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Question

Choose the correct statement:
A: The sum of any two rational numbers is not always a rational number.
B: The difference of any two rational numbers is always a rational number.
C: The difference of any two rational numbers is not always a rational number.
D: Subtraction of two rational numbers is commutative.
[1]

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Solution

Answer: Option B

We know, rational numbers are closed under addition. That is why, for any two rational numbers a and b, a+b is also a rational number.
For example if a=38,b=57, then
a+b=38+57=1956.
1956 is a rational number.

It is true that the difference between two rational numbers must be a rational number.
Let us consider two rational numbers, 45 and 15.
Difference =4515=35.
35 is a rational number, therefore, the difference between two rational numbers must be a rational number.

Subtraction of two rational numbers is not commutative.
Consider the rational numbers 58 and 28 then:
=5828=38
Now, 2858=38
Since, 58282838, we can say that subtraction of two rational numbers is not commutative.

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