—do not invent them. What you can control is accuracy on every whole-number step.
Section checkpoint
You should now be able to read large whole numbers, choose the correct operation from ordinary English cues, evaluate mixed expressions with BODMAS/PEMDAS, and reject left-to-right myths that produce attractive wrong answers. The next section builds on this with fractions and decimals—the same priority rules still apply once those number forms appear inside expressions.
Evaluate: 18 + 6 × 3 − 4. What is the correct value?
A Port of Spain market stall sells 4 packs of doubles mix at $28 each and 3 juice bottles at $12 each. Total cost is written as 4 × 28 + 3 × 12. What is the total?
Which evaluation of 36 ÷ 6 × 3 is correct under BODMAS/PEMDAS?
A community group has 240 chairs. They set out 8 rows of 25 chairs for an event and store the rest. How many chairs are stored?