Q: List 5 rational numbers in common fraction form that are not integers?

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They are both rational numbers

Most rational numbers are not whole numbers. Any number which can be expressed in the form of a ratio p/q where p and q are integers with no common factor and q > 1 is a rational number which is not a whole number.

They are positive integers, rational numbers, real numbers, odd numbers.

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.

A rational number is a fraction with an integer in the numerator, and a non-zero integer in the denominator. If you consider pi/2, pi/3, pi/4 (common 'fractions' of pi used in trigonometry) to be 'fractions', then these are not rational numbers.

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They can be represented as a fraction of two integers.

They are both rational numbers

It is a trivial difference. If you multiply every term in the equation with rational numbers by the common multiple of all the rational numbers then you will have an equation with integers.

Most rational numbers are not whole numbers. Any number which can be expressed in the form of a ratio p/q where p and q are integers with no common factor and q > 1 is a rational number which is not a whole number.

They are positive integers, rational numbers, real numbers, odd numbers.

No, by the very definition of rational it can be a fraction with only integers. Common sense would suggest that since irrational means not rational that is impossible.

They are both rational integers or whole numbers Their lowest common multiple is 168

They are called irrational numbers; numbers that can be expressed as a ratio of integers are called rational numbers. Some common irrational numbers are pi (3.14159...) and the square root of two.

Of the "standard sets" -10 belongs to: ℤ⁻ (the negative integers) ℤ (the integers) ℚ⁻ (the negative rational numbers) ℚ (the rational numbers) ℝ⁻ (the negative real numbers) ℝ (the real numbers) ℂ (the complex numbers) (as ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ). Other sets are possible, eg the even numbers.

Both are: -- integers -- real numbers -- rational numbers -- perfect squares -- less than 10 -- four letters long Their GCF is 1.

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.

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.