Finding Equivalent Ratio
Ratios mean comparing two numbers or quantities. To make a comparison, you can use addition, subtraction, multiplication, and division.

Equivalent ratios are considered identical if you do a comparison. It means both of the numbers follow a certain rule.
To identify whether two ratios are equivalent, it is better to write them as a fraction and find the pattern.
Step-by-step guide to finding equivalent ratios
- Understand the concept of a ratio: A ratio is a comparison of two or more values. It is often written as “a:b” or “a/b” and represents the relationship between a and b.
- Identify the two ratios that you want to compare. For example, let’s say you want to find the equivalent ratio of 2:3 to 6:9.
- Find a common multiple of the two ratios. In this case, the common multiple is 18.
- Multiply each value in the first ratio by the same number to get an equivalent ratio. So, 2 x (18/2) = 18 and 3 x (18/3) = 18. The equivalent ratio is now 18:18 or 1:1.
- Repeat step 4 for the second ratio, so 6 x (18/6) = 18 and 9 x (18/9) = 18. The equivalent ratio is now 18:18 or 1:1.
- Compare the two equivalent ratios and you will see that they are equal. So the ratio of 2:3 is equivalent to the ratio 6:9.
Note: The above method is an example of finding a common multiple. Another method is finding a common denominator.
Finding Equivalent Ratio – Examples 1
Are the ratios 4:7 and 12:21 equivalent?
Solutions:
Step 1: Convert a ratio to a fraction. 47,1221
Step 2: Use a common denominator to compare them.
47=×3×3=1221, so 47 and 1221 are equal.
Finding Equivalent Ratio – Examples 2
Are the ratios 2:5 and 16:35 equivalent?
Step 1: Convert a ratio to a fraction. 25,1635
Step 2: Use a common denominator to compare them.
25=×8×8=1640, so 25 and 1635 are not equal.
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