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### Course: 6th grade (Eureka Math/EngageNY) > Unit 1

Lesson 2: Topic B: Collections of equivalent ratios- Ratios and double number lines
- Ratios with double number lines
- Solving ratio problems with tables
- Ratio tables
- Ratio tables
- Ratios with tape diagrams
- Create double number lines
- Ratios with tape diagrams
- Relate double number lines and ratio tables
- Ratios and measurement
- Ratios and units of measurement
- Ratios on coordinate plane
- Ratios on coordinate plane
- Part to whole ratio word problem using tables
- Part-part-whole ratios

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# Ratios and double number lines

Double number lines are a helpful tool for understanding and solving ratio problems. They visually represent the relationship between two quantities, making it easier to find the cost or amount of a single unit. Examples include calculating the price of avocados, building model trains, and making snowballs.

## Want to join the conversation?

- at1:49why does he use fractions i don,t get how he got the fraction(80 votes)
- ratios and fractions are acually NOT the same but are very close and can mess u up VERY easiely so be carfull...

u can tell it's a ratio because it can go like:56:17

(the bigger # can go first)

but for fractions... when it's like that then it's an improper fraction so u HAVE 2 change it in 2 a mixed fraction

(hope that makes sense)(42 votes)

- how would you make a ratio in to a fraction(22 votes)
- Basically a ratio
**IS**a fraction. One fourth : one to four.

Hope this helps!(86 votes)

- at2:28I found the same answer by doing: 5x2 = 10 9x2 = 18 which as a ratio is10:18then, i divided the ratio by 10 leaving me with 1:1.8 meaning that, 1 pound of avocados = $1.80. Is this also the correct way to do this problem?(18 votes)
- That is a great way of doing it because powers of 10 are just decimal movers.(24 votes)

- why do you use fraction at1:50(8 votes)
- You use a fraction at1:50because a ratio can be written in three different ways:

2:3

2/3

2 to 3

I hope this helped!(21 votes)

- I'm confused bout the part where you do the 5:9 part when you get 1.80(15 votes)
- he divided 5 and 9(4 votes)

- I still don't get it... Can anybody explain it to me in other easier words?! And also if we don't exactly get our answer do we have to round them? I don't get it.(8 votes)
- Hi! Double number line diagrams are best used when the quantities have different units. Double number line diagrams can help make visible that there are many, even infinitely many, pairs of numbers in the same ratio—including those with rational number entries. As in tables, unit rates (R) appear in the pair (R, 1). If you have more questions feel free to ask!(13 votes)

- this is very helpful i made a 25 dang i should've watched(8 votes)
- Maybe if you take notes of what he says in the video, when you are practicing you can look back at your notes and find your answer. Hope this helped!(3 votes)

- please help me i . dont understand(5 votes)
- i don't know what you don't understand.But I can help you with simplifying. So if you had 4:8 you could divide both numbers by the same number that in this case is 4 so after dividing you should have gotten 1:2. but you can check by multiplying the numbers again by 4. Hope this helped!(2 votes)

- I dont understand.Please can anybody help?Thanks in advance.(6 votes)
- Double number line diagrams are useful for visualizing ratio relationships between two quantities. They are best used when the quantities have different units. (The unit rate appears paired with 1.) Double number line diagrams help more easily they are many equivalent forms of the same ratio.

Hope this helped have a blessed day :/(2 votes)

- i don't get how you got 1.80 is there a easier way?(3 votes)
- since ratios and fractions are relevant it easy to get messed up. But if you use decimals, i.e. 1.80 it is more easier to understand how the simplification of ratios works.(6 votes)

## Video transcript

- [Narrator] We're told that
the double number line shows that five pounds of avocados cost $9. And so what is going on here
with this double number line? This shows how as we increase
the number of avocados, how the cost increases. So for example, when we have
zero pounds of avocados, it costs us $0. When we have five pounds of avocados, it costs us $9. And so, if you look at
any point over here, let's say you look right over here. This would be, let's
see, this is one, right? This is one, two, three, four, five. If you look at one, this
point on the cost number line would tell you how much one
pound of avocado would cost. Two pounds of avocados,
how much would that cost? You would look at this second
number line right over there. So they ask us, based on the ratio shown in the double number
line, what is the cost for one pound of avocados? So pause the video and think about it. Remember, one pound of avocados
on this top number line, we look at this second number line, the cost would be right over here. What is this going to be? Well, we could just set it up as a ratio. The ratio of pounds of avocados to cost is going to be, let me
do this in some colors. So if I have five pounds of avocados, it is going to cost me $9. So the ratio of pounds to
dollars is five to nine. So if I were to have one pound of avocado, one pound of avocado, I have divided by five to
get one pound of avocado. I would have to do the
same thing for the cost. So if I divide nine by five, this is going to be nine fifths dollars. Nine fifths dollars would
be the cost of one pound. Well, nine fifths isn't
always the most natural way to write money, so you
can view this nine fifths is equal to one and four fifths, which is equal to one and eight 10ths, which is equal to 1.8, or you could say this is $1.80. So if you were to go onto
this double number line, the cost of one pound of avocado, this point right over here would be $1.80. If you said two pounds of avocados, well, now you would double it. So this would be $3.60, and you would go on and on and on all the way until you got to $9 here. Let's do another example. So here, we are told the
double number line shows how many model trains
Irene can build in a week. So we can see, in zero weeks
she can't build any trains, but in one week she can build nine trains. And they asked us, which
table represents the rate of Irene building model trains? So pause this video and see
if you can figure it out. So once again, every week
she can build nine trains. So one way to think about it is the ratio of week to trains would be one to nine. So let's see. If I look at this table, I
just wanna see where the ratio between weeks to trains
stays at one to nine. So five to 45, that is still one to nine. To go from one to five,
I've multiplied by five. And then to go to nine to 45,
I've also multiplied by five. So this one checks out. And another way to think about
it, is 45 is nine times five. So nine times. That might be an easier
way to think about it. Over here, 12 to 108, that's, once again, 12 times nine is 108. And then 26 to 234. Let's see, 26 times 10
would be 260, minus 26. Yeah, it would be 234. So this is nine times. So in all of these cases,
the ratio of trains or the ratio of weeks to
trains is one to nine. So this one is looking good,
so I'll just circle that in. But let's just make sure
that this one doesn't work. Over here, the ratio of weeks
to trains is nine to one, not one to nine. The train should be nine times the weeks, while here the weeks is
nine times the train. So just looking at that first one, we know that this is
not going to work out. Let's do one last example. The double number line shows
how many snowballs Jacob and his friends can make in one minute. No minutes, they can make zero snowballs. In one minute, they can make 12. Complete the table to
show the same information as the double number line. So once again, pause this video and see if you can work this out. Well, we can think about it as a ratio. The ratio of minutes to snowballs is one to 12. So minutes to snowballs is one to 12. Or another way to think about it is, the snowballs is going to
be 12 times the minutes. And so over here, if I have 12 snowballs, we already know that's
going to be one minute. If I have 48 snowballs,
let's just think about it. To go from 12 to 48 you
have to multiply by four. So you have four times as many snowballs, it's gonna take you four
times as many minutes. And then if you go to five,
to go from one to five you multiply by five, so
you're gonna have five times as many snowballs as you
would be able to make in one minute. So five times 12 is 60, and we're done. It could be one to 12,
four to 48, five to 60. For every five minutes,
you can make 60 snowballs, or they make 60 snowballs.