Question

State whether the given statement is true or false.
Every fraction is a rational number.

Answer 1

Hint – A fraction is anything that can be written inform of $\dfrac{p}{q}$ whereas a rational number is anything which is of the form of $\dfrac{a}{b}$ such that $ b \ne 0$. Use these definitions to decide whether the above given statement is true or not.

Complete step-by-step answer:
As we know a rational number is a number which is represented in the form of $\dfrac{a}{b}$, where $b \ne 0$ and a and b has not any common factors except 1.
Then it can be represented as a fraction of two integers.
For example $\dfrac{{10}}{{15}}$
As we see this a fraction but not written in lowest form of fraction so first convert this fraction into lowest form of fraction.
$ \Rightarrow \dfrac{{10}}{{15}} = \dfrac{{2 \times 5}}{{3 \times 5}}$
Now cancel out the common terms we have,
$ \Rightarrow \dfrac{{10}}{{15}} = \dfrac{2}{3}$
So this fraction converts into a rational number where ($3 \ne 0$) and has no common factors except 1.
Therefore every fraction is a rational number when written in lowest form of fraction.
So the given statement is true.
Hence option (A) is correct.

Note – There is a great bit of confusion figuring out whether any number like 2 are rational numbers or not, 2 can be written as $\dfrac{2}{1}$ thus it clearly satisfies the definition of a rational number now 2 is also an improper fraction as 2 can be written as $\dfrac{{16}}{8},\dfrac{{18}}{9}$etc. Clearly the numerator part is greater than the denominator part thus it falls under the category of improper fraction.