Information Processing (Term 2) — Exercise Solutions

How to Use This Page

This page provides complete, step-by-step solutions for the Information Processing chapter in the TN State Board Class 6 Maths Term 2 textbook. Each solution is worked out in full so you can follow the reasoning — not just the final answer.

Tips:

• Try each problem on your own first, then check the solution here.
• Pay close attention to the Common Mistakes section near the end.
• Use the Exam Checklist to make sure you have covered every concept before your test.

Key Concepts (Quick Recap)

Number Patterns

A number pattern is a sequence of numbers that follows a definite rule. For example:

• Even numbers: 2, 4, 6, 8, 10, … (add 2 each time)
• Squares: 1, 4, 9, 16, 25, … (n² for n = 1, 2, 3, …)
• Triangular numbers: 1, 3, 6, 10, 15, … (each term is the sum of consecutive natural numbers)

To find the next term, identify the rule governing the pattern and apply it.

Fibonacci Sequence

The Fibonacci sequence is a special number pattern where each term is the sum of the two preceding terms.

Starting values: 0, 1

Rule: F(n) = F(n−1) + F(n−2)

The sequence begins: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

Example: To find the 8th Fibonacci number:

• F(8) = F(7) + F(6) = 13 + 8 = 21

Tree Diagrams for Arithmetic

A tree diagram is a visual way to represent an arithmetic expression. It shows:

• Leaf nodes — the numbers (operands)
• Branch nodes — the operations (+, −, ×, ÷)

How to read a tree diagram:

1. Start from the bottom (leaf nodes). 2. Combine the leaves using the operator at the branch node above them. 3. Move upward until you reach the top (root) to get the final result.

Example: A tree with branches 4 and 5 meeting at a + node represents 4 + 5 = 9.

Converting Between Tree Diagrams and Expressions

Tree Diagram → Expression:

1. Identify the innermost (lowest) operations first. 2. Write each sub-expression using brackets. 3. Combine sub-expressions with the next operator upward.

Expression → Tree Diagram:

1. Identify the last operation performed (the root). 2. Split the expression into left and right sub-expressions. 3. Continue splitting each sub-expression until you reach single numbers (leaves).

Exercise 5.1 — Patterns and Sequences

Q1. Find the next three terms in the pattern: 2, 6, 18, 54, …

Observe the relationship between consecutive terms:

• 6 ÷ 2 = 3
• 18 ÷ 6 = 3
• 54 ÷ 18 = 3

Each term is multiplied by 3 to get the next term. The rule is: multiply by 3.

• Next term: 54 × 3 = 162
• Next term: 162 × 3 = 486
• Next term: 486 × 3 = 1,458

Q2. Find the missing term: 1, 1, 2, 3, 5, 8, 13, ___

This is the Fibonacci sequence. Each term is the sum of the two previous terms.

• 1 + 1 = 2
• 1 + 2 = 3
• 2 + 3 = 5
• 3 + 5 = 8
• 5 + 8 = 13

Next term = 8 + 13 = 21

Q3. Find the next term: 3, 6, 9, 12, __

Observe the pattern:

• 6 − 3 = 3
• 9 − 6 = 3
• 12 − 9 = 3

Each term increases by 3. Next term = 12 + 3 = 15

Q4. Find the missing number: 1, 4, 9, 16, 25, __

These are perfect squares:

• 1 = 1²
• 4 = 2²
• 9 = 3²
• 16 = 4²
• 25 = 5²

Next term = 6² = 36

Q5. Find the rule and the next term: 100, 96, 91, 85, 78, __

Look at the differences:

• 96 − 100 = −4
• 91 − 96 = −5
• 85 − 91 = −6
• 78 − 85 = −7

The difference decreases by 1 each time (−4, −5, −6, −7, …).

Next difference = −8. Next term = 78 − 8 = 70

Additional Questions

Q1. Draw tree diagrams and find the answers for the following:

(i) A book fair had the following sales over five days: Day 1 — ₹1,82,192; Day 2 — ₹1,28,194; Day 3 — ₹80,520; Day 4 — ₹92,004; Day 5 — ₹50,020. Find the total sales.

The tree diagram has five leaf nodes (the five day amounts) combining through addition.

Step-by-step addition:

• Day 1 + Day 2 = 1,82,192 + 1,28,194 = 3,10,386
• + Day 3 = 3,10,386 + 80,520 = 3,90,906
• + Day 4 = 3,90,906 + 92,004 = 4,82,910
• + Day 5 = 4,82,910 + 50,020 = 5,32,930

(ii) A water project was estimated at ₹1,82,71,000. Machinery cost ₹69,12,000. How much more is needed?

Tree diagram:

Amount needed = ₹1,82,71,000 − ₹69,12,000

(iii) A garden has 55 pots with 62 flowers in each pot. How many flowers are there in total?

Tree diagram:

Total flowers = 62 × 55

(iv) A scholarship of ₹62,000 is distributed equally among 50 students. How much does each student receive?

Tree diagram:

Per student = ₹62,000 ÷ 50

Q2. Convert the following numerical expressions into tree diagrams and find the answers:

(i) (10 × 5) + (2 × 16)

Tree diagram:

Step-by-step:

• Left branch: 10 × 5 = 50
• Right branch: 2 × 16 = 32
• Root: 50 + 32 = 82

(ii) (5 × 3) − (8 × 6) + 9

Tree diagram:

Step-by-step:

• Left-left: 5 × 3 = 15
• Left-right: 8 × 6 = 48
• Left branch: 15 − 48 = −33
• Root: −33 + 9 = −24

(iii) [9 + (3 × 2)] − [(6 × 4) + 5]

Tree diagram:

Step-by-step:

• Left sub-expression: 9 + (3 × 2) = 9 + 6 = 15
• Right sub-expression: (6 × 4) + 5 = 24 + 5 = 29
• Root: 15 − 29 = −14

(iv) [(4 − 1) × 16] + [(16 + 9) × 3]

Tree diagram:

Step-by-step:

• Left-left: 4 − 1 = 3
• Left branch: 3 × 16 = 48
• Right-left: 16 + 9 = 25
• Right branch: 25 × 3 = 75
• Root: 48 + 75 = 123

(v) {[(10 × 6) + 5] × [4 + (3 − 2)]} ÷ [4 × (2 + 9)]

Tree diagram:

Step-by-step:

• Numerator part 1: (10 × 6) + 5 = 60 + 5 = 65
• Numerator part 2: 4 + (3 − 2) = 4 + 1 = 5
• Numerator: 65 × 5 = 325
• Denominator: 4 × (2 + 9) = 4 × 11 = 44
• Root: 325 ÷ 44 = 325/44 (≈ 7.39)

(vi) 4 + [8 × 6 + {(4 × 3) − (10 ÷ 4)}]

Tree diagram:

Step-by-step:

• Innermost left: 4 × 3 = 12
• Innermost right: 10 ÷ 4 = 2.5
• Subtraction: 12 − 2.5 = 9.5
• Multiply: 8 × 6 = 48
• Addition inside bracket: 48 + 9.5 = 57.5
• Root: 4 + 57.5 = 61.5

Q3. Convert the following tree diagrams into numerical expressions:

(a) Tree diagram representing: [4 × (6 + 2)] − [(4 − 2) ÷ 2]

The tree has a subtraction at the root. The left branch multiplies 4 by the sum (6 + 2). The right branch divides the difference (4 − 2) by 2.

Expression: [4 × (6 + 2)] − [(4 − 2) ÷ 2]

Step-by-step evaluation:

• Left: 4 × (6 + 2) = 4 × 8 = 32
• Right: (4 − 2) ÷ 2 = 2 ÷ 2 = 1
• Root: 32 − 1 = 31

(b) Tree diagram representing: (12 × 6) + (6 ÷ 3)

The tree has addition at the root. The left branch multiplies 12 and 6. The right branch divides 6 by 3.

Expression: (12 × 6) + (6 ÷ 3)

Step-by-step evaluation:

• Left: 12 × 6 = 72
• Right: 6 ÷ 3 = 2
• Root: 72 + 2 = 74

(c) Tree diagram representing: [4 × (10 − 2)] + [(4 + 9) × 3]

The tree has addition at the root. The left branch multiplies 4 by the difference (10 − 2). The right branch multiplies the sum (4 + 9) by 3.

Expression: [4 × (10 − 2)] + [(4 + 9) × 3]

Step-by-step evaluation:

• Left: 4 × (10 − 2) = 4 × 8 = 32
• Right: (4 + 9) × 3 = 13 × 3 = 39
• Root: 32 + 39 = 71

Common Mistakes

1. Forgetting the order of operations (BODMAS): Many students solve left-to-right without following brackets, orders, division, multiplication, addition, and subtraction. Always evaluate brackets first, then × and ÷ before + and −.

2. Confusing the Fibonacci rule: Remember, each Fibonacci number is the sum of the two preceding terms — not the previous term multiplied or added to a fixed number. F(n) = F(n−1) + F(n−2), always.

3. Incorrect bracket placement in tree diagrams: When converting a tree to an expression, every sub-expression must be enclosed in brackets. Missing brackets changes the meaning entirely. For example, 4 × 6 + 2 is not the same as 4 × (6 + 2).

4. Sign errors in subtraction: When subtracting a larger number from a smaller one (e.g., 15 − 29), students sometimes swap the numbers. 15 − 29 = −14, not 14.

5. Arithmetic errors with large numbers: In problems like the book fair total (five-day addition), double-check each step. Write out the addition in columns to avoid carry errors.

6. Mixing up tree diagram direction: In a tree diagram, operations at the bottom (leaf-level) are performed first, and the root at the top is performed last. Reading top-down and solving in that order gives wrong answers.

7. Forgetting to simplify fractions: When division does not result in a whole number (e.g., 325 ÷ 44), leave the answer as a fraction (325/44) unless the question asks for a decimal. Do not round without instruction.

Exam Checklist

Before your exam, make sure you can do each of the following:

• [ ] Identify the rule behind a number pattern and find the next terms
• [ ] Generate the Fibonacci sequence from any two starting values
• [ ] Draw a tree diagram from a given arithmetic expression
• [ ] Convert a tree diagram back into a correct numerical expression with proper brackets
• [ ] Apply BODMAS correctly when evaluating complex expressions
• [ ] Solve word problems involving addition, subtraction, multiplication, and division of large numbers
• [ ] Check your final answer by re-reading the tree diagram or re-evaluating the expression step by step