Equivalent Ratios How to Find Equivalent Ratios

Welcome to Math with Mr. In this video, I'm going to be covering equivalent ratios. And as you can see on your screen, we have four problems or examples that we're going to go through together in order to get this down. On the left side, numbers one and two, we're going to find few examples, few equivalent ratios for each of those. And then on the right side, numbers three and four, we're going to pick out the equivalent ratios out of the choices and So, let's take look at number one here where we have 8 to 12. Now, equivalent ratios are just like equivalent fractions. We use multiplication or division. Whatever you do to one number of the ratio, you have to do the same thing to the other using multiplication or division, and you get an equivalent ratio. So, for example, can multiply both of these by three, and I'll get an equivalent ratio. So, 8 * 3 is 24. 12 * 3 is 36. So, 24 to 36 is equivalent, it holds the same value as the ratio 8 to 12. Now, can multiply both of them by 10 and get 80 to 120. As long as do the same thing to both numbers of that ratio, get an equivalent ratio. So, multiplication, can multiply both those numbers by anything in the world. So, you know, an infinite number of answers there as long as do the same thing to both the left and the right-hand side. Now, division is little more limited because need common factor between the 8 and the 12. So, for example, can't use five because can't do 8 / 5 and 12 / 5. Five is not factor. I'm not going to get whole number when divide both the 8 and the 12. Can you think of common factor between the 8 and the 12? Hopefully, you're thinking either two or four. So, for example, division, could do 8 / 2 is 4. And 12 / 2 is 6. That would be an equivalent ratio. Or could use the greatest common factor, which is four, and divide both by four. So, 8 / 4 is 2. And 12 / 4 is 3. This one would actually be 2 to 3 would be the simplest form of 8 to 12. And simplest form is an equivalent ratio as well as being simplest form. So, there's number one. Again, multiplication or division. And if you do the same thing to both the numbers of the ratio, you get an equivalent ratio. So, let's take look at number two, 27 to 18. Let's use division first. So, can you think of common factor between 27 and 18? Hopefully, you're either thinking three or nine. So, let's divide them both by three to start. And we would get nine to six, which is equivalent. Or like mentioned, you can divide both by nine and get three to two. Or our other choice for equivalent ratios is multiplication. So, let's multiply both of them by two, and we would get 54 to 36. Now, let's take look at number three where we have 20 to 15. Now, we need to find the equivalent ratios out of our choices there, and So, let's start with which is 4 to 3. So, let's think, how would we get 20 to equal this four here? Order matters. So, the when we're looking at equivalent ratios, this 20 needs to be matched with this four, the first number of the equivalent ratio. And the 15 needs to be matched with this three. So, 20 divided by five gives us that four. Let's do the same thing to the 15 and see if we get three. 15 divided by five is three. So, this is an equivalent ratio. Now, 3 to 4, that has the same numbers, right? It has three and four just like but it's not in the correct order. Order matters when it comes to ratios. 20 divided by five does not give me three, and 15 divided by five does not give me four. So, is not equivalent because order matters. how do get 20 to equal 40, right? Well, could do 20 * 2. What happens if we multiply 15 by two? Well, we get this 30. So, does work out. It is an equivalent ratio. Now, all right, we have 10 to start with. We could do 20 divided by two would give me this 10. Is 15 divided by two 15? No. So, is not equivalent. Number four, we have four to 10. So, let's take look at where we have 40 to 100. So, we have to think, okay, how do we get this four to equal 40? Well, we can multiply it by 10. What happens when we do 10 * 10? That gives us this 100. So, we do have an equivalent ratio there with 40 to 100. we have five to two. can't really get this four to equal that five using multiplication or division. But can do 10, can do this 10 divided by two to give me that five. But just like number three, order matters. So, can't take that 10 divided by two and give me the first number in ratio. does not work because order matters. we have 12 to 30. could do 4 * 3 gives me this 12, and the 10 * 3 gives me that 30. So, did the same thing to both the four and 10. So, that means get an equivalent ratio. So, would be equivalent. Now, 2 to 5 is very similar to choice right? It involves two and five. But it's in different order. So, let's see if this one works. know 4 divided by two gives me this two. And this 10 divided by two gives me this five. So, can divide both of them by two, and would get this ratio two to five. So, is equivalent. All right. So, there you have it. There is equivalent ratios. Hopefully, that helped. Thanks so much for watching. Until next time. Peace.