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## MAP Recommended Practice

### Unit 35: Lesson 11

Comparing negative numbers- Ordering negative numbers
- Ordering negative numbers
- Ordering small negative numbers
- Ordering rational numbers
- Ordering rational numbers
- Compare rational numbers
- Negative numbers, variables, number line
- Compare rational numbers using a number line
- Writing numerical inequalities

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# Ordering rational numbers

Sal puts 7/3, -5/2, 0, -2, -12/4, -3.25 in order from least to greatest.

## Want to join the conversation?

- what does" rational" mean?(12 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.(2 votes)

- is a negative plus a negative, a positive?(6 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)(3 votes)

- When will my dad come back?(8 votes)
- never. he has gone out to buy milk and will never come back. sorry for your loss :((3 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(4 votes)

- did he put the negative sign on the 12?(4 votes)
- yeah because a negative times a positive equals a negative.(2 votes)

- In the title does the word rational have any impact on ordering(2 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.(2 votes)

- Sir i didn't understand on how to order the rational numbers please want a more clear version(2 votes)
- When Sal says ordering rational numbers, this is just a way of saying putting a given set of numbers in order from least to greatest. This can become a problem when some of the numbers are fractions, others are decimals, and some are whole numbers. In order to correct for this you can turn all the numbers into one form. In the video this is done by turning all the numbers into fractions, but you could also get the same effect by turning them all to decimals if you find that easier.(2 votes)

- How do you know where the decimal is at on the number line?(0 votes)
- magnify the number line so it looks like this:

|*_____*|________|*_______*|________|*_______*|________|*______*|________|*_____*|

-1......-0.9........-0.8.......-0.7.......-0.6........-0.5.......-0.4.......-0.3.......-0.2.....0.1

Hope this helps(6 votes)

- 3.25 is not the least(2 votes)
- What is a rational number(1 vote)
- It is any number that can be expressed as a ratio of two integers. It includes integers, truncated decimals, and repeating decimals. It is opposed to irrational numbers which are go on forever and never repeat such as π. √2, etc.(2 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.