6th Maths Term 2: Conversion of Tree Diagrams into Numerical Expressions

Conversion of Tree Diagrams into Numerical Expressions

Chapter: 6th Maths : Term 2 Unit 5 : Information Processing

When the nodes for addition and subtraction are interchanged the value remains the same which is represented using tree diagram as given below.

Conversion of Tree Diagrams into Numerical Expressions

For instance, consider the tree

Tree Diagram Example

We could first find as 10, then as 5.

When we multiply the results 10 and 5 we get 50. When the nodes for addition and subtraction are interchanged the value remains the same which is represented using tree diagram as given below.

Interchanged Nodes Diagram

Does it mean that the branches also can be interchanged? Yes, when the node is addition it is possible.

Addition Node Branch Swap

But it is not possible when the node represents subtraction.

Subtraction Node Restriction

Therefore from this tree diagram:

Final Tree Expression

The expression can be converted into either (10−5) × (8 + 2) or (8 + 2) × (10 − 5) or (2 + 8) × (10 − 5) or (10 − 5) × (2 + 8) without changing the value.

Example 11:

Convert the tree diagram into numerical expression.

Tree diagram

Example 11 Tree

Numerical Expression

15 − 6 + 9
Example 12:

Convert the Tree diagram into a numerical expression.

Tree diagram

Example 12 Tree

Numerical Expression

8 × 9 + 10
Example 13:

Convert the Tree diagram into a numerical expression.

Tree diagram

Example 13 Tree

Numerical Expression

10 × 6 + 6 ÷ 2
Example 14:

Convert the Tree diagram into a numerical expression.

Tree diagram

Example 14 Tree

Numerical Expression

[7 × 9 + 2] + [6 – 3 + 3]