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 × (b + c) = (a × b) + (a × 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

** **

__Example 15: __

Convert ‘5a’ into Tree** **diagram

**Solution:**

** **

__Example 16:__

** **Convert '3a + b' into Tree diagram

**Algebraic expression**

**3a+b**

**Tree diagram**

** **

__Example 17: __

'6 times a and 7 less’** **Convert into a Tree diagram.

**Algebraic expression **

** 6a − 7**

**Tree diagram**

** **

__Example 18: __

Convert the tree diagram** **into an algebraic expression.

**Tree diagram**

**Algebraic expression**

**8b **÷ **6**

** **

__Example 19: __

Convert the tree diagram** **into an algebraic expression.

**Tree diagram**

**Algebraic expression**

**(7 + t) 5**

** **

__Example 20: __

Verify whether given trees** **are equal or not

**Tree diagram**

( a + b) + c = a + (b+c)

Yes, they are equal.

** **

**Try these**

**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

Tags : Information Processing | Term 2 Chapter 5 | 6th Maths , 6th Maths : Term 2 Unit 5 : Information Processing

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