# 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. \(\frac{4}{7}, \frac{12}{21}\)

**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 – Example**s 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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