Simplification
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Shortcut Techniques
Study MaterialShortcut Techniques – Simplification
Shortcut techniques in Simplification help candidates solve lengthy arithmetic expressions quickly and accurately in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, and placement examinations.
Instead of performing lengthy calculations step-by-step, shortcut methods focus on:
- Fast arithmetic calculations
- VBODMAS-based solving tricks
- Approximation techniques
- Fraction simplification methods
- Square and cube shortcuts
- Algebraic identity tricks
- Mental calculation techniques
Why Learn Shortcut Techniques?
- Improves calculation speed significantly.
- Reduces chances of calculation mistakes.
- Helps solve lengthy expressions faster.
- Useful in approximation and elimination methods.
- Improves overall quantitative aptitude performance.
Shortcut #1: VBODMAS Priority Rule
Always solve arithmetic expressions according to VBODMAS sequence.
VBODMAS Order:
V → B → O → D → M → A → S
Correct Bracket Order
- Vinculum
- () Small Bracket
- {} Curly Bracket
- [] Square Bracket
Example:
[12 + {8 − (3 × 2)}]
= [12 + {8 − 6}]
= [12 + 2]
= 14
Shortcut #2: Fast Multiplication Near Base Values
When numbers are close to powers of 10, use algebraic identities.
Formula:
(a + b)(a − b) = a² − b²
Example:
99 × 101
= (100 − 1)(100 + 1)
= 100² − 1²
= 10000 − 1
= 9999
Shortcut #3: Square Calculation Trick
Use identities for fast square calculations.
Formula:
(a − b)² = a² + b² − 2ab
Example:
297²
= (300 − 3)²
= 300² + 3² − 2 × 300 × 3
= 90000 + 9 − 1800
= 88209
Shortcut #4: Cube Identity Trick
Use cube identities to simplify lengthy expressions.
- a³ + b³ = (a + b)(a² − ab + b²)
- a³ − b³ = (a − b)(a² + ab + b²)
✔ Frequently useful in algebraic simplification questions.
Shortcut #5: Fraction Simplification
Before multiplication, simplify common factors between numerator and denominator.
Example:
48/72
Divide numerator and denominator by 24:
= 2/3
✔ Simplifying early reduces calculation time significantly.
Shortcut #6: Decimal Multiplication Trick
Ignore decimal points initially and multiply normally.
Place decimal point later according to total decimal places.
Example:
0.2 × 0.02 × 0.002
2 × 2 × 2 = 8
Total decimal places:
1 + 2 + 3 = 6
Answer = 0.000008
Shortcut #7: Percentage to Fraction Conversion
Memorize important percentage-fraction equivalents for fast calculations.
| Percentage | Fraction |
|---|---|
| 50% | 1/2 |
| 25% | 1/4 |
| 75% | 3/4 |
| 20% | 1/5 |
| 12.5% | 1/8 |
Shortcut #8: Division by Powers of 10
Move decimal point to the left according to number of zeros.
| Expression | Result |
|---|---|
| 563 ÷ 10 | 56.3 |
| 563 ÷ 100 | 5.63 |
| 563 ÷ 1000 | 0.563 |
Shortcut #9: Approximation Technique
Use approximation in lengthy calculations and MCQ-based questions.
Example:
19.98 × 5.02
≈ 20 × 5
≈ 100
✔ Approximation helps eliminate incorrect options quickly.
Shortcut #10: Even and Odd Property Tricks
- Even + Even = Even
- Odd + Odd = Even
- Even + Odd = Odd
- Even × Any Number = Even
- Odd × Odd = Odd
Example:
(135 × 27) + 16
Odd × Odd = Odd
Odd + Even = Odd
Therefore, result will be Odd.
Shortcut #11: Digital Sum Technique
Digital sum helps verify calculations quickly.
Method
Add digits repeatedly until a single digit is obtained.
| Number | Digital Sum |
|---|---|
| 5678 | 5 + 6 + 7 + 8 = 26 → 2 + 6 = 8 |
| 9999 | 9 + 9 + 9 + 9 = 36 → 3 + 6 = 9 |
✔ Useful for checking multiplication and division calculations.
Shortcut #12: BODMAS Sign Handling Trick
Always be careful with negative signs inside brackets.
Example:
12 − [8 − (3 − 2)]
= 12 − [8 − 1]
= 12 − 7
= 5
Shortcut #13: Reciprocal Trick
Division by a fraction becomes multiplication by reciprocal.
Example:
5 ÷ (2/3)
= 5 × (3/2)
= 15/2
= 7.5
Shortcut #14: Multiplication by 5 Trick
To multiply by 5:
- Multiply by 10
- Then divide by 2
Example:
48 × 5
= 480 ÷ 2
= 240
Shortcut #15: Multiplication by 25 Trick
To multiply by 25:
- Multiply by 100
- Then divide by 4
Example:
64 × 25
= 6400 ÷ 4
= 1600
Important Exam Tips
- Always follow VBODMAS sequence correctly.
- Practice squares up to 50 and cubes up to 20.
- Use algebraic identities for fast calculations.
- Apply approximation in lengthy calculations.
- Be careful with decimal placement.
- Simplify fractions before multiplication.
- Use elimination techniques in MCQs.
Shortcut techniques in Simplification help candidates improve calculation speed, reduce errors, and solve aptitude questions efficiently in competitive examinations.