Fractions and Rational Numbers – What is the Difference?

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Most of us are going through years of math class at school and we are still confused about some basic things. For example: Why can not you divide by zero? Why is .999 … equal to 1, and not a little less? 19659002] Unfortunately, most of these things are supposed to be covered in elementary school and most elementary teachers do not understand basic math concepts. Instead, they are supposed to teach only a set of "skills".

One of the simplest concepts that is usually inadequately explained is the difference between fractions and rational numbers. Let's see if we can clarify it now

A fraction is a number that expresses a part of a whole in the form of a quotient of integers (where the denominator does not). is not zero).

A Rational Number is a number that can be expressed as a quotient of integers (where the denominator is not zero) or as a number repetitive or final decimal. Each fraction corresponds to the first part of this definition. Therefore, each fraction is a rational number.

But even if each fraction is a rational number, not all rational numbers are a fraction.

Why? Consider this:

Each integer (all integers, including zero, and their negatives …. – 3, -2, -1, 0 , 1, 2, 3 …) is a rational number because it can be expressed as a quotient of integers, as in the case of 4 = 8/2 or 1 = 3/3 or – 3 = 3 / -1 and so on. So integers such as 4 or 1 can be expressed as the quotient of integers.

But an integer is not a fraction . 4 is an integer, but it is not a fraction. 4 is not expressed as the quotient of integers. The difference lies in the wording.

A fraction is a number that expresses a part of a whole. An integer does not express a part.

A rational number is a number that can be expressed as a quotient of whole numbers, or as part of a whole, but the fraction is a number is (must be) expressed as a quotient of whole numbers, or as part of a whole – there is a difference. The difference is subtle, but it is real.

There are slightly different variations of the definition of a fraction, including: "A fraction is the ratio of two integers or, to put it simply, an integer divided by another integer."

This definition also shows that an integer is not a fraction, because an integer is not a ratio. It may be expressed as a ratio, but is not a ratio in itself; he may be divided by another whole number, but he is not divided by .

In summary, fractions are a subset of numbers. Rational numbers contain integers and fractions do not.

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Source by Brian Foley

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