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# Ordering rational numbers

Learn how to order numbers from least to greatest using a number line. Convert fractions and decimals to mixed numbers or whole numbers, then plot them on the number line. Master this skill by practicing with examples like 7/3, -5/2, 0, -2, -12/4, and -3.25.

## Want to join the conversation?

• In the title does the word rational have any impact on ordering
(17 votes)
• No. The definition of a rational number is a number that can be turned into a fraction. The opposite, an IRrational number, is a number that cannot be turned into a fraction, like π.
(41 votes)
• what does" rational" mean?
(14 votes)
• Rational means based on or in agreement with reason or logic.
When referring to math, rational means containing quantities which are expressible, as a ratio of whole numbers.
(17 votes)
• is a negative plus a negative, a positive?
(5 votes)
• no look at this example (-4+-5=-9) if you want to go back into positive numbers you would have to do this (-4 - -8 = 4)
(2 votes)
• I heard in school that zero is a middle number does that still mean it is a number or a middle number
(5 votes)
• 0 is a unique integer. It is neither positive or negative. Hope it helps
(5 votes)
• did he put the negative sign on the 12?
(4 votes)
• yeah because a negative times a positive equals a negative.
(2 votes)
• mic quality just went 2016
(4 votes)
• is -0 a thing?
(2 votes)
• No, because 0 is a unique integer. It is neither negative nor positive. There can't be a "negative" zero since it's neutral. Hope this helps
(3 votes)
• (yawn) This is sooooooooooo easy
(3 votes)
• How to not forget what you teach
(2 votes)
• Taking notes is probably the best way to remember what you are trying to learn.
(3 votes)
• -81/80, -5/8, -3/6, -25/51,-1/5,-5/6,-101/200,-1/4,-23/22,-3/17,-20/21,-7/8,-12/25,-3/14 in order from least to greatest
(3 votes)

## Video transcript

- [Voiceover] What I'd like to do in this video is order these six numbers from least to greatest. So the least of them being on the left hand side, and the greatest on the right. And I encourage you to pause this video, and see if you can do it on your own, before we work through it together. So assuming you've had a go at it, so let's do it together, and to help us there, let's plot these numbers on a number line, and I have a number line up here, so there you go, there is a handy number line. And let's just take them one by one. So the first number here, we have 7/3. So let's see if we can express that in a different way, if we can write that as a mixed number. So 7/3, how many wholes are here? And the whole is going to be 3/3. So this is going to be 3/3, plus another 3/3, is going to get us to 6/3. And so you're going to have one more third left. So this is 7/3. Three plus three, plus one is seven. So this is 3/3 is one whole, three thirds is one whole, so this is two and 1/3. So seven thirds, same thing as one, two, and you see, between consecutive integers, we have three spaces, so we are essentially marking off thirds, so two and 1/3, is going to be 1/3 of the way between two and three, so it's going to be right over there, so that is 7/3. Then we have negative 5/2, so same logic. Negative, let me do that in that green color. So, I can do it over here. Negative five over two, well that's the same thing as the negative of 5/2, and 5/2 is going to be 2/2 plus another 2/2, plus 1/2 so this is two and 1/2, this is one, this is one, and that's 1/2. So this is going to be one, plus one, plus 1/2, two and 1/2, we have our negative out there, so it's negative two and 1/2. Let's see, negative one, negative two, and the negative two and 1/2 is going to be halfway between negative two, and negative three, so it's going to be right over there. So that is negative 5/2. Then we have zero, not too difficult. It's actually labeled on our number line for us. Then we have negative two. Negative two, once again, on our number line for us. Two, two steps, two whole numbers to the left of zero. So negative two is going to put us right over there. Then we have negative 12/4 so it might jump out at you immediately, 12 divided by four is three, so this is going to be the same thing as negative three. So this is negative 12/4 or if you want to use the type of logic that we used in these first two numbers, you could say negative 12/4 is the same thing as the negative of 12/4 which is 4/4 plus another 4/4 so that gets us to 8/4 plus another 4/4 that's 12/4. This is one, two, and three, or negative three. So negative three is the same thing as negative 12/4. And then finally, one more number, negative 3.25. So you could view this, this is the same thing, negative 3.25 is the same thing as negative three and 25/100 and 25/100 is the same thing as 1/4. 25 is 1/4 of 100. So this is the same thing as negative three and 1/4. So let's see, let's go negative one, negative two, negative three, and then we have to go a fourth, and we're not going to be able to do it super precisely, but it's going to be less than 1/3, so it's going to be right over there. So that right over there, is negative 3.25. So we wanted the numbers ordered from least to greatest, well, we've done that. The least is negative 3.25, Then negative 12/4, then negative 5/2, then negative two, then zero, then 7/3, and we are done.