QUESTION

# Is the following statements true or false- “Every rational number is an integer”.

Hint: To solve such a question we first define what is a Rational number and what is an Integer. Rational numbers are the numbers that can be written in the form of p/q, where q is not equal to zero and a number which is not a fraction is called an Integer.

We have to see if the following statements are True or False- Every rational number is an integer.

To get the answer of this question we either prove the fact that every rational number is an integer then the statement would be true or we go for finding a number which is Rational number but not an integer then the above statement would be False.

Every integer is a rational number. To show this we suppose there is an integer m then it can be written as $\dfrac{m}{1}$ which is rational.

Therefore, every integer is a rational number.

But not every rational number is an integer. To show this we suppose a number as $\dfrac{7}{5}$ it is a rational number because it can be written in the form of $\dfrac{p}{q}$ where q is non zero but it is not an integer because it does not have 1 in the denominator, or it is in the form of fraction.

Hence, we obtain that not every rational number is an integer.

Therefore, the given statement Every rational number is an integer is False.

Note: The possibility of error in the question is you can get confused in between the statement ‘every integer can is a rational number’ and the ‘statement every rational number is an integer’. Always in this type of question try to get a counterexample to disprove a statement.