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.
