Question

Which property would be useful in proving that the product of two rational numbers is ALWAYS rational?

Answer 1

C. A rational number is a number that can be expressed as the ratio of two whole numbers. The product of the rational numbers a/b and c/d are also equal to a rational number ac/bd.

Answer 2

Answer:

C)$\frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}$

Step-by-step explanation:

We have to find the property which would be useful in proving that the product of two rational numbers is always rational.

Rational number: It  is that number which can be expressed as $\frac{p}{q}$ where p and q are both integers, $q\neq 0$

We know that product of two rational numbers  is always a rational number.

Let $\frac{a}{b}$ and $\frac{c}{d}$ are twp rational numbers.

Product of these two rational numbers is given by

$\frac{a}{b}\times \frac{c}{d}$

$=\frac{ac}{bd}$

a, b, c and d are integers and $b\neq 0,d\neq 0$

Product of two integers is always an integer.

Therefore, ac and bd are integers and $bd\neq 0$

Hence, we can say that product of two rational numbers is always a rational number.

Option C is true.