Question Video: Determining the Rationality of a Number Mathematics • 6th Grade

Video Transcript

Is 12 and five-sixths a rational number?

Let’s begin by remembering the definition of a rational number, which is a number that can be expressed as 𝑝 over 𝑞 where 𝑝 and 𝑞 are integers and 𝑞 is not equal to zero. Although we have a mixed number here, 12 and five-sixths, could we write this as a complete fraction 𝑝 over 𝑞? In other words, could we write this as a top-heavy or improper fraction? If we consider our value of 12, then how many sixths would we have in 12 whole ones? Well, we’d have seventy-two sixths plus the fractional value of five-sixths, which would give us a fraction of 77 over six.

Another way, of course, to do this is to take our denominator six and multiply it by 12 and then add on the value of five. Either way, we can see that 12 and five over six is equivalent to 77 over six. So, is this value a rational number? And the answer is yes.