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Why are integers always included in rational numbers?

Updated: 8/20/2019
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A rational number is a number than can be written p/q with p and q integers

Any integers can be written this was with q=1

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Q: Why are integers always included in rational numbers?
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Related questions

Are integers always sometimes or never rational numbers?

All integers are rational numbers, but not all rational numbers are integers.2/1 = 2 is an integer1/2 is not an integerRational numbers are sometimesintegers.


Are integers rational numbers?

Integers are whole numbers. Rational numbers can be fractions / decimals. But it is NEVER a whole number E.G. of rational numbers : 3/4 or 1.5


Are rational numbers always integers?

Most of the time yes, positive or negative whole numbers count as rational numbers. So do positive or negative fractions.


What rational number can always be written in what form?

All rational numbers can always be written in the form of a ratio, p/q, where p and q are integers and q > 0.


Is an integer always a rational number?

a rational number is an integer when it does not have a decimal. An integer is a whole number, no parts of a number... -3, -2, -1, 0, 1, 2, 3 are all integers 2.14 and 6.789 are rational numbers but not integers. see the pattern?


an integer is always a rational number, but a rational number is not always an integer. Provide an example to show that this statement is true?

Integers are counting numbers or include them. 1/2 is a rational number that is not a couinting number.


Would the difference of a rational number and a rational number be rational?

The difference of two rational numbers is rational. Let the two rational numbers be a/b and c/d, where a, b, c, and d are integers. Any rational number can be represented this way. Their difference is a/b-c/d = ad/bd-cb/bd = (ad-cb)/bd. Products and differences of integers are always integers. This means that ad-cb is an integer, and so is bd. Thus, (ad-cb)/bd is a rational number (since it is the ratio of two integers). This is equivalent to the difference of the original two rational numbers.


Are integers always rational?

Before answering this question, we reviewed all of the integers, and we discovered that, by George, all integers are rational.


Why is the sum and product of two rational numbers is rational?

A rational number can be stated in the form a/b where and b are integers. Adding or multiplying such numbers always gives another number that can be expressed in this form also. So it is also rational.


Is the product of three rational numbers rational or irrational?

A rational number in essence is any number that can be expressed as a fraction of integers (i.e. repeating decimal). Taking the product of any number of rational numbers will always yield another rational number.


If a number is an integer then is it a rational?

Yes, integers are always rational.


Is a rational number a real number?

Yes, a rational number is a real number. A rational number is a number that can be written as the quotient of two integers, a/b, where b does not equal 0. Integers are real numbers. The quotient of two real numbers is always a real number. The terms "rational" and "irrational" apply to the real numbers. There is no corresponding concept for any other types of numbers.