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Calculate the number p and q?
p/q form of the number is 0.3 is: (A) (B)
What is the reciprocal of a positive rational number?
It is another positive rational number. The reciprocal of p/q is q/p.
If a divided b equals 1 and a plus b equals q then how large is ab?
a/b = 1 so a = b. Then a b = q implies that a = b = q/2 So ab = (q/2)*(q/2) = q2/4
Is it possible to divide one rational number by another to obtain an irrational number as a quotient?
No. Rational numbers are defined as fractions of whole numbers. Suppose we have two rational numbers A = m/n and B = p/q. Then their quotient is defined as A/B = (m*q) / (n*p). Since m,n,p and q are whole, the products m*q and n*p are whole as well, making A/B a rational number.
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.
