In today’s post, we are going to learn a little more about rational numbers.
In an earlier post, we saw how to represent numbers on a number line and in another, what types of rational numbers exist.
Now we are going to get to know them in a bit more detail.
Properties of Rational Numbers
Rational numbers are those that can be represented as a ratio of two integers. It is to say, that we can represent them as a fraction a/b, where a and b are integers and b is a number other than zero.
The term ”rational” comes from the word ratio, meaning part of a whole. (for example: ”We had a ratio of three per person.”)
Each rational number can be represented by infinite equivalent fractions. For example, the rational number 2.5 can be represented by the following fractions:
And by all the fractions equivalent to these.
The set of all rational numbers is represented by the following symbol:
Remember that any integer is also a rational number and can be represented as a ratio of two integers.
For example, the number 5 can be represented by the following fractions:
This means that the set of integers is contained within the set of rational numbers. Mathematically we write it as:
To place the numbers on a number line, or real numbers, there are numbers that cannot be represented as a ratio of two integers.
These numbers are called irrational numbers, and the most well known are these:
The Rational Numbers of Ancient Egypt
Rational numbers emerge with the need to distribute a quantity D in d parts, where D is not a multiple of d.
To calculate the amount that will be distributed to each part, you need to perform the operation D:d, which does not result in an integer because D is not a multiple of d.
To find the result of this operation, there are numbers that appear and are able to represent the form D/d, but they are different from integers.
In Ancient Egypt, they already had made these types of ”parts of an integer” deals using almost exclusively unit fractions, that had 1 as the numerator. It is to say that we can represent 1/b as a fraction, where b is a positive integer.
These unit fractions were represented by hieroglyphics in the shape of an ”open mouth” that represented the vinculum (line in a fraction), and a numerical hieroglyphic written below, which represented the denominator of the fraction.
For example, to represent 1/4 they wrote it in the following way:
Any non-unit fraction was represented as the sum of different unit fractions. Therefore, the sums of unit fractions are known as Egyptian fractions.
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