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

*parts, where*

**d***is not a multiple of*

**D***.*

**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

*is not a multiple of*

**D****.**

*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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Learn More:

- Fractions and Rational Numbers
- Locating Numbers on the Number Line
- Equivalent Fractions on a Number Line
- Do You Know What an Equivalent Fraction Is?
- Understand What a Fraction Is and When It Is Used