# 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

1. 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.
2. 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.
3. Find a common multiple of the two ratios. In this case, the common multiple is 18.
4. 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.
5. 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.
6. 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. $$\frac{4}{7}, \frac{12}{21}$$
Step 2: Use a common denominator to compare them.
$$\frac{4}{7}= \frac{×3}{×3}=\frac{12}{21}$$, so $$\frac{4}{7}$$ and $$\frac{12}{21}$$ are equal.

### Finding Equivalent Ratio – Examples 2

Are the ratios 2:5 and 16:35 equivalent?
Step 1: Convert a ratio to a fraction. $$\frac{2}{5}, \frac{16}{35}$$
Step 2: Use a common denominator to compare them.
$$\frac{2}{5}= \frac{×8}{×8}=\frac{16}{40}$$, so $$\frac{2}{5}$$ and $$\frac{16}{35}$$ are not equal.

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