By definition, every rational number x can be expressed as a ratio p/q where p and q are integers and q is not zero. Consider -p/q. Then by the properties of integers, -p is an integer and is the additive inverse of p. Therefore p + (-p) = 0Then p/q + (-p/q) = [p + (-p)] /q = 0/q.Also, -p/q is a ratio of two integers, with q non-zero and so -p/q is also a rational number. That is, -p/q is the additive inverse of x, expressed as a ratio.
a rational number
Assume the two numbers are P & Q, the equation is P + Q = 53, rearranging this gives Q = 53 - P
It is another positive rational number. The reciprocal of p/q is q/p.
p=q
By definition, every rational number x can be expressed as a ratio p/q where p and q are integers and q is not zero. Consider -p/q. Then by the properties of integers, -p is an integer and is the additive inverse of p. Therefore p + (-p) = 0Then p/q + (-p/q) = [p + (-p)] /q = 0/q.Also, -p/q is a ratio of two integers, with q non-zero and so -p/q is also a rational number. That is, -p/q is the additive inverse of x, expressed as a ratio.
A rational number is any number of the form p/q where p and q are integers and q is not zero. If p and q are co=prime, then p/q will be rational but will not be an integer.
In number systems Rational number is not represented just by q . they are represented in the form of p and q . P/q is rational number where q is not equal to zero.
a rational number
The assertion in the question is not always true. Multiplying (or dividing) 0 by a negative number does not yields 0, not a negative answer.Leaving that blunder aside, let p and q be positive numbers so that p*q is a positive number.Thenp*q + p*(-q) = p*[q + (-q)] = p*[q - q] = p*0 = 0that is p*q + p*(-q) = 0Thus p*(-q) is the additive opposite of p*q, and so, since p*q is positive, p*(-q) must be negative.A similar argument works for division.
a rational number
Q=3-P Q=7-P If Q is a private good, MC=8, how much is optimal?
A rational number can be expressed as a ratio in the form, p/q, where p and q are integers and q > 0.
Assume the two numbers are P & Q, the equation is P + Q = 53, rearranging this gives Q = 53 - P
If x is a rational number, then x = p/q where p and q are integers and q is non-zero.If division by x is defined, then x cannot be zero so that p is also non-zero.Then, to divide any number by x = p/q, simply multiply the number by q/p.
Any rational number (by definition).
A rational number is a number of the form p/q where p and q are integers and q > 0.If p/q and r/s are two rational numbers thenp/q + r/s = (p*s + q*r) / (q*r)andp/q - r/s = (p*s - q*r) / (q*r)The answers may need simplification.