Lecture 2 – Number System & Remainder
For: STHP / IBA Sukkur Scholarship Test (Mathematics Part-II)
Teaching Style: Very Easy | Roman Urdu Explanation | Exam-Oriented
Lecture Objectives
- Number system ke basics clear karna
- Division algorithm (remainder rule) samajhna
- Exam-type remainder questions solve karna
- Common MCQ traps se bachna
1. Number System – Basic Types
Natural Numbers (N):
1, 2, 3, 4, 5, …
1, 2, 3, 4, 5, …
Whole Numbers (W):
0, 1, 2, 3, 4, …
0, 1, 2, 3, 4, …
Integers (Z):
…, -3, -2, -1, 0, 1, 2, 3, …
…, -3, -2, -1, 0, 1, 2, 3, …
Roman Urdu:
STHP / IBA test mein usually definitions se direct MCQs aate hain, is liye types yaad honi chahiyein.
2. Division Algorithm (Golden Rule)
Formula:
Number = (Divisor × Quotient) + Remainder
Number = (Divisor × Quotient) + Remainder
Roman Urdu Explanation:
Jab bhi remainder ka sawal aaye, pehla step hamesha actual number nikalna hota hai.
3. Solved Exam-Type Question
Question:
A number when divided by 11 gives quotient 3 and remainder 0. What is the remainder when the same number is divided by 15?
A number when divided by 11 gives quotient 3 and remainder 0. What is the remainder when the same number is divided by 15?
Step 1: Formula use karein
Number = (11 × 3) + 0 = 33
Step 2: 33 ko 15 se divide karein
15 × 2 = 30
Remainder = 33 − 30 = 3
Correct Answer: 3
4. Important Remainder Rules (MCQs Favorite)
- Remainder hamesha divisor se chhota hota hai
- Agar remainder 0 ho → number completely divisible hota hai
- Pehlay number find karo, baad mein divide karo
5. Common Mistakes Students Make
- Quotient ko direct divide kar dete hain (galat)
- Formula apply nahi karte
- Remainder ko negative likh dete hain (not allowed)
6. Practice Exercise – Lecture 2
MCQs:
- A number divided by 7 gives quotient 5 and remainder 2. The number is ______.
- If a number is divisible by 9, remainder will be ______.
Short Questions:
- Write division algorithm formula
- Find remainder when 47 is divided by 6
- If remainder is 0, what does it mean?
Homework
- Division formula learn karein
- At least 15 remainder MCQs practice karein
- Past paper questions attempt karein
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