Why is the product of two rational numbers always rational? Select from the drop-down menus to correctly complete the proof. Let ab and cd represent two rational numbers. This means a, b, c, and d are , and b and d are not 0. The product of the numbers is acbd , where bd is not 0. Both ac and bd are , and bd is not 0. Because acbd is the ratio of two , the product is a rational number.

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Nitro13 Nitro13 · Answer 1 · 2018-11-20T02:04:42+01:00

is there any picture if not then i believe the answer is Integers, d is not zero, multiplication.

i don't know how to explain it though let me try to figure this out more if i find anything more out ill type it in the text!!

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parmesanchilliwack parmesanchilliwack · Answer 2 · 2018-12-03T06:20:19+01:00

Answer: The proof is mentioned below.

Step-by-step explanation:

Let a/b and c/d are two rational numbers where b ≠ 0 and d ≠ 0 ( by the property of rational number.) And, a, b, c and d are integers.

Proof that: [tex]\frac{a}{b}\times \frac{c}{d} = \frac{ac}{bd}[/tex] is also a rational number, for which bd≠ 0

Since a and b are integers therefore ab are also integers ( because integers are closed under multiplication)

Similarly cd is also an integer.

⇒ [tex]\frac{ac}{bd}[/tex] is a fraction in which both numerator and denominator are integers.

Moreover, b≠0 and d≠0 ⇒ bd≠0 ( because product of non zeros number is also non zero.)

Thus, by the property of rational number [tex]\frac{ac}{bd}[/tex] is also a rational number for which bd≠ 0

Therefore, The product of two rational is numbers always rational.