Answer:
The product of two rational numbers is always rational
Step-by-step explanation:
- DEFINITION: a number is said to be rational if and only if it is expressed in p/q form i.e, as a fraction(p/q) where, p,q are integers and [tex]q\neq 0.[/tex]
- now, let a/b and c/d be two rational numbers.
- the product of them : ac/bd.
- FACT : if we multiply 2 integers, then the product will be an integer.
- so, ac and bd are both integers for sure and bd is not zero because none of b or d is zero.
- therefore, as ac/bd satisfy the definition of a rational number, it is a rational number.
- hence, we can now generalize that, The product of two rational numbers is always rational.
