Samacheer Kalvi Class 6 Maths Solutions Term 2 Chapter 5 Information Processing Exercise 5.1

Question 1. Convert the following numerical expressions into Tree diagrams
(i) 8 + (6 × 2)
(ii) 9 – (2 × 3)
(iii) (3 × 5) – (4 – 2)
(iv) [(2 × 4) + 2] × (8 – 2)]
(v) [(6 + 4) × 7] – [2 × (10 – 5)]
(vi) [(4 × 3) – 2] + [8 × (5 – 3)]
Answer:

(i) \(8 + (6 \times 2)\)

(ii) \(9 - (2 \times 3)\)

(iii) \((3 \times 5) - (4 - 2)\)

(iv) \([(2 \times 4) + 2] \times (8 - 2)\)]

(v) \([(6 + 4) \times 7] - [2 \times (10 - 5)]\)

(vi) \([(4 \times 3) - 2] + [8 \times (5 - 3)]\)

In simple words: A tree diagram shows how an expression is built using numbers and operations. The operations are shown in circles, and the numbers are at the bottom. Lines connect the operations to their numbers or other operations, showing the order you would solve them in, usually from bottom up.

🎯 Exam Tip: Always make sure the operators are placed correctly according to the order of operations (PEMDAS/BODMAS) in the expression. The highest-level operation should be at the very top of the tree.

Question 2. Convert the following tree diagrams into numerical expressions.
(i)
(ii)
(iii)
(iv)
Answer:
(i) The numerical expression is \(9 \times 8\).
(ii) The numerical expression is \((7 + 6) - 5\).
(iii) The numerical expression is \((8 + 2) - (6 + 1)\).
(iv) The numerical expression is \((5 \times 6) - (10 \div 2)\).
In simple words: To convert a tree diagram to an expression, start from the bottom (the numbers) and work your way up to the top. Combine numbers with their operators at each step, using brackets to show the order of operations clearly, just like building a math sentence.

🎯 Exam Tip: Always follow the order of operations when writing the expression from a tree diagram. Parentheses/brackets represent operations that are performed first, or are lower down in the tree structure.

Question 3. Convert the following algebraic expressions into tree diagrams.
(i) 10v
(ii) 3a - b
(iii) 5x + y
(iv) 20t × p
(v) 2(a + b)
(vi) (x × y) - (y × z)
(vii) 4x + 5y
(viii) (lm - n) ÷ (pq + r)
Answer:

(i) \(10v\)

(ii) \(3a - b\)

(iii) \(5x + y\)

(iv) \(20t \times p\)

(v) \(2(a + b)\)

(vi) \((x \times y) - (y \times z)\)

(vii) \(4x + 5y\)

(viii) \((lm - n) \div (pq + r)\)

In simple words: To make a tree diagram from an algebraic expression, first find the last operation that would be done if you were to solve it. This operation goes at the top. Then, break down each part of that operation into smaller tree diagrams until all numbers and variables are at the very bottom. This shows the order of calculations.

🎯 Exam Tip: Remember to use implied multiplication (e.g., in `10v` it means `10 × v`) and include these multiplication nodes in your tree diagrams.

Question 4. Convert Tree diagrams into Algebraic expressions.
(i)
(ii)
(iii)
(iv)
(v)
Answer:
(i) The algebraic expression is \(p + q\).
(ii) The algebraic expression is \(l - m\).
(iii) The algebraic expression is \((a \times b) - c\) (or \(ab - c\)).
(iv) The algebraic expression is \((a + b) - (c + d)\).
(v) The algebraic expression is \((8 \div a) + [(6 \div 4) + 3]\).
In simple words: To write an algebraic expression from a tree diagram, start from the bottom leaves (numbers or variables) and move upwards. Combine the items connected by each operator. Remember to use brackets around parts that are evaluated together (like sub-branches of the tree). The top-most operator will connect the main parts of the expression.

🎯 Exam Tip: Pay close attention to how variables are multiplied (e.g., \(ab\) for \(a \times b\)). Ensure all operations, especially divisions and subtractions, are written in the correct order as shown by the tree structure.