Question

Because of the commutative property of multiplication, it is true that

3/4

×

4

=

4

×

4/3


. However, these expressions can be calculated in different ways even though the solutions will be the same.


Below, show two different ways of solving this problem.

Answer 1

It is Commutative

Explanation:

An operation ∆ is said to be Commutative if a∆b=b∆a ∀ a,b ∈ ℝ.

Given the operation ∆ defined by:

a∆b=a X b

[Tex]a=\frac{3}{4}, b=4[/tex]

a∆b=[Tex]\frac{3}{4}X4[/tex]

[Tex]=\frac{3X4}{4}[/tex]=3

Similarly, for the right hand side.

[Tex](\frac{4}{3})^{-1}=\frac{3}{4}[/tex]

Therefore:

b∆a=[Tex]4X \frac{3}{4}[/tex]

[Tex]=\frac{4X3}{4}[/tex]=3

These are the two ways of solving this problem and we have in fact shown that the operation is commutative as:

a∆b=b∆a=3