If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

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? • do you all ways have to multiply by 2 ? • the questions i have to do are so much harder than the ones he shows! • Please stop adding the copy and paste posts. It is distracting! • , why always apples and oranges? • 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 =   