yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Equivalent ratios


3m read
·Nov 11, 2024

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.

All right, now let's work through this together. 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 7 to 6, if I multiply the 7 times 2 to get 14, then I would also multiply the 6 times 2 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 the 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 7 to 21, we would multiply by 3, and to go from 6 to 18, you would also multiply by 3. So that works! If we multiply both of these numbers by 3, we get 21 to 18. Let me circle that in, that one is for sure equivalent.

What about 42 to 36? Well, to go from 7 to 42, we're going to have to multiply by 6, and to go from 6 to 36, we also multiply by 6. So this once again is an equivalent ratio; we multiply each of these by 6, and we keep the same order. So that is equivalent right over there.

63 to 54. Let's see, to go from 7 to 63, you multiply by 9, and to go from 6 to 54, you also multiply by 9. So once again, 63 to 54 is an equivalent ratio. Therefore, we've already selected three, but let's just verify that this doesn't work.

To go from 7 to 84, you would multiply by 12. To go from 6 to 62, what was this? You'd multiply by 10 and two-thirds. 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.

All right, let's look at this first one: so 8 to 6. First, you might say, "Well, gee, these numbers are smaller than 16 and 12." But remember, to get an equivalent ratio, you can multiply or divide these numbers by the same number. So to get from 16 to 8, you could view that as, well, we just divided by 2, and to go from 12 to 6, you also divide by 2. 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 2. To go from 12 to 24, we also multiply by 2. So this is an equivalent ratio.

What about 4 to 3? Well, to go from 16 to 4, we would have to divide by 4, and to go from 12 to 3, we are going to divide by 4 as well. So we're dividing by the same thing in each of these numbers, so this is also going to be an equivalent ratio. So we've selected our 3, 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 4 and multiply by 3. So this would be times 3 over 4; you would get 12.

And to go from 12 to 8, let's see, you could divide by 3 and multiply by 2. So this you could use times two-thirds. So you'd be multiplying or dividing by different numbers here, so this one is not equivalent.

Then 24 to 16, to go from 16 to 24, you would multiply by, let's see, that’s one and a half. So this right over here, you'd multiply by one and a half, and to go from 12 to 16, you would multiply, that is by one and one-third, so times one and one-third. So you're not multiplying by the same amount, so once again, not an equivalent ratio.

More Articles

View All
The rise of industrial capitalism | AP US History | Khan Academy
[Instructor] The period from the end of the Civil War to the start of the 20th Century was one of incredible economic transformation in the United States. In 1865, the United States was the 4th largest industrial economy in the world. By the 1890s, it had…
Worked example: Identifying isotopes and ions | Chemistry | Khan Academy
An isotope contains 16 protons, 18 electrons, and 16 neutrons. What is the identity of the isotope? I encourage you to pause the video and see if you can figure it out. I’ll give you a hint: you might want to use this periodic table here. All right, so I…
The Treasury Bond Collapse is Real.
With interest rates rising almost everywhere around the world, we are now facing yet another financial meltdown. I know, here we go again, right? But this time, there might just be some weight to the reports. By the end of this video, you’ll discover why …
Marc Andreessen at Startup School SV 2016
Okay, so, uh, up next we have a fireside chat with, uh, Mark Andreessen. Uh, come on out, Mark! I think he’s right back. [Applause] There, they know who you are. No introductions needed. So, uh, thanks for coming back. This is, uh, your third startup scho…
Missing numbers in three digit subtraction
Let’s say that we are told that 495 is equal to 621 minus blank. What would blank be? Pause this video and see if you can figure that out. Okay, now let’s do this together. One technique is to try to visualize this on a number line. 495 is what you get w…
Ramen VR (S19) - YC Tech Talks: Gaming 2020 (November 9th, 2020)
Uh, hi everyone. I’m Andy. I’m one of the co-founders at Ramen VR, and Lauren and I are my other co-founder working on Zenith, a massively multiplayer online world. Zenith is kind of like Dark Souls meets World of Warcraft in that it combines adrenaline …