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Why is the sum of two rational numbers always rational numbers?
Suppose p/q and r/s are rational numbers where p, q, r and s are integers and q, s are non-zero.Then p/q + r/s = ps/qs + qr/qs = (ps + qr)/qs. Since p, q, r, s are integers, then ps and qr are integers, and therefore (ps + qr) is an integer. q and s are non-zero integers and so qs is a non-zero integer. Consequently, (ps + qr)/qs is a ratio of two integers in which the denominator is non-zero. That is, the sum is rational.
Why is the sum or product of two rational numbers rational?
Suppose p/q and r/s are rational numbers where p, q, r and s are integers and q, s are non-zero.Then p/q + r/s = ps/qs + qr/qs = (ps + qr)/qs.Since p, q, r, s are integers, then ps and qr are integers, and therefore (ps + qr) is an integer.q and s are non-zero integers and so qs is a non-zero integer.Consequently, (ps + qr)/qs is a ratio of two integers in which the denominator is non-zero. That is, the sum is rational.Also p/q * r/s = pr/qs.Since p, q, r, s are integers, then pr and qs are integers.q and s are non-zero integers so qs is a non-zero integer.Consequently, pr/qs is a ratio of two integers in which the denominator is non-zero. That is, the sum is rational.
Why are rational numbers closed under addition?
Suppose x and y are rational numbers.That is, x = p/q and y = r/s where p, q, r and s are integers and q, s are non-zero.Then x + y = ps/qs + qr/qs = (ps + qr)/qsThe set of integers is closed under multiplication so ps, qr and qs are integers;then, since the set of integers is closed addition, ps + qr is an integer;and q, s are non-zero so qs is not zero.So x + y can be represented by a ratio of two integers, ps + qr and qs where the latter is non-zero.
Does anyone have a non-fictional humorous article?
Does the non-fiction Bible count? Look at Prov.1:26; Ps.2:4 then look at our Nation now.
Where is the location of photo-system 1 in the chloroplast?
PS 1 is located on the non- pressed surfaces of the thyllakoid in the choloroplast
Which one of these is the best and strongest PS vita casing the PS vita vault case the PS vita custom crystal case or the PS vita travel pouch?
the ps vita vault case
Why does thermocol dissolve in benzene?
Thermocol is another name for polystyrene (PS), which is a type of plastic. Benzene is an industrial solvent, and it's primary use is to make styrene. The chemical structure of benzene, a non-polar organic hydrocarbon solvent, and of PS is such that benzene will dissolve styrene and polystyrene.
What does abbreviation dmd Ps mean?
dmd Ps
What does PS stand for in DDS PS?
Professional Service
Can a PS vita connect to a PS 2000?
no such thing
could you send certified PS form 3800 and PS form 3811 mailed to you?
could you send certified ps form 3800 and ps form 3811 mail to me
Did plainville stock company make diamond jewelry?
Most if not all of PS Co jewelry is paste jewelry, ie, non-precious or semi-precious gems were used
