### Video Transcript

Is every rational number an

integer?

In this question, we have two very

mathematical terms, rational and integer. Let’s take the word integer

first. This will be defined as a number

that has no a fractional part. It includes the counting numbers,

for example, one, two, three, four, zero, and the negatives of the counting

numbers. A rational number is defined as

one, which can be expressed as 𝑝 over 𝑞 where 𝑝 and 𝑞 are integers and 𝑞 is not

equal to zero.

So let’s take some numbers which

are rational. For example, we could have this

fraction six over one, which fits the form of a rational number. Six and one are integers and the

one, this 𝑞-value on the denominator, is not equal to zero. This would be equivalent to the

value six, which is an integer. Let’s take another rational

number. Here, we have the example negative

two-fifths. We should ask ourselves if negative

two-fifths is an integer, a number that has no fractional part. And this would be no. We couldn’t write this in any way

as a number that has no fractional part. Therefore, the answer to the

question “is every rational number an integer?” is no.

If we consider the Venn diagram

where we have the set of rational numbers, then contained within this set will be

the set of integers. Using this diagram is helpful to

illustrate that every integer is a rational number, but not every rational number is

an integer.