Mathematicians have taken all the numbers in the world and sorted them into categories, based on their characteristics. Generally, the categories, or sets, go from most to least complicated: complex numbers, imaginary numbers, real numbers, rational numbers, integers, whole numbers and natural numbers. Most numbers belong to more than one category.
Here, we'll talk specifically about the category, or set, of rational numbers. The set of rational numbers:
Consist of positive numbers, negative numbers and zero Can be written as a fraction
The name rational is based on the word 'ratio.' A ratio is a comparison of two or more numbers and is often written as a fraction. A number is considered a rational number if it can be written as one integer divided by another integer. Sometimes this is referred to as a simple fraction.
The number 1/2 is a rational number because it is written as the integer 1 divided by the integer 2. The number 5 is a rational number because we can write it as 5/1. We can also write it as 15/3 or 50/10 because 15 divided by 3 or 50 divided by 10 both equal 5. The mixed number 1 ½ is also a rational number because we can write it as 3/2.
Any number that can be rewritten as a simple fraction is a rational number. This means that natural numbers, whole numbers and integers, like 5, are all part of the set of rational numbers as well because they can be written as fractions, as are mixed numbers like 1 ½.
Rational numbers can be positive, negative or zero. When we write a negative rational number, we put the negative sign either out in front of the fraction or with the numerator. That's the standard mathematical notation. For example, we would write -5/7 as opposed to 5/-7.
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