📊 Study Notes – Tables
(For Haryana Patwari / Lekhpal – Quantitative Aptitude)
Tables are pre‑calculated lists that help you perform arithmetic operations quickly and accurately.
Common tables:
• Multiplication Table (1–12)
• Addition/Subtraction Table (for quick mental addition)
• Factor & Divisor Table
• Power Table (squares, cubes, etc.)
• Unit‑Conversion Table (e.g., 1 km = 1000 m)
• Time‑Table (multiples of 5, 10, 15, 30, etc.)
These tables reduce mental effort and minimise calculation errors, which is especially useful in field work where quick decisions are required.
1️⃣ Simple Explanation
| Concept | What it is | Why it matters |
|---|---|---|
| Multiplication Table | Shows products of two integers (1–12) | Saves time for frequent multiplication |
| Addition/Subtraction Table | Pre‑calculated sums/differences of two numbers | Useful for quick mental addition |
| Factor/Divisor Table | Lists factors of a number | Helps in simplifying fractions, finding common divisors |
| Power Table | Squares, cubes, fourth powers, etc. | Quickly compute areas, volumes, interests |
| Unit‑Conversion Table | Conversion constants (e.g., 1 kg = 1000 g) | Avoids long unit conversions |
Tip: Memorize the 1–12 multiplication table. The rest can be derived by simple rules (e.g., 9×4 = 36 → 3+6 = 9).
2️⃣ Key Points
| Area | Key Points |
|---|---|
| Multiplication | • 1×n = n, 10×n = n followed by 0. • For 5×n: n×5 = (n×10)/2. • For 9×n: (n×10) – n. |
| Addition | • Use “carry over” for sums >9. • For quick mental addition of two 2‑digit numbers, add the tens, then the units, finally add any carry. |
| Factor Table | • A number n has factors that multiply in pairs to n. • To find if a number is divisible by 3, 9, 11: use digit sum rules. |
| Power Table | • Square of a number: (a+b)² = a² + 2ab + b². • Cube of a number: (a+b)³ = a³ + 3a²b + 3ab² + b³. |
| Unit Conversion | • Keep a quick reference of common units: 1 km = 1000 m, 1 kg = 1000 g, 1 l = 1000 ml. |
| Time Table | • Multiples of 5: 5, 10, 15, …, 60. • Useful for calculating wages per hour or per day. |
| Practical Use | • In field work, use tables to verify calculations instantly. • Keep a small laminated sheet of the 1–12 multiplication table handy. |
3️⃣ Worked Example
Problem
A farmer has 7 acres of land. He wants to know how many square feet are in the total area.
(1 acre = 43,560 sq ft)
Solution Using Tables
-
Multiplication Table (7 × 43,560)
- We can split 43,560 into 43,000 + 560.
- 7 × 43,000 = 301,000 (use 7×43 = 301, then add three zeros).
- 7 × 560 = 3,920 (7×56 = 392, add one zero).
- Sum: 301,000 + 3,920 = 304,920 sq ft.
-
Factor Table (Optional check)
- 43,560 ÷ 7 = 6,228 → 7×6,228 = 43,596? Wait, wrong.
- Let's double‑check: 7 × 6,228 = 43,596 (not 43,560).
- Mistake: We should use exact multiplication from the table: 7×43,560 = 304,920.
- Factor table helps confirm 304,920 ÷ 7 = 43,560.
Result
The farmer’s land covers 304,920 square feet.
Why Tables Help
- Speed: 7×43,560 = 304,920 is almost instant with the table.
- Accuracy: Reduces the chance of slip‑ups that occur with long multiplication.
- Confidence: Quick verification using factor tables (304,920 ÷ 7 = 43,560) builds confidence.
4️⃣ Quick Revision Summary
| Topic | Key Takeaway |
|---|---|
| Multiplication | Memorize 1–12 tables; use patterns for 5, 9, 10. |
| Addition | Add tens and units separately; manage carry. |
| Factors | List factors as pairs; use digit sum tests for divisibility. |
| Powers | Use formulas for squares and cubes; memorize common powers. |
| Unit Conversion | Keep a concise unit‑conversion sheet. |
| Time Table | Know multiples of 5, 10, 15, 30 for quick payroll calculations. |
| Practical Use | Always carry a small laminated multiplication table; refer to it for quick checks in the field. |
Practice Tip: Write your own table in a notebook and quiz yourself daily. When you can answer a table question in < 5 seconds, you’re ready for the exam!