Simplification and approximation questions are the bread and butter of banking exams and placement tests. The good news? They’re mostly about speed, not difficulty. If we master BODMAS and learn when to approximate vs compute exactly, we can blitz through these in under a minute each.
BODMAS / PEMDAS
The order of operations everyone learns in school but still gets tripped up by in exams.
Critical point: Division and multiplication have the same priority — we go left to right. Same with addition and subtraction. This is where most people mess up.
Example: 24 ÷ 6 × 2 = ?
- Left to right: (24 ÷ 6) × 2 = 4 × 2 = 8
- NOT: 24 ÷ (6 × 2) = 24 ÷ 12 = 2 ← WRONG
Example: 48 - 12 + 7 = ?
- Left to right: (48 - 12) + 7 = 36 + 7 = 43
Tricky BODMAS Examples
Example: 3 + 4 × 2 - 6 ÷ 3
- First, multiplication and division (left to right): 4 × 2 = 8 and 6 ÷ 3 = 2
- Now: 3 + 8 - 2 = 9
Example: (8 + 2)² ÷ 5 - 3 × 4
- Brackets: (10)² ÷ 5 - 3 × 4
- Orders: 100 ÷ 5 - 3 × 4
- Division/Multiplication: 20 - 12
- Subtraction: 8
The Vinculum (Bar) — Of/Of
In some problems, we see “of” — this means multiplication and has the same priority as multiplication/division.
Example: 1/3 of 27 + 4 × 2 = ?
- 1/3 of 27 = 9
- 4 × 2 = 8
- 9 + 8 = 17
Approximation Strategies
In timed exams, especially banking/placement tests, we often don’t need exact answers. The options are usually spread far enough that a good approximation is enough.
Strategy 1: Round to Nearest Convenient Number
- 498 → round to 500
- 7.89 → round to 8
- 33.3% → round to 1/3
- 24.98% → round to 25% = 1/4
Example: 498.7 × 31.2 ÷ 9.87 = ?
- ≈ 500 × 31 ÷ 10
- = 15500 ÷ 10
- = ≈ 1550 (actual: 1573.6)
If options are 1250, 1425, 1575, 1720 → we’d pick 1575 (closest to our estimate, and we rounded down slightly overall).
Strategy 2: Percentage-Based Estimation
Use the fact that we know our fraction-decimal equivalents.
Example: 37.5% of 4816 = ?
- 37.5% = 3/8
- 4816 ÷ 8 = 602
- 602 × 3 = 1806
No approximation needed here — fraction equivalents gave us the exact answer fast!
Strategy 3: Break Down Complex Expressions
Example: 786 × 764 = ?
- Notice: 786 = 775 + 11, 764 = 775 - 11
- This is (a+b)(a-b) = a² - b²
- = 775² - 11²
- = 600625 - 121
- = 600504
Strategy 4: Use of “Close to” Reference Points
- 19 × 21 = 20² - 1² = 399
- 48 × 52 = 50² - 2² = 2496
- 997 × 1003 = 1000² - 3² = 999991
Digit Sum Method (Casting Out 9s)
This is a quick way to verify if our answer is correct. It doesn’t tell us the exact answer, but it can catch errors.
Method:
- Find the digit sum of each number (keep adding digits until single digit, treating 9 as 0)
- Perform the same operation on the digit sums
- The digit sum of the result should match the digit sum of our answer
Example: Verify: 347 × 28 = 9716
- Digit sum of 347: 3+4+7 = 14 → 1+4 = 5
- Digit sum of 28: 2+8 = 10 → 1+0 = 1
- Product of digit sums: 5 × 1 = 5
- Digit sum of 9716: 9+7+1+6 = 23 → 2+3 = 5
- Both give 5 → likely correct ✓
Limitation: This method can’t detect errors that are multiples of 9. For example, 9720 also has digit sum 18 → 9 → hmm, that’s different. So it would catch that error. But swapping digits (like 9716 vs 9761) might not always be caught.
Simplification of Fractions and Mixed Expressions
Chain Rule Simplification
When we have a chain like a × b / c × d / e, work in pairs to cancel common factors early.
Example: (144 × 25 × 49) / (35 × 18 × 20) = ?
Cancel before multiplying:
- 144/18 = 8
- 25/5 = 5 (taking 5 from 35)
- 49/7 = 7 (taking 7 from the remaining 35/5 = 7)
- Remaining: 8 × 5 × 7 / 20 = 280/20 = 14
In simple language, always cancel common factors between numerator and denominator before multiplying. This keeps numbers small and manageable.
Worked Examples
Example 1: Simplify: 5/8 of 480 + 3/5 of 250 - 7/12 of 360
- 5/8 × 480 = 300
- 3/5 × 250 = 150
- 7/12 × 360 = 210
- 300 + 150 - 210 = 240
Example 2: Approximate: 3987.05 × 11.02 ÷ 39.97
- ≈ 4000 × 11 ÷ 40
- = 44000 ÷ 40
- = 1100 (actual: 1098.1)
Example 3: What value should replace ? in: 55% of 800 + 40% of 350 = ? + 220
- 55% of 800 = 440
- 40% of 350 = 140
- 440 + 140 = ? + 220
- ? = 580 - 220 = 360
Example 4: Simplify: (13.96)² - (5.99)² + (8.01)²
Approximate: 14² - 6² + 8² = 196 - 36 + 64 = 224
(Exact would be very close: 195.0816 - 35.8801 + 64.1601 = 223.3616, so with options like 218, 224, 230, 236 we’d pick 224)
Example 5: Simplify: √(144 × 81) + √(256 × 49) - √(196 × 64)
- √(144 × 81) = 12 × 9 = 108
- √(256 × 49) = 16 × 7 = 112
- √(196 × 64) = 14 × 8 = 112
- 108 + 112 - 112 = 108
When to Approximate vs Compute Exactly
| Situation | Strategy |
|---|---|
| Options are spread far apart (e.g., 1200, 1550, 1900) | Approximate aggressively |
| Options are close together (e.g., 1540, 1560, 1580) | Compute exactly |
| Expression has clean fractions (1/4, 3/8, etc.) | Compute exactly using fraction-decimal equivalents |
| Numbers are close to round numbers (499, 1002) | Round and adjust |
| Expression involves squares/cubes | Use algebraic identities |
| Need to verify our answer | Use digit sum method |
Common Exam Patterns
- “Simplify the expression” → Follow BODMAS strictly, cancel common factors early
- “What approximate value should replace ?” → Round everything, pick closest option
- “What should come in place of ?” → Isolate the unknown, simplify both sides
- “Which of the following is closest to…” → Approximate, then eliminate wrong options
- Mixed fraction/percentage expressions → Convert everything to fractions first
Practice Problems
Q1: Simplify: 12.5% of 640 + 37.5% of 480 - 66.67% of 180
Q2: Approximate: 7985 ÷ 401 × 199
Q3: Verify using digit sums: Is 528 × 47 = 24816?
Answers:
A1: 12.5% = 1/8, 37.5% = 3/8, 66.67% = 2/3. So: 640/8 + 3×480/8 - 2×180/3 = 80 + 180 - 120 = 140
A2: ≈ 8000 ÷ 400 × 200 = 20 × 200 = 4000 (actual: 3962.3)
A3: Digit sum of 528: 5+2+8 = 15 → 6. Digit sum of 47: 4+7 = 11 → 2. Product: 6×2 = 12 → 3. Digit sum of 24816: 2+4+8+1+6 = 21 → 3. They match, so it’s likely correct ✓. (Actual: 528 × 47 = 24816 ✓)