Equivalent ratios

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.