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Yes.

Since they are rational numbers, let's call the first one a/b and the second one c/d where a,b,c, and d are integers.

Now we can subtract by finding a common denominator. Let's use bd.

So we have ad/bd-cb/bc= (ad-bc)/CD which is rational since we know ad and bc are integers being the product of integers and CD is also an integers.

Call ad-bd=P and call CD=Q where P and Q are integers. We now see the difference is of two rationals is rational.

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Q: Is the difference of two rational numbers always a rational number?

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Yes, that's true.

Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All natural numbers are rational.

Yes.

-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.

No. Example: The difference of 2/5 & 1/3: 2/5 - 1/3 = 1/15 ∈ ℚ (is a rational number) ∉ ℕ (is not a natural number).

Related questions

Yes, that's true.

Yes. The rational numbers are a closed set with respect to subtraction.

Yes, it is.

No. 5 and 2 are real numbers. Their difference, 3, is a rational number.

The question cannot be answered because it is nonsensical. The difference between two rational numbers is very very rarely a whole number.

Yes. This is the same as asking for one rational number to be subtracted from another; to do this each rational number is made into an equivalent rational number so that the two rational numbers have the same denominator, and then the numerators are subtracted which gives a rational number which may possibly be simplified.

No,, not always. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

The product of two rational numbers is always a rational number.

The product of two rational numbers is always a rational number.

Yes.

Another rational number.

Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All natural numbers are rational.

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