Question

Every rational number is an integer.
True or False.
Give reasons.​

Answer 1

No, every rational number is not an integer.

The integers are the positive and negative whole numbers and zero: ⋯−2,−1,0,1,2,…The rational numbers are numbers that can be represented by a ratio of integers. Since every integer can be represented as itself divided by 1, every integer is a rational number, but that doesn’t mean they are the only rational numbers.Some rational numbers are not whole numbers, like 1/2, 3/5, or −23/17 for instance.In math we say that the integers are a proper subset of the rationals because of the above observation.

Answer 2

The statement "every rational number is an integer" is a false statement.

• In mathematics, a real number is called a rational number when the real number can be expressed as  $\frac{p}{q}$ , where p and q($\neq 0$) are two integers and p and q are coprime to each other.
• A real number is called an integer when it is a whole number and not a fractional number and cannot be expressed as $\frac{p}{q}$ , where p and $q(\neq 0, 1)$ are two integers and p and q are coprime to each other.
• We can take an example of a rational number $\frac{1}{2}$. We can observe that this is a fractional number and not a whole number. So $\frac{1}{2}$  is not an integer.
• So any rational number which is fractional cannot be an integer. Hence every rational number cannot be an integer.

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