Simplification
Pointwise AISSEE Class 6 Mathematics guide for Simplification (Topic 7). Master VBODMAS precedence, vinculum evaluation, bracket removal order, and nested operational reduction.
Overview & Fundamental Concept
Pointwise AISSEE Class 6 Mathematics guide for Simplification (Topic 7). Master VBODMAS precedence, vinculum evaluation, bracket removal order, and nested operational reduction.
Official Syllabus Coverage Breakdown
| Syllabus Item | Prescribed Scope | Exam Relevance & Pedagogical Objective |
|---|---|---|
| Item 7 | BODMAS / VBODMAS rules of precedence: Vinculum, Brackets (bar, round, curly, square), Of, Division, Multiplication, Addition, Subtraction. | Master the VBODMAS hierarchy, nested bracket removals, operational tie-breaking, and arithmetic operator reduction for AISSEE Class VI. |
1. The VBODMAS Precedence Hierarchy
- Order of Operations: When an arithmetic expression contains multiple mathematical operations and brackets, it must be evaluated strictly according to the VBODMAS hierarchy.
- The 7 Levels of VBODMAS:
- • V — Vinculum (Bar Bracket $\overline{a - b}$): Evaluated first before all brackets and symbols.
- • B — Brackets: Removed in strict inner-to-outer sequence: 1. Round brackets $( )$, 2. Curly braces $\{ \}$, 3. Square brackets $[ ]$.
- • O — Of: Represents multiplication ($\times$), but holds higher precedence than division and multiplication.
- • D — Division ($\div$): Evaluated after 'Of' from left to right.
- • M — Multiplication ($\times$): Evaluated after division.
- • A — Addition ($+$): Evaluated after multiplication.
- • S — Subtraction ($-$): Evaluated last.
| Priority Rank | Letter | Mathematical Operation | Symbol | Execution Priority |
|---|---|---|---|---|
| 1st | V | Vinculum (Bar) | $\overline{x - y}$ | Highest priority — evaluate first |
| 2nd | B | Brackets | ( ), { }, [ ] | Inner round, then curly, then outer square |
| 3rd | O | Of (Multiplication) | of | Evaluated before regular $\div$ and $\times$ |
| 4th | D | Division | $\div$ | Left-to-right priority |
| 5th | M | Multiplication | $\times$ | Left-to-right priority |
| 6th | A | Addition | $+$ | Group positive terms |
| 7th | S | Subtraction | $-$ | Lowest priority — final step |
Cadet Mnemonic • VBODMAS Military Protocol
Remember the operational command chain:
- Vinculum • Brackets • Of
- Division • Multiplication
- Addition • Subtraction
2. The 'Of' Precedence vs Regular Multiplication
- The Crucial 'Of' Rule: The word 'of' indicates multiplication, but it MUST be executed before division. For example: $$36 \div 4 \text{ of } 3 = 36 \div (4 \times 3) = 36 \div 12 = 3$$ If computed as $(36 \div 4) \times 3 = 9 \times 3 = 27$, the answer is completely wrong!
- Vinculum (Bar) Rule: A bar placed over an expression acts as the tightest bracket. For example: $15 - \overline{8 - 3} = 15 - (8 - 3) = 15 - 5 = 10$. Notice that the minus sign outside the bar does NOT distribute until the expression under the bar is evaluated.
AISSEE Trap Alert • The Classic 'Of' Trap
In expressions like '100 ÷ 5 of 4', you MUST do 5 of 4 = 20 first! Result is 100 ÷ 20 = 5. Do NOT do 100 ÷ 5 = 20, then 20 × 4 = 80.
3. Signs Multiplication & Left-to-Right Processing
- Sign Multiplication Rules:
• $(+) \times (+) = (+)$
• $(-) \times (-) = (+)$ (Two negatives make a positive)
• $(+) \times (-) = (-)$
• $(-) \times (+) = (-)$ - Removing Brackets Preceded by Minus: When a bracket preceded by a negative sign is removed, the signs of ALL terms inside the bracket change: $$-(a - b + c) = -a + b - c$$
- Left-to-Right Tie-Breaking: When consecutive divisions appear, evaluate strictly from left to right: $$24 \div 4 \div 2 = (24 \div 4) \div 2 = 6 \div 2 = 3$$ Never compute from right to left ($24 \div (4 \div 2) = 24 \div 2 = 12$ is incorrect!).
Exam Trick • Chain Division Shortcut
For a chain of divisions $a \div b \div c \div d$, keep the first number on top and multiply all subsequent divisors in the denominator: $\frac{a}{b \times c \times d}$. Example: $120 \div 4 \div 3 \div 2 = \frac{120}{4 \times 3 \times 2} = \frac{120}{24} = 5$!
Visual Concept Blueprint • Vector Architecture
Speed Shortcuts & Mental Calculation Strategies
Master these high-yield time-saving heuristics curated by top AISSEE scorers to eliminate calculation bottlenecks and answer questions in under 45 seconds.
Shortcut Technique 1: Innermost Bracket First
Always locate the deepest nested bracket (usually round brackets) and resolve its content to a single number before moving outward.
Shortcut Technique 2: Positive/Negative Grouping
In the final addition/subtraction step, sum all positive numbers together, sum all negative numbers together, then perform one final subtraction.
Shortcut Technique 3: Fraction Bar as Bracket
A horizontal fraction bar acts as a bracket grouping the entire numerator and entire denominator. Simplify numerator and denominator separately before dividing.
Interactive 3D Revision Flashcards Deck
Click any card to flip and reveal the key exam rule or topper secret.
REVISION FLASHCARD
What is the core rule & definition for Simplification?
CADET MEMORY KEY
Precedence Order: \text{V} \to \text{B} \to \text{O} \to \text{D} \to \text{M} \to \text{A} \to \text{S}
REVISION FLASHCARD
Cadet Shortcut: How to solve Simplification in under 30 seconds?
CADET MEMORY KEY
Fast MCQ Elimination: Check the last digit (unit digit) and estimate the order of magnitude to eliminate 2 distractors in under 10 seconds.
REVISION FLASHCARD
Exam Trap Alert: What pitfall do most candidates fall into?
CADET MEMORY KEY
Left to Right: When division and multiplication appear consecutively, execute from left to right.
REVISION FLASHCARD
Rapid Memory Anchor for AISSEE Hall Recall:
CADET MEMORY KEY
Sign Inside Bracket: A minus sign outside a bracket flips all signs inside when the bracket is removed.
REVISION FLASHCARD
What is the value of 18 − 6 ÷ 2 × 3?
CADET MEMORY KEY
Follow BODMAS: 1. Division first: 6 ÷ 2 = 3. Expression becomes 18 − 3 × 3. 2. Multiplication next: 3 × 3 = 9. 3. Subtraction last: 18 − 9 = 9.
Common Traps & Examination Pitfalls
Avoid the Speed-Guess Trap: Under AISSEE pressure, candidates frequently misread units (e.g., mixing metres and centimetres, or per hour and per second) and confuse complementary ($90^\circ$) with supplementary ($180^\circ$) angles. Read every stem carefully and check units before selecting your OMR option.
Key Identities & Formulas
VBODMAS Order
$$\text{V} \to \text{B} \to \text{O} \to \text{D} \to \text{M} \to \text{A} \to \text{S}$$
Standard universal order of mathematical simplification.
Chain Division Identity
$$a \div b \div c = \frac{a}{b \times c}$$
Consecutive divisions multiply in the denominator.
Negative Sign Distribution
$$-(a - b) = -a + b$$
Minus outside inverts all internal signs.
Step-by-Step Solved Examination Models
Solved Example 1
Model Problem
Simplify the expression using BODMAS: $24 + 16 \div 4 \times (8 - 5) - 10$.
Detailed Solution:
Step 1: Bracket: $(8 - 5) = 3$. Expression becomes $24 + 16 \div 4 \times 3 - 10$.
Step 2: Division: $16 \div 4 = 4$. Expression becomes $24 + 4 \times 3 - 10$.
Step 3: Multiplication: $4 \times 3 = 12$. Expression becomes $24 + 12 - 10$.
Step 4: Addition & Subtraction: $36 - 10 = 26$.
Solved Example 2
Model Problem
Evaluate: $15 - [8 + \{6 - (4 - 2)\}]$.
Detailed Solution:
Innermost bracket first: $(4 - 2) = 2$.
Curly bracket: $\{6 - 2\} = 4$.
Square bracket: $[8 + 4] = 12$.
Finally: $15 - 12 = 3$.
Solved Example 3
Model Problem
Simplify the expression: $25 - [16 + \{12 - (9 - \overline{6 - 2})\}]$.
Detailed Solution:
1. Evaluate vinculum first: $\overline{6 - 2} = 4$. Expression becomes: $25 - [16 + \{12 - (9 - 4)\}]$.
2. Evaluate round brackets: $(9 - 4) = 5$. Expression becomes: $25 - [16 + \{12 - 5\}]$.
3. Evaluate curly braces: $\{12 - 5\} = 7$. Expression becomes: $25 - [16 + 7]$.
4. Evaluate square brackets: $[16 + 7] = 23$. Expression becomes: $25 - 23$.
5. Final subtraction: $25 - 23 = 2$... wait: let's check: $25 - 23 = 2$. Let's make options: A) 2, B) 4, C) 6, D) 8 with correct option A.
2. Evaluate round brackets: $(9 - 4) = 5$. Expression becomes: $25 - [16 + \{12 - 5\}]$.
3. Evaluate curly braces: $\{12 - 5\} = 7$. Expression becomes: $25 - [16 + 7]$.
4. Evaluate square brackets: $[16 + 7] = 23$. Expression becomes: $25 - 23$.
5. Final subtraction: $25 - 23 = 2$... wait: let's check: $25 - 23 = 2$. Let's make options: A) 2, B) 4, C) 6, D) 8 with correct option A.
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Question 1 of 10
Exam Standard
Evaluate: $45 - 5 \times 7 + 12 \div 3$.
Correct Answer: Option (A)
Division first: $12 \div 3 = 4$. Multiplication next: $5 \times 7 = 35$. Now calculate: $45 - 35 + 4 = 10 + 4 = 14$.
Question 2 of 10
Exam Standard
What is the value of $100 - 3 \times (20 + 5) + 40 \div 8$?
Correct Answer: Option (A)
Bracket first: $(20 + 5) = 25$. Division: $40 \div 8 = 5$. Multiplication: $3 \times 25 = 75$. Calculation: $100 - 75 + 5 = 25 + 5 = 30$.
Question 3 of 10
Exam Standard
Simplify: $\frac{1}{2} \text{ of } 48 + 15 \div 3 - 7$.
Correct Answer: Option (A)
'Of' takes precedence: $\frac{1}{2} \times 48 = 24$. Division: $15 \div 3 = 5$. Result: $24 + 5 - 7 = 29 - 7 = 22$.
Question 4 of 10
Exam Standard
Solve: $72 \div 9 \times 3 + 18 - 6$.
Correct Answer: Option (A)
Division: $72 \div 9 = 8$. Multiplication: $8 \times 3 = 24$. Addition and Subtraction: $24 + 18 - 6 = 42 - 6 = 36$.
Question 5 of 10
Exam Standard
Find the value of: $50 - [20 + \{15 - (8 - 3)\}]$.
Correct Answer: Option (A)
$(8 - 3) = 5$. Curly bracket: $\{15 - 5\} = 10$. Square bracket: $[20 + 10] = 30$. Final: $50 - 30 = 20$.
Question 6 of 10
Exam Standard
Simplify: $3.5 \times 2 + 8.4 \div 2 - 1.2$.
Correct Answer: Option (A)
$3.5 \times 2 = 7.0$. $8.4 \div 2 = 4.2$. Then: $7.0 + 4.2 - 1.2 = 11.2 - 1.2 = 10.0$.
Question 7 of 10
Exam Standard
Evaluate: $18 + 12 \div (4 + 2) \times 5$.
Correct Answer: Option (A)
Bracket: $(4 + 2) = 6$. Division: $12 \div 6 = 2$. Multiplication: $2 \times 5 = 10$. Addition: $18 + 10 = 28$.
Question 8 of 10
Exam Standard
If $A = 20 \div 5 \times 2$ and $B = 20 \times 2 \div 5$, what is $A + B$?
Correct Answer: Option (A)
In $A$: $20 \div 5 = 4$, $4 \times 2 = 8$. In $B$: $20 \times 2 = 40$, $40 \div 5 = 8$. Thus, $A + B = 8 + 8 = 16$.
Question 9 of 10
Exam Standard
Simplify: $60 \div 5 \text{ of } 2 + 14 - 3$.
Correct Answer: Option (A)
'Of' first: $5 \text{ of } 2 = 10$. Division: $60 \div 10 = 6$. Then: $6 + 14 - 3 = 20 - 3 = 17$.
Question 10 of 10
Exam Standard
Find the value of: $120 \div [15 \times (8 - 6) - 10]$.
Correct Answer: Option (A)
$(8 - 6) = 2$. Multiplication: $15 \times 2 = 30$. Subtraction: $30 - 10 = 20$. Division: $120 \div 20 = 6$.
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Last-Minute Cadet Revision Matrix
Rapid recall checkpoints to review 24 hours before stepping into the examination hall.
| Concept Checkpoint | High-Yield Exam Rule & Memory Anchor |
|---|---|
| Vinculum First | Vinculum has higher priority than all parentheses, brackets, and arithmetic operators. |
| Bracket Order | Remove round brackets ( ) first, then curly { }, and finally square brackets [ ]. |
| Of vs Multiply | 'Of' must always be evaluated prior to regular division and multiplication. |
| Chain Division | Consecutive division operations must strictly proceed from left to right. |
Frequently Asked Questions
How many questions from Simplification appear in the AISSEE Class VI exam?
Typically, 2 to 3 questions directly test Simplification in the 50-question Mathematics paper, contributing 6 to 9 marks towards the 150-mark section total.
Is there any negative marking for incorrect answers in AISSEE Class VI?
No. The National Testing Agency (NTA) does not apply negative marking in the AISSEE Class VI entrance examination. Candidates should attempt every single question.
What is the best way to revise Simplification before the exam?
Review the high-yield formulas, practice the 10 interactive drill MCQs on this page, and memorize the revision checkpoints matrix.