Simple and Decimal Fractions
⚡ Unlock time-saving calculation tricks and mental math techniques. Solve complex problems in seconds with proven shortcut methods used by top performers.
Shortcut Techniques
Study MaterialShortcut Techniques – Simple and Decimal Fractions
Shortcut techniques for Simple and Decimal Fractions help candidates solve aptitude questions quickly with better accuracy. These methods are extremely useful in SSC, Banking, Railway, CAT, CDS, NDA, UPSC, and placement examinations where time management plays a crucial role.
Instead of lengthy calculations, shortcut methods focus on:
- Fast decimal calculations
- Fraction simplification tricks
- Recurring decimal conversion methods
- Quick comparison of fractions
- Mental multiplication and division
- Approximation techniques
Benefits of Learning Shortcut Techniques
- Improves calculation speed significantly.
- Reduces chances of calculation mistakes.
- Useful in simplification and approximation questions.
- Helps solve MCQs faster.
- Improves overall aptitude performance.
Shortcut #1: Common Fraction to Decimal Conversion
Memorizing common fraction-decimal values saves a lot of time in exams.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
| 1/3 | 0.333... | 33.33% |
| 2/3 | 0.666... | 66.66% |
✔ Memorizing these values helps in percentage and ratio problems too.
Shortcut #2: Decimal to Fraction Conversion Trick
To convert decimal into fraction quickly:
- Remove the decimal point.
- Write denominator as 1 followed by zeros.
- Simplify the fraction.
Example: Convert 0.75 into fraction.
0.75 = 75/100
= 3/4
Shortcut #3: Multiplication by Powers of 10
Move the decimal point to the right according to the number of zeros.
| Expression | Shortcut Result |
|---|---|
| 5.63 × 10 | 56.3 |
| 5.63 × 100 | 563 |
| 0.073 × 1000 | 73 |
✔ Shift decimal point right while multiplying by 10, 100, 1000...
Shortcut #4: Division by Powers of 10
Move the decimal point to the left according to the number of zeros.
| Expression | Shortcut Result |
|---|---|
| 563 ÷ 10 | 56.3 |
| 563 ÷ 100 | 5.63 |
| 73 ÷ 1000 | 0.073 |
Shortcut #5: Multiplication of Decimal Numbers
Ignore decimal points initially, multiply numbers normally, then place decimal point 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 #6: Comparing Fractions Quickly
Convert fractions into decimal values for faster comparison.
| Fraction | Decimal Value |
|---|---|
| 3/5 | 0.6 |
| 7/9 | 0.777... |
| 6/7 | 0.857... |
Therefore:
6/7 > 7/9 > 3/5
Shortcut #7: Recurring Decimal Conversion
Pure Recurring Decimal
Write repeating digits once in numerator and same number of 9s in denominator.
| Recurring Decimal | Fraction |
|---|---|
| 0.3̅ | 3/9 = 1/3 |
| 0.53̅ | 53/99 |
| 0.142857̅ | 142857/999999 |
Mixed Recurring Decimal
Formula:
(All digits − Non-repeating digits) / (9s followed by 0s)
Example:
0.16̅
= (16 − 1)/90
= 15/90
= 1/6
Shortcut #8: Annexing Zeros Trick
Adding zeros to the extreme right side of a decimal does not change its value.
| Equivalent Values |
|---|
| 0.8 = 0.80 = 0.800 |
| 5.2 = 5.20 = 5.200 |
✔ Useful for aligning decimal points during calculations.
Shortcut #9: Cross Multiplication Technique
Useful for comparing fractions quickly without converting into decimals.
Example: Compare 5/7 and 6/9
5 × 9 = 45
6 × 7 = 42
Since 45 > 42
Therefore:
5/7 > 6/9
Shortcut #10: Simplification Using Algebraic Identities
Use identities to reduce lengthy calculations.
- (a + b)² = a² + b² + 2ab
- (a − b)² = a² + b² − 2ab
- (a + b)(a − b) = a² − b²
- a³ + b³ = (a + b)(a² − ab + b²)
Example:
99 × 101
= (100 − 1)(100 + 1)
= 100² − 1²
= 10000 − 1
= 9999
Shortcut #11: Percentage-Fraction Conversion Trick
Memorize important percentage-fraction conversions.
| Percentage | Fraction |
|---|---|
| 50% | 1/2 |
| 25% | 1/4 |
| 75% | 3/4 |
| 20% | 1/5 |
| 12.5% | 1/8 |
Shortcut #12: Approximation Method
Use approximation for faster calculations in MCQs.
Example:
19.98 × 5.02
≈ 20 × 5
≈ 100
Important Exam Tips
- Memorize common fraction-decimal equivalents.
- Practice recurring decimal conversions regularly.
- Use approximation techniques in lengthy calculations.
- Apply cross multiplication for fraction comparison.
- Always count decimal places carefully.
- Use algebraic identities for fast simplification.
- Practice mental calculations daily.
Shortcut techniques for Simple and Decimal Fractions help candidates improve speed, reduce calculation errors, and solve aptitude questions efficiently in competitive examinations.