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.
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.
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Quad Strike or Quick Strike. (QS)
Queer sort
erhh.. quick silver
There are questions, or there is qs
None in English, if you mean paired Qs.
In the construction industry, what is the role of a QS??
The term Keeping up with your Ps and Qs is generally quoted as Minding your Ps and Qs. This is an old term, which means to Mind your Pints and Quarts, which means to mind your own business, basically, or to take care of a task.
Hi There, QS means to add enough of the major ingredinet until you have a total of 100% of the formula. It also stands for quantity sufficient. MDW
X Qs me. 'Excuse me'. Possibly also an exaggerated form, 'Excuuuuse me!'.
Casting Qs - 2010 Interview with Lynne Quirion Part 2 3-6 was released on: USA: 30 August 2011
If no Ls are Qs then the converse is true that no Qs are Ls. If all Qs are Js, then at least some Js are Qs. Therefore, at least some Js are not Ls. You cannot conclude that some Js are Ls, however. It could be that all Js are not Ls. This cannot be concluded from the information given.