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Oct01

Getting to Know Rational Numbers and Their Properties

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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 whole numbers. It is to say, that we can represent them as a fraction a/b, where a and b are whole numbers 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:

rational numbers

And by all the fractions equivalent to these.

The set of all rational numbers is represented by the following symbol:

rational numbers

Remember that any whole number is also a rational number and can be represented as a ratio of two whole numbers.

For example, the number 5 can be represented by the following fractions:

rational numbers

This means that the set of whole numbers is contained within the set of rational numbers. Mathematically we write it as:

rational numbers

To place the numbers on a number line, or real numbers, there are numbers that cannot be represented as a ratio of two whole numbers.

These numbers are called irrational numbers, and the most well known are these:

rational numbersrational numbers

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 a whole number 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 whole numbers.

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 whole number.

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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