Operations on Numbers

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(The Real Power of Number System)

Because Concepts Matter! | Concept Studies

Hi Champions! 👋 Today’s post is one of my favourites because this is the point where numbers start behaving like magic. If you understand how operations work on different types of numbers, you will solve 40% of Quantitative Aptitude questions instantly.

Let’s begin our journey into the real machinery of Maths — the “Operations on Numbers”. I’m preparing just like you, and sharing everything that has helped me speed up calculations, save time in exams, and avoid silly mistakes.



🔢 1. Basic Operations on Numbers

These four operations are the backbone of all quantitative chapters:

  • Addition (+)
  • Subtraction (–)
  • Multiplication (×)
  • Division (÷)

Understanding their behaviour with integers, decimals, fractions and negative numbers is essential.

➤ Addition Rules

  • Adding two positives → positive
  • Adding two negatives → negative
  • Adding a positive & negative → subtract and keep bigger number’s sign
Example: 25 + (–18) = 25 – 18 = 7

➤ Subtraction Rules

Subtracting a number is the same as adding its negative.

Example: 12 – (–8) = 12 + 8 = 20

➤ Multiplication Rules

  • + × + = +
  • - × - = +
  • + × - = -
Example: (–6) × (–3) = +18

➤ Division Rules

Same sign → positive result, different sign → negative result.

Example: (–42) ÷ 6 = –7

🧮 2. BODMAS – The Heart of Calculations

Without BODMAS, many aptitude questions become confusing. Remember the sequence:

BODMAS = Brackets → Orders → Division → Multiplication → Addition → Subtraction

Example:

Solve: 25 – 5 × 3 + 4
Step 1: 5 × 3 = 15
Step 2: 25 – 15 + 4 = 10 + 4 = 14

➗ 3. Division Algorithm & Remainders

Every number follows this relationship:

Dividend = Divisor × Quotient + Remainder

This forms the basis of remainders, modular arithmetic, cyclicity and unit digit tricks.

Example:

Divide 29 by 4.
4 × 7 = 28 → remainder = 1
Hence, 29 = 4 × 7 + 1

🧩 4. Modulus (|a|) – Absolute Value

Absolute value indicates distance from zero.

  • |5| = 5
  • |–5| = 5
  • |–7 + 2| = |–5| = 5

🔁 5. Cyclicity (Unit Digit Patterns)

Numbers follow patterns when raised to powers. This is the secret weapon for solving power-based questions in seconds.

Example: Unit Digit of 7ⁿ

7¹ → 7
7² → 49 → 9
7³ → 343 → 3
7⁴ → 2401 → 1

The cycle is 7, 9, 3, 1 (repeats every 4 steps).

➕ 6. Digital Sum (Casting Out 9’s)

Digital sum is used for:

  • Quick checking
  • Multiplication shortcuts
  • Error elimination in options

How to Find Digital Sum:

Add digits until a single digit remains.

Example: 583 → 5 + 8 + 3 = 16 → 1 + 6 = 7

🧠 7. Special Properties of Numbers

➤ Even & Odd Rules

  • Even + Even = Even
  • Odd + Odd = Even
  • Even + Odd = Odd
  • Even × Even = Even
  • Even × Odd = Even
  • Odd × Odd = Odd

➤ Factors-based Behaviour

  • Multiplying increases factors.
  • Adding usually does not increase factors.

📘 8. Mixed Operation Examples

Example 1

Evaluate: 18 ÷ 3 + 12 × 2 – 5
Step 1: 18 ÷ 3 = 6
Step 2: 12 × 2 = 24
Step 3: 6 + 24 – 5 = 25

Example 2

Simplify: 45 – (12 ÷ 4) × 3
Step 1: 12 ÷ 4 = 3
Step 2: 3 × 3 = 9
Step 3: 45 – 9 = 36

📝 9. Practice Questions for You

  1. Find the value: 32 – 18 ÷ 3 + 4 × 2
  2. Unit digit of 957
  3. Find digital sum of 8723
  4. Solve: 45 – 6 × 5 + 12 ÷ 3
  5. If 87 = 5 × Q + R, find remainder R.

Answers will be provided in the next follow-up post!

🌟 10. What’s Next?

In the next post, we will cover:

  • Advanced Order of Numbers
  • Comparing Fractions
  • Decimal Operations
  • Converting between forms

Stay tuned! We are building a rock-solid foundation — concept by concept, lesson by lesson.

Because Concepts Matter!

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