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## 6th grade (Illustrative Mathematics)

### Course: 6th grade (Illustrative Mathematics) > Unit 2

Lesson 5: Lesson 5: Defining equivalent ratios# Equivalent ratios

One way to identify equivalent ratios is to determine if you can multiply or divide the corresponding parts of the ratio by the same amount. To do this, look at the two ratios and see if there is a common factor that you can use to scale one ratio to the other. If you can scale one ratio to the other by multiplying or dividing every part of the ratio by the same number, then the two ratios are equivalent.

## Want to join the conversation?

- Is finding equivalent ratios basically finding equivalent fractions?(64 votes)
- yes, you can even write ratios as fraction: like 2/3 = 2:3(49 votes)

- Guys, I really need help. I'm not sure how to label this sort of problem, but I think it could be called 'estimating the ratio?' I'm trying to average 76/23. The answer is 4/1. But what process do I use (or way of thinking) in order to average 76/23 out? I never know whether to average to the nearest 10th, 5th, or what. Please let me know. (If this question has been posted in the wrong place, give me a heads up.) Thanks.(37 votes)
- for this you would probably round to the nearest 10th making the ratio 80/20. Then, you would divide by 20: 80 divided by 20 = 4 and 20 divided by 20 = 1(21 votes)

- So do you always multiply by the same number to figure out the ratio?(14 votes)
- Yes, you would need to multiply both sides of the ratio by the same number, for it to be equivalent(2 votes)

- please upvote I need the badge(18 votes)
- do you all ways have to multiply by 2 ?(9 votes)
- No, it can be times 6 or divide by 7.It depends on the problem.(3 votes)

- the questions i have to do are so much harder than the ones he shows!(18 votes)
- Please stop adding the copy and paste posts. It is distracting!(14 votes)
- why do we have to make math more complicated? all you need to know is the basics, STOP MAKING IT MORE COMPLICATED JUST KEEP IT HOW IT WAS BEFORE(8 votes)
- we live, we love, we lie.(8 votes)
- 0:52, why always apples and oranges?

please answer me 😞(6 votes)- mostly because some people can understand with simpler objects (or in this case fruits) and also because apple and oranges are good(3 votes)

## Video transcript

- [Instructor] We're asked
to select three ratios that are equivalent to seven to six. So pause this video
and see if you can spot the three ratios that are
equivalent to seven to six. Alright, now let's work
through this together, and the main thing to realize
about equivalent ratios is we just have to multiply or divide the corresponding parts of the ratio by the same amount. So before I even look at these choices, for example, if I have seven to six, if I multiply the seven times two to get 14, then I would also
multiply the six times two to get 12. So, for example, 14 to 12
is the exact same ratio. Now you might be tempted to pick 12 to 14, but that is not the same ratio. Order matters in a ratio. This could be ratio of oranges to apples. And we're saying for every seven oranges, there are six apples. You wouldn't be able to say
it the other way around. So you would rule this one out even though it's dealing with
some of the right numbers. It's not in the right order. Now let's think about 21 to 18. To go from seven to 21, we would multiply by three. And to go from six to 18, you would also multiply by three. So that works. If we multiply both of
these numbers by three, we get 21 to 18. So let me circle that in. That one is for sure equivalent. What about 42 to 36? Well, to go from seven to 42, we're going to have to multiply by six. And to go from six to thirty-six, we also multiply by six. So this, once again,
is an equivalent ratio. We multiply each of these by six and we keep the same order. So that is equivalent right over there. 63 to 54. Let's see, to go from seven
to 63, you multiply by nine. And to go from six to 54,
you also multiply by nine. So once again, 63 to 54
is an equivalent ratio. And so we've already selected three, but let's just verify
that this doesn't work. So to go from seven to 84,
you would multiply by 12. To go from six to 62, you multiply by 10 and 2/6 or 10 1/3, so this one is definitely not an equivalent ratio. Let's do another example. So once again, we are asked
to select three ratios that are equivalent to 16 to 12. So pause this video and see
if you can work through it. Alright, let's look at this first one. So eight to six. So at first you might say well, gee, these numbers are smaller than 16 and 12. Remember, you can, to
get an equivalent ratio you can multiply or divide these numbers by the same number. So, to get from 16 to eight, you could do that as, well,
we just divided by two. And to go from 12 to six,
you also divide by two. So this actually is an equivalent ratio. I'll circle that in. What about 32 to 24? Well to go from 16 to
32, we multiply by two. To go from 12 to 24, we
also multiply by two. So this is an equivalent ratio. What about four to three? Well, to go from 16 to four, we would have to divide by four. And to go from 12 to three, we are going to divide by four as well. So we're dividing by the same thing, each of these numbers. So, this is also going to
be an equivalent ratio. So we've selected our three,
so we are essentially done. But, we might as well
see why these don't work. Now let's think about it. To go from 16 to 12, how do we do that? Well, to go from 16 to 12, you could divide by four and multiply by three. So this would be times 3/4. You would get 12. And to go from 12 to eight, so you could divide by
three and multiply by two. So this you could view as times 2/3. So you'd be multiplying or dividing by different numbers here, so
this one is not equivalent. And then 24 to 16? To go from 16 to 24,
you would multiply by, let's see, that's 1 1/2. So this right over here would be, you would multiply by 1 1/2. And to go from 12 to
16, you would multiply, that is, by 1 1/3. So, times 1 1/3. So you're not multiplying
by the same amount. So once again, not an equivalent ratio.