🔢 What is Modulus? (Absolute Value Explained)
Modulus (also called absolute value) refers to:
The distance of a number from 0 on the number line — always a non-negative value.
Whether a number is positive or negative, its modulus is always positive (or zero).
📘 Modulus Symbol & Notation
The modulus of a number x is written as:
|x| modulus of x
Example:
- ∣5∣=5
- ∣−5∣=5
🧠 Modulus in Simple Terms (Roman Urdu Explanation)
Modulus ka matlab hai:
Kisi number ki positive value lena, chahe wo negative ho ya positive.
Key Idea:
- Negative numbers become positive.
- Positive numbers stay the same.
- Zero remains zero.
🔸 Modulus Examples & Explanation
| Expression | Result | Reason | ||
|---|---|---|---|---|
| ( | 5 | ) | 5 | Already positive |
| ( | -5 | ) | 5 | Negative turns positive |
| ( | 0 | ) | 0 | Distance from zero is zero |
📏 Visualizing Modulus on a Number Line
- ∣+5∣=5→ 5 steps to the right of zero.
- ∣−5∣=5 → 5 steps to the left of zero.
✅ Both have the same distance (5) from zero.
📌 Key Properties of Modulus
✔ Always non-negative (≥ 0)
✔ Removes the negative sign (if any)
✔ Different from remainder (%) (Modulus ≠ Mod in programming)
BODMAS Rule – Full Form, Examples & Step-by-Step Guide
📌 What is BODMAS? (Order of Operations Explained)
BODMAS is a fundamental rule in mathematics that defines the correct sequence to solve arithmetic expressions. It ensures everyone calculates problems the same way to avoid confusion.
BODMAS ka matlab hai:
Maths ke equations ko solve karne ka sahi order (sequence). Agar is rule ko follow nahi kiya, toh answer galat ho sakta hai!
🔤 BODMAS Full Form & Meaning
| Letter | Stands For | Meaning | Example |
|---|---|---|---|
| B | Brackets | ( ), { }, [ ] | (2 + 3) × 4 |
| O | Orders | Exponents, Roots (², √) | 3² or √9 |
| D | Division | ÷ | 10 ÷ 2 |
| M | Multiplication | × | 5 × 3 |
| A | Addition | + | 4 + 6 |
| S | Subtraction | − | 8 − 5 |
📘 BODMAS Rule (Step-by-Step Order)
- Brackets → Solve innermost brackets first
( ) → { } → [ ] - Orders → Calculate powers & roots (e.g., 3², √16)
- Division & Multiplication → Left to right (whichever comes first)
- Addition & Subtraction → Left to right
🔍 BODMAS Examples (With Solutions)
Example 1: Simple Brackets
Q: 6 + (2 × 3)
✅ Solution:
- Brackets first:
(2 × 3) = 6 - Then add:
6 + 6 = **12**
Example 2: Division & Multiplication (Left to Right)
Q: 18 ÷ 3 × 2
✅ Solution:
- Division first:
18 ÷ 3 = 6 - Then multiply:
6 × 2 = **12**
Example 3: Powers & Nested Brackets
Q: 5 + 2² × (3 + 1)
✅ Solution:
- Brackets:
(3 + 1) = 4 - Orders:
2² = 4 - Multiplication:
4 × 4 = 16 - Addition:
5 + 16 = **21**
🧠 BODMAS in Simple Roman Urdu
BODMAS ka order yeh hai:
- Pehle brackets solve karo → ( ), { }, [ ]
- Phir powers/roots nikalo → 5², √25
- Divide/Multiply (jo pehle aaye) → 10 ÷ 2 × 3
- Last mein Add/Subtract → 7 + 4 − 5
Note: Agar same level ke operations hain (like × & ÷), toh left to right solve karo.
❓ Frequently Asked Questions (FAQs)
Q1. What if I ignore BODMAS?
❌ Answer wrong hoga! Example:8 ÷ 2 × 4
- Wrong way:
2 × 4 = 8 → 8 ÷ 8 = 1(❌ Incorrect) - Correct way:
8 ÷ 2 = 4 → 4 × 4 = 16(✅ BODMAS)
Q3. What comes first: Multiply or Divide?
➡ Left to Right! Example:12 ÷ 3 × 2 = 4 × 2 = 8 (Not 12 ÷ 6 = 2)
BODMAS AND MODULUS OR ABSOLUTE VALUE PRACTICE MCQS FOR EXAM ENTRY TEST PREPARATION
1. What is the value of ∣−7∣?
a) -7
b) 7
c) 0
d) 14
✅ Answer: b) 7
2. If ∣x∣=5, what are the possible values of x?
a) Only 5
b) Only -5
c) Both 5 and -5
d) None of these
✅ Answer: c) Both 5 and -5
3. What is ∣0∣?
a) 1
b) -0
c) 0
d) Undefined
✅ Answer: c) 0
5. Solve: ∣3−8∣=?
a) -5
b) 5
c) 11
d) -11
✅ Answer: b) 5
6. What is the correct solution to: 6 + 4 × 2?
a) 20
b) 14
c) 10
d) 12
✅ Answer: b) 14 (Multiplication before addition)
7. According to BODMAS, which operation comes first in: (8 – 3) × 2²?
a) Subtraction
b) Multiplication
c) Exponent
d) Brackets
✅ Answer: d) Brackets
8. Solve: 15 ÷ 3 + 2 × 4
a) 12
b) 13
c) 14
d) 15
✅ Answer: b) 13 (Division → Multiplication → Addition)
9. What is the value of 3 × (4 + 2) – 5?
a) 15
b) 13
c) 17
d) 21
✅ Answer: b) 13