Question

Is subtraction associative in rational numbers? explain with an example.

Answer 1

Answer:  No, subtraction is NOT associative in rational numbers.

Step-by-step explanation:  We are asked to state whether subtraction is associative in rational numbers or not. To explain with an example.

Let a, b and c be three rational numbers. Then, according to the associative property, we must have

$(a-b)-c=a-(b-c).$

The subtraction is NOT associative in rational numbers.

For example, let us consider that

$a=\dfrac{1}{2},~b=\dfrac{3}{2},~c=\dfrac{5}{2}.$

Then,

$L.H.S.=(a-b)-c=\left(\dfrac{1}{2}-\dfrac{3}{2}\right)-\dfrac{5}{2}=-1-\dfrac{5}{2}=\dfrac{-2-5}{2}=-\dfrac{7}{2},\\\\\\R.H.S.=a-(b-c)=\dfrac{1}{2}-\left(\dfrac{3}{2}-\dfrac{5}{2}\right)=\dfrac{1}{2}-(-1)=\dfrac{1}{2}+1=\dfrac{3}{2}.$

So, L.H.S. ≠ R.H.S.

Hence, subtraction is NOT associative in rational numbers.

Answer 2

Answer:

This is the answer

step by steps

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