0
Want this question answered?
Be notified when an answer is posted
Add your answer:
Earn +20 pts
Why is the difference between two rational numbers always a rational number?
Suppose x and y are two rational numbers. Therefore x = p/q and y = r/s where p, q, r and s are integers and q and s are not zero.Then x - y = p/q - r/s = ps/qs - qr/qs = (ps - qr)/qsBy the closure of the set of integers under multiplication, ps, qr and qs are all integers,by the closure of the set of integers under subtraction, (ps - qr) is an integer,and by the multiplicative properties of 0, qs is non zero.Therefore (ps - qr)/qs satisfies the requirements of a rational number.
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 is the multiplication of rational numbers always result in a rational number?
It follows from the closure of integers under addition and multiplication.Any rational number can be expressed as a ratio of two integers, where the second is not zero. So two rational numbers may be expressed as p/q and r/s.A common multiple of their denominators is qs. So the numbers could also have been expressed as ps/qs and qr/qs.Both these have the same denominator so their sum is (ps + qr)/qs.Now, because the set of integers is closed under multiplication, ps, qr and qs are integers and because the set of integers is closed under addition, ps + qr is an integer.Thus the sum has been expressed as a ratio of two integers, ps + qr, and qs and so it is a rational number.
Is the dfference of two positive rational number always positive plz help explain.?
Yes.Suppose a and b are two positive rational numbers. Then a can be expressed in the form p/q where p and q are positive integers, and b can be expressed in the form r/s where r and s are positive integers.Then b - a = r/s - p/q = (qr - ps)/qs.Now, since p, q, r and s are integers, thenby the closure of the set of integers under multiplications, qr, ps and qs are integers;q and s are positive => qs is positive, andby the closure of the set of integers under addition (and subtraction), qr - ps is an integer.That is, b - a = (qr - ps)/qs is a ratio of two integers, where the denominator of the ratio is positive.
What does qs stand for?
quality seconds
Mind your PS and Qs?
to be careful how you behave
What does keeping up with your PS and Qs mean?
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.
What does the idiom mind your PS andQs mean?
Mind your Ps and Qs means to use good manners.
What is the plural possessive of p and q?
The plural possessive of "p and q" is "p's and q's" or "p and q's."
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 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.
Why is the difference between two rational numbers always a rational number?
Suppose x and y are two rational numbers. Therefore x = p/q and y = r/s where p, q, r and s are integers and q and s are not zero.Then x - y = p/q - r/s = ps/qs - qr/qs = (ps - qr)/qsBy the closure of the set of integers under multiplication, ps, qr and qs are all integers,by the closure of the set of integers under subtraction, (ps - qr) is an integer,and by the multiplicative properties of 0, qs is non zero.Therefore (ps - qr)/qs satisfies the requirements of a rational number.
What actors and actresses appeared in Ps and Qs - 1992?
The cast of Ps and Qs - 1992 includes: Lesley Joseph as Herself - Host Jonathan Meades as Himself - Host Miles Richardson Tony Slattery as Himself - Host
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 is the difference of two rational numbers are rational numbers?
Suppose A and B are two rational numbers. So A = p/q where p and q are integers and q > 0 and B = r/s where r and s are integers and s > 0. Then A - B = p/q - r/s = ps/qs - qr/qs = (ps - qr)/qs Now, p,q,r,s are integers so ps and qr are integers and so x = ps-qr is an integer and y = qs is an integer which is > 0 Thus A-B can be written as a ratio of two integers, x/y where y>0. Therefore, A-B is rational.
Why is the multiplication of rational numbers always result in a rational number?
It follows from the closure of integers under addition and multiplication.Any rational number can be expressed as a ratio of two integers, where the second is not zero. So two rational numbers may be expressed as p/q and r/s.A common multiple of their denominators is qs. So the numbers could also have been expressed as ps/qs and qr/qs.Both these have the same denominator so their sum is (ps + qr)/qs.Now, because the set of integers is closed under multiplication, ps, qr and qs are integers and because the set of integers is closed under addition, ps + qr is an integer.Thus the sum has been expressed as a ratio of two integers, ps + qr, and qs and so it is a rational number.
How you can add two rational numbers?
If the two rational numbers are expressed as p/q and r/s, then their sum is (ps + rq)/(qs)
