Question

In subtraction associative in rational numbers? Explain with an example
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Answer 1

Answer:

It is not possible

Step-by-step explanation:

We need three terms for checking associativity so let us take three simple rational numbers:

$1/2$,$2/3$,$3/4$

Now we need to check whether:

$(1/2-2/3)-3/4 = 1/2-(2/3-3/4)$

We can perform the checking by calculating the left hand side and right hand side separately.

LHS:

$=>(1/2-2/3)-3/4$

Solving we get:

$=> (1/2-2/3)-3/4=-1/6-3/4$

Calculating the subtraction:

$=>(1/2-2/3)-3/4=-11/12$

∴ LHS = $-11/12$

RHS:

$=> 1/2-(2/3-3/4)$

Solving as follows:

$=> 1/2-(2/3-3/4)=1/2-(-1/12)$

Completing the calculations:

$=> 1/2-(2/3-3/4) =7/12$

∴ RHS = $7/12$

Clearly the left hand side and right hand side operations do not match.

Therefore from the above example we proved that the associative property is not valid on subtraction of any rational numbers in general, since when groupings of three terms are different, the resulting values differ.

Hope it helps