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Must the difference between two rational numbers be a rational number?
Yes.
Must a rational number be rational?
Yes, if it wasn't it wouldn't be a rational number.
Which number can be multiplied to a rational number to explain that the product of two rational numbers is rational?
It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
Can you add two rational numbers and get a rational number?
Every time. The sum of two rational numbers MUST be a rational number.
May the sum of a rational and an irrational number only be a rational number?
No. In fact the sum of a rational and an irrational MUST be irrational.
Is -14 rational number?
nope. rational numbers must be positive.
The mode of a list of rational numbers must be a rational number?
false
Adding rational number and an irrational number to get a rational number?
The sum of a rational and an irrational number is always irrational. Here is a brief proof:Let a be a rational number and b be an irrational number, and c = a + b their sum. By way of contradiction, suppose c is also rational. Then we can write b = c - a. But since c and a are both rational, so is their difference, and this means that bis rational as well. But we already said that b is an irrational number. This is a contradiction, and hence the original assumption was false. Namely, the sum c must be an irrational number.
Is 4.121314 is a rational?
No, a rational number must be a whole number, for example 40 and 5643 and 948.
The sum of a rational number and an irrational number is?
The sum of a rational and irrational number must be an irrational number.
Is 0.555555 both rational and irrational rational neither rational nor irrational irrational?
No number can be both rational and irrational. And, at the level that you must be for you to need to ask that question, a number must be either rational or irrational (ie not neither). 0.555555 is rational.
Is the product of two rational numbers irrational?
The product of two rational numbers is always a rational number.
