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### Course: Pre-algebra>Unit 3

Lesson 3: 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?
• yes, you can even write ratios as fraction: like 2/3 = 2:3
• 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.
• 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
• So do you always multiply by the same number to figure out the ratio?
• Yes, you would need to multiply both sides of the ratio by the same number, for it to be equivalent
• do you all ways have to multiply by 2 ?
• No, it can be times 6 or divide by 7.It depends on the problem.
• the questions i have to do are so much harder than the ones he shows!
• Same here!
• Please stop adding the copy and paste posts. It is distracting!
• , why always apples and oranges?
• mostly because some people can understand with simpler objects (or in this case fruits) and also because apple and oranges are good
• Standard Form of Ratio
The standard form of the ratio is given below:

Ratio = a : b = Numerator : Denominator

Or

Ratio = a / b = Numerator / Denominator

How to Find Equivalent Ratios?
As we know, two or more ratios are equivalent if their simplified forms are the same. Thus, to find a ratio equivalent to another we have to multiply the two quantities, by the same number.

Another way to find equivalent ratios is to convert the given ratio into fraction form and then multiply the numerator and denominator by the same number to get equivalent fractions. Then again we can write the resulting fraction as an equivalent ratio.

Also, if we have to compare any two equivalent ratios, then we can divide the two quantities by the highest common factor and get the simplest form of ratio. Hence, we can compare them.

The examples of equivalent ratios are:

2 : 4 :: 4 : 8
10 : 20 :: 20 :40
1 : 2 :: 2 : 4
0.5 : 1 :: 2:4
Solved Examples
Q.1: Find the equivalent ratios of 8 : 18.

Solution: Let us first write the given ratio as a fraction.

⇒ 8/18

Now multiply the numerator and denominator by 2

= (8 × 2)/(18 × 2)

= 16/36

Or we can write, the above fraction as a ratio;

= 16 : 36

So, 16 : 36 is an equivalent ratio of 8 : 18.

Q.2. Find any two equivalent ratios of 4 : 5.

Solution: Let us first write the given ratio as a fraction.

4:5 ⇒ 4/5

Now multiply the numerator and denominator by 2, to get the first equivalent fraction.

= 4/5

= (4 × 2)/(5 × 2)

= 8/10

Or

4:5 =

Again, multiply and divide ⅘ by another natural number, such as 3, as given below:

= 4/5

= (4 × 3)/(5 × 3)

= 12/15

Or

4:5 =
• This is just an Example! Ok, have a Blazerific day
• Is finding equivalent ratios basically finding equivalent fractions?
• Yes! Just like we can multiply or divide top and bottom of a fraction by the same nonzero number to create equivalent fractions, we can multiply or divide all numbers in a ratio by the same nonzero number to create equivalent ratios.

Have a blessed, wonderful day!
• Can you also figure out if they are equivalent with addition and subtraction?
• No. Ratios are a type of fraction. Equivalent fractions are always created by multiplying both the numerator and denominator with a common factor, or by dividing our a common factor. For example: 1/2 * (3/3) = 3/6 or you can start with 3/6 and remove the common factor of 3 to get back to 1/2.

Hope this helps.

## 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.