A large slice of any aptitude paper is pure calculation: simplify this expression, approximate that product. These are free marks — provided you respect the order of operations and don't over-compute.
Order of operations — BODMAS
Brackets → Orders (powers, roots) → Division & Multiplication (left to right) → Addition & Subtraction (left to right).
How to Approach It
These are the cheapest marks on the paper, so your only enemy is carelessness. The aim is to be accurate at speed and never give one away to a slipped order of operations.
- Map the operation order first. Before touching the numbers, locate the brackets and powers and note where the divisions and multiplications sit. This prevents the most common error: adding before you multiply.
- Work brackets from the inside out. Resolve the innermost bracket first, then peel outward, treating each solved bracket as a single number.
- Decide: exact or approximate? If the question says 'approximately' or the options are far apart, round each term to a friendly value. If it demands an exact figure, keep fractions rather than decimals.
- Confirm the size of your answer. Finish with a quick estimate or a digit-sum check. A result wildly different from your rough expectation signals a step went wrong.
Techniques & Methods
- BODMAS, left to right. Brackets → Orders → (÷ and × together, left to right) → (+ and − together). e.g. 8 + 12 ÷ 4 × 2 = 8 + (3×2) = 14.
- Round, then compare. In 'approximate' questions, round each term to a friendly value before computing. e.g. 48.7 × 4.1 ≈ 50 × 4 = 200.
- Percentage as a fraction. Swap common percentages for fractions so terms cancel. e.g. 37.5% of 64 = 3/8 × 64 = 24.
- Digit-sum check. Confirm a result by checking that digit sums agree. e.g. 27 × 3 = 81: 9×3 → 9, and 8+1 → 9. Consistent.
The Edge
For "approximate the value" questions, round every number first — 4.98 × 19.9 is just 5 × 20 = 100. The options are spaced far apart on purpose, so exact arithmetic only wastes time. Division and multiplication share a tier and are done left to right, not multiplication-first: 36 ÷ 6 × 2 = 12, not 3.Worked example
Simplify: 12 + 6 ÷ 2 × 3
- Apply BODMAS: no brackets or powers, so handle ÷ and × next — crucially left to right, not multiplication first.
- Working left to right: 6 ÷ 2 = 3, then 3 × 3 = 9.
- Only now do the addition: 12 + 9.
- That gives 21. (The wrong answer 36 comes from adding 12 + 6 first.)
Answer: Value = 21
Worked example
Approximate: 4.98 × 19.9
- The word 'approximate' is your signal to round before multiplying, since the answer choices are spaced far apart.
- Round each factor: 4.98 ≈ 5, and 19.9 ≈ 20.
- Multiply the rounded values: 5 × 20 = 100.
- The exact product is 99.1, so 100 is the right approximation — far faster than long multiplication.
Answer: Approximately 100
Worked Drills
Worked example
8 + 2 × 5 =
- Multiply first: 2 × 5 = 10.
- Then add: 8 + 10 = 18.
Answer: 18 (option a)
Worked example
100 − 20 × 3 =
- Multiply first: 20 × 3 = 60.
- Then subtract: 100 − 60 = 40.
Answer: 40 (option a)
Worked example
12 × 12 − 11 × 11 =
- Compute each product: 144 and 121.
- Subtract: 144 − 121 = 23.
Answer: 23 (option b)
Worked example
7 + 7 ÷ 7 + 7 × 7 − 7 =
- Do ÷ and × first: 7 ÷ 7 = 1 and 7 × 7 = 49.
- Now left to right: 7 + 1 + 49 − 7 = 50.
Answer: 50 (option a)
Worked example
The value of 0.5 × 0.5 + 0.5 ÷ 0.5 is:
- Multiply and divide first: 0.5 × 0.5 = 0.25 and 0.5 ÷ 0.5 = 1.
- Add: 0.25 + 1 = 1.25.
Answer: 1.25 (option c)
Worked example
√(0.0064) equals:
- 0.08 × 0.08 = 0.0064.
- So √0.0064 = 0.08.
Answer: 0.08 (option a)
Worked example
If 2x + 3 = 11, then 5x − 2 equals:
- Solve 2x + 3 = 11 → x = 4.
- 5(4) − 2 = 18.
Answer: 18 (option b)
Worked example
The square root of 4096 is:
- 64 × 64 = 4096.
- So √4096 = 64.
Answer: 64 (option c)
Worked example
12.5% of 64 + (1/8) of 80 equals:
- 12.5% = 1/8, so 1/8 of 64 = 8.
- 1/8 of 80 = 10. Sum: 8 + 10 = 18.
Answer: 18 (option b)
⚠ Watch out
- Do division and multiplication left to right — neither has priority over the other.
- Resolve everything inside brackets before touching what's outside.
- In approximation, round consistently; don't round one factor up and forget the other.
Takeaways
- Order before numbers. Map brackets, powers and the ÷/× tier before you compute anything.
- Left to right wins. Division and multiplication share a tier — 36 ÷ 6 × 2 = 12, not 3.
- Round for 'approximate'. Friendly values turn long products into mental arithmetic.
- Fractions beat percentages. 12.5% → 1/8 lets terms cancel cleanly.