Conversion of Algebraic Expressions into Tree Diagrams
There is more fun with trees.
Conversion of Algebraic Expressions into Tree Diagrams
There is more fun with trees. Observe the following trees
The above tree is nothing but the familiar equation $a \times (b + c) = (a \times b) + (a \times c)$. Thus we can see the algebraic expressions as trees.
- • The tree on the left has less number of nodes and looks simple.
- • The tree on the right has more number of nodes
- • Can we conclude that the value of both the trees are different
Convert ‘5a’ into Tree diagram
Solution:
Convert '3a + b' into Tree diagram
Algebraic expression
3a+b
Tree diagram
'6 times a and 7 less’ Convert into a Tree diagram.
Algebraic expression
6a − 7
Tree diagram
Convert the tree diagram into an algebraic expression.
Tree diagram
Algebraic expression
8b ÷ 6
Convert the tree diagram into an algebraic expression.
Tree diagram
Algebraic expression
(7 + t) 5
Verify whether given trees are equal or not
Tree diagram
( a + b) + c = a + (b+c)
Yes, they are equal.
1. Check whether the Tree diagrams are equal or not
2. Check whether the following algebraic expressions are equal or not by using Tree diagrams
i) (x − y) + z and x − (y + z)
(x – y) + z ≠ x – (y + z). They are not equal.
ii) (p × q) × r and p × (q × r)
(p × q) × r = p × (q × r). They are equal.
iii) a − (b − c) and (a − b) − c
a – (b – c) ≠ (a – b) – c. They are not equal.
Do You Know
Consider the numerical expression 9 – 4. which means 4 is to be subtracted from 9. 9 – 4 can be represented as – 9 4 (so far we have come across with operation in between the operands)
Suppose the expression is 9 – 4 × 2. This can be represented as × – 9 4 2 gives the meaning of
Step 1: × 9 – 4 2
Step 2: (9 – 4) × 2
Take the expression + × − 9 4 2 5
Step 1: + × 9 − 4 2 5
Step 2: + (9 − 4 ) × 2 5
Step 3: [(9 − 4) × 2] + 5
This is reading an expression from “left to right”. Similarly, we can read expressions from “right to left” also
9 4 2 5 + × − can be read as “right to left” expression which gives the meaning of
- 9 4 2 5 + × => (9 − 4) 2 5 + ×
- => (9 − 4) × 2 5 +
- => [(9 − 4) × 2] + 5
Hence an expression can be read as “left to right” or “right to left” giving the same answer which is similar to name 4 as Naangu (நான்கு), Four, Nalagu (నాలుగు) and Char (चार), all of them representing the collection of four objects. Similarly the numerical expression
[ (9 – 4) × 8 ] ÷ [ (8 + 2) × 3] can be written as ÷ × – 9 4 8 × + 8 2 3 ( left to right) or 8 9 4 – × 3 8 2 + × ÷ ( right to left ).
Try these:
1) × – + 9 7 8 2
2) ÷ × + 2 3 8 5