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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

Learning by Doing

objective: To reiterate the concept that multiplication of rational numbers
is commutative.

Materials Required: White chart paper, pencil, geometry box, coloured
pencils, scissors

Procedure: 3
A 5 E B
• Draw two identical squares of suitable side length (say

ABCD and PQRS each of side 10 cm). 7 2
• Divide the 1st square ABCD into 7 equal parts horizontally G I H
2
and colour its parts yellow. Again, divide the square into
7 3
5 equal parts vertically and colour its parts red. What
5
does the double-shaded part (rectangle AEIG) represent?
• Divide the 2nd square PQRS into 5 equal parts horizontally D F C
3 2
and colour its parts red. Again, divide the square into 7
5 P 7 T Q
equal parts vertically and colour its 2 parts yellow. What
7
does the double-shaded part (rectangle PTXV) represent? 3
5
• Cut the rectangles AEIG and PTXV from both squares. Try
to superimpose one another.
V X W
observation:

We observe that:
2 3 S U R
The rectangle AEIG represents × .
7 5
3 2 A(T) E(X)
The rectangle PTXV represents × .
5 7
After superimposing, the two figures cover each other
completely. G(P) I(V)
2 3 3 2
Therefore, × = × .
7 5 5 7
Conclusion:
a c a c c a
If and are two rational numbers, then × = × , i.e., multiplication is
b d b d d b
commutative.

Mathematics-8 34