We begin by recalling that the set of rational numbers, written ℚ, is the set of all quotients of integers. Which of the following expressions is rational given ? = 1 and ? = 3 4? We can represent this information in the following Venn diagram.Įxample 6: Identifying the Rational Expression from a List of Given Expressions Represent fractions as mixed numbers for example, 5 3 = 1 2 3, which is also a rational number. We can represent numbers like this using a line It is worth noting that any decimal expansion with a finite number of digits or a repeating expansion is rational. 5, so we can also represent rational numbers as decimals. This is not the only way of representing rational numbers we have also seen that 1 2 = 0. For example, we can think about 5 3 as 5 lots of 1 3.
![rational numbers help rational numbers help](https://vessellagator.files.wordpress.com/2010/08/screen-shot-2012-09-28-at-6-09-44-pm.png)
One way of conceptualizing rational numbers like these is toĬonsider them as multiples of simpler fractions. Similarly, 5 3 and 1 2 7 are rational numbers. For example, 1 and 2 are integers, so 1 2 ∈ ℚ. We can also use this definition to find some examples of rational numbers. It is worth noting that a number cannot be rational and irrational at the same time. We can then recall that the set of natural numbers is a subset of the integers,Īlthough it is beyond the scope of this explainer to prove this result, some numbers such as √ 2 or ? are not rationalĪnd are called irrational. This means that the set of integers isĪ subset of the set of rational numbers. First, we can note that all integers are rational numbers, Using this definition, we can see some interesting properties of the set of rational numbers.
![rational numbers help rational numbers help](http://image1.slideserve.com/2511024/subtracting-integers-n.jpg)
![rational numbers help rational numbers help](https://www.swiss-algebra-help.com/image-files/numberset.png)
Of the form ? ? where ? and ? are integers and ? is nonzero. The set of rational numbers, written ℚ, is the set of all quotients of integers.