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## Related Questions

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### What is Enslaved workers?

###### Asked in Math and Arithmetic

### Prove that if a and b are rational numbers then a multiplied by b is a rational number?

If a is rational then there exist integers p and q such that a =
p/q where q>0.
Similarly, b = r/s for some integers r and s (s>0)
Then a*b = p/q * r/s = (p*r)/(q*s)
Now, since p, q r and s are integers, p*r and q*s are integers.
Also, q and s > 0 means that q*s > 0
Thus a*b can be expressed as x/y where
p and r are integers implies that x = p*r is an integer
q and s are positive integers implies that y = q*s is a positive
integer.
That is, a*b is rational.

###### Asked in Irrational Numbers

### Can the product of two rational numbers be irrational?

No.Suppose a and b are two rational numbers.
Then they can be written as follows: a = p/q, b = r/s where p,
q, r and s are integers and q, s >0.
Then a*b = (p*r)/(q*s).
Using the properties of integers, p*r and q*s are integers and
q*s is non-zero. So a*b can be expressed as a ratio of two integers
and so the product is rational.