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# Conversion of Tree Diagrams into Numerical Expressions

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 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. Does it mean that the branches also can be interchanged ? Yes, when the node is addition it is possible. But it is not possible when the node represents subtraction. Therefore from this tree diagram. 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 Numerical   Expression

15− 6 + 9 .

Example 12:

Convert the Tree diagram into a numerical expression.

Tree diagram Numerical Expression

8 × 9 + 10 .

Example 13:

Convert the Tree diagram into a numerical expression.

Tree diagram Numerical Expression

10 × 6 + 6 ÷ 2 .

Example 14:

Convert the Tree diagram into a numerical expression.

Tree diagram Numerical Expression

[7 × 9 + 2] + [6 – 3 + 3].

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