Simplification and approximation tricks for exam prelims

Simplification questions in prelims aren't testing whether you can do arithmetic — they're testing whether you can do it fast, under BODMAS rules, without losing a step. And "approximate the value" questions are testing something different: whether you're willing to round instead of calculating exactly. Both skills save time the same way — by refusing to do more work than the question actually needs.

BODMAS shortcut: solve brackets from the inside out, but scan the whole expression first

Before touching any calculation, scan the full expression for terms that cancel, simplify, or combine easily — division that reduces to a whole number, terms that are identical with opposite signs, or a bracket that simplifies to zero. Fixing the order in your head before calculating avoids redoing work.

Worked example: 45 ÷ 9 × 3 + [ (12 − 8) × 5 ] − 6

• Bracket first: (12 − 8) = 4, then 4 × 5 = 20
• Left to right for ÷ and ×: 45 ÷ 9 = 5, then 5 × 3 = 15
• Now: 15 + 20 − 6

The only real risk in BODMAS questions is treating ÷ and × (or + and −) as having a fixed priority between them — they don't. Solve them strictly left to right as they appear.

Fraction shortcut: convert to a common, simple base before adding

When simplification involves several fractions, look for a common denominator that's easy to spot rather than multiplying all denominators together blindly.

Worked example: 3/4 + 5/6 − 1/3

• LCM of 4, 6, 3 = 12
• Convert: 3/4 = 9/12, 5/6 = 10/12, 1/3 = 4/12
• Combine: 9/12 + 10/12 − 4/12 = 15/12

Decimal shortcut: recognize common fraction-to-decimal equivalents

Memorizing a short list of fraction-decimal pairs turns a lot of "calculate this decimal expression" questions into pattern recognition instead of long division.

Worked example: 0.125 × 64

• Recognize 0.125 = 1/8
• 64 / 8 = 8

Approximation: round each number to the nearest convenient value first

"Find the approximate value" questions are explicitly telling you exact computation isn't required. Round each number to something you can work with mentally, then adjust only if the answer options are close together.

Worked example: approximate value of 288.97 ÷ 6.02 × 4.98

• Round: 288.97 ≈ 290, 6.02 ≈ 6, 4.98 ≈ 5
• 290 ÷ 6 ≈ 48.3
• 48.3 × 5 ≈ 241.5

Rounding direction matters when options are close

When two answer choices are within a few units of each other, rounding every number in the same direction (all up or all down) keeps errors from partially cancelling out — round consistently rather than mixing rounding directions to stay closer to the true value.

Worked example: approximate value of 49.8² (options: 2400, 2480, 2550)

• Round 49.8 up to 50 (a single consistent rounding, not mixed)
• 50² = 2500

Squares and cubes inside approximation questions

Approximation questions frequently bury a square or cube inside a longer expression. Recognizing them and applying the squares/cubes shortcut directly is faster than treating the whole expression as one long calculation.

Worked example: approximate value of √168 + 11.9²

• √168 ≈ √169 = 13 (nearest perfect square)
• 11.9² ≈ 12² = 144, adjust slightly down since 11.9 < 12 → ≈ 141.6

Surds and powers: simplify the base before calculating

When an expression has powers or roots with a common base hidden in different forms, rewrite everything to the same base first — this often makes the whole expression cancel down before you multiply anything out.

Worked example: (8² × 4³) ÷ 2⁵

• Rewrite in base 2: 8² = 2⁶, 4³ = 2⁶, 2⁵ stays as is
• Numerator: 2⁶ × 2⁶ = 2¹²
• Divide: 2¹² ÷ 2⁵ = 2⁷

Where this actually helps

Simplification and approximation are usually the first questions in a prelims quant section, and they're built to be fast points if you don't overthink them. The biggest time loss isn't slow arithmetic — it's treating an approximation question like a simplification question, or missing an obvious cancellation because the expression wasn't scanned before diving in.