Equivalent ratios are those that can be simplified or reduced to the same value. In other words, two ratios are considered equivalent if one can be expressed as a multiple of the other. Some examples of equivalent ratios are 1:2 and 4:8, 3:5 and 12:20, 9:4 and 18:8, etc.
|1.||What are Equivalent Ratios?|
|2.||How to Find Equivalent Ratios?|
|3.||Equivalent Ratios Table|
|4.||FAQs on Equivalent Ratios|
What are Equivalent Ratios?
In math, the definition of the equivalent ratio states that "Two or more ratios that express the same relation or comparison of numbers are known as equivalent ratios." It is similar to the concept of equivalent fractions. The equality of two ratios is also known as proportion. The antecedent and consequent values are different, but still, if we reduce them to the simplest form, we will get the same value. For example, to find whether 2:3 and 16:24 are equivalent ratios or not, we will have to reduce both ratios to their simplest form. 2:3 is already in simplest form as the HCF of 2 and 3 is 1. The HCF of 16 and 24 is 8. So, let us divide both these numbers by 8 to find the reduced form. This implies (16÷8):(24÷8) = 2:3. It is clear that 2:3 and 16:24 results in the same value, therefore they are equivalent ratios.
How to Find Equivalent Ratios?
When it comes to finding equivalent ratios, the two cases might come up to you. One is to check and identify whether the given ratios are equivalent or not, and the second is when you will be asked to find equivalent ratios of a given ratio. Let us learn both one by one.
If we have to check whether the given ratios are equivalent or not, there are two methods to do the same - the cross multiplication method and the HCF method. Follow the steps given below to find equivalent ratios using the cross multiplication method:
Find whether 10:8 and 30:24 are equivalent ratios or not.
- Step 1: Write both the ratios in fractional form (numerator over denominator).
- Step 2: Do the cross multiplication. Multiply 10 by 24 and 8 by 30.
- Step 3: If both products are equal, it means that they are equivalent ratios. Here 10 × 24 = 8 × 30 = 240. Therefore, they are equivalent ratios.
Now, let us understand the HCF method for identifying equivalent ratios using the same example.
- Step 1: Find the HCF of the antecedent and consequent of both ratios. Here, HCF (10, 8) = 2, and HCF (30, 24) = 6.
- Step 2: Divide the terms in both ratios by their respective HCF. So, we get (10÷2):(8÷2) = 5:4 and (30÷6):(24÷6) = 5:4.
- Step 3: If the reduced form of both ratios is equal, it means they are equivalent. Here, 10:8 = 30:24.
Now let us learn how to find equivalent ratios of a given ratio using an equivalent ratio table.
Equivalent Ratios Table
There is an infinite number of equivalent ratios possible for a given ratio as we can multiply any natural number to both the terms of a ratio to get its equivalents. An equivalent ratio table contains some of the equivalent ratios of a given ratio in a tabular format which makes it simple to understand. You can also make your own equivalent ratio table of any ratio. For example, let us multiply 1:3 by different natural numbers starting from 2 and get its equivalent ratios. Here, it is important to note that we can even divide the terms of a ratio by their common factor to find the equivalent ratios, wherever possible.
1:3 = (1×2):(3×2) = 2:6
1:3 = (1×3):(3×3) = 3:9
1:3 = (1×4):(3×4) = 4:12
1:3 = (1×5):(3×5) = 5:15
In the tabular form , it can be represented as:
|Equivalent Ratios of 1:3|
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Check these interesting articles related to the concept of equivalent ratios.
Equivalent Ratios Examples
Example 1: Find two equivalent ratios of 10:11.
Solution: To write the equivalent ratios of a given ratio, we can multiply the terms by any natural number starting from 2. We can divide as well if the terms are not co-prime numbers. Here 10 and 11 are co-primes, so let us multiply them by 2 and 3 to find their equivalents.
10:11 = (10×2):(11×2) = 20:22
10:11 = (10×3):(11×3) = 30:33
Therefore, 20:22 and 30:33 are the two equivalent ratios of 10:11.
Example 2: Are the given ratios - 15:10 and 30:15 equivalent or not?
Solution: To find whether the given ratios are equivalent or not, let us use the cross multiplication method. We can write these ratios as 15/10 and 30/15. Now, multiply 15 by 15 and 10 by 30.
15 × 15 = 225
10 × 30 = 300
Here, 225 ≠ 300. Therefore, 15:10 and 30:15 are not equivalent ratios.
Example 3: What will be the value of x if 2:3 is equivalent to 10:x?
Solution: It is given that 2:3 = 10:x. It means that we have to multiply 2:3 with a natural number such that the answer will be of form 10:x, where x is any natural number. Let us look at the antecedents 2 and 10. If we multiply 2 by 5, we get 10. It means we will have to multiply 3 with 5.
2:3 = (2×5):(3×5) = 10:15
Therefore, 2:3 and 10:15 are equivalent ratios, and the required value of x is 15.
FAQs on Equivalent Ratios
What is the Definition of Equivalent Ratios?
Two or more ratios are equivalent if they have the same value when reduced to the lowest form. For example, 1:2, 2:4, 4:8 are equivalent ratios. All three ratios have the same value 1:2 when reduced to the simplest form.
How do you Find the Equivalent Ratios?
To find equivalent ratios of a given ratio, we either multiply the terms or divide the terms by a natural number. If the terms are co-prime (do not have any common factor other than 1), then we avoid using division operation and multiplying the terms by any natural number. For example, the equivalent ratios of 18:36 are 3:6, 1:2, 9:18, 4:8, 36:72, etc.
What are the Two Methods in Identifying Equivalent Ratios?
The two methods to identify whether the given ratios are equivalent or not are given below:
- Cross multiplication method
- HCF method
What are Three Equivalent Ratios for 3/5?
The three equivalent ratios of 3:5 are 6:10, 9:15, and 12:20. We get these by multiplying 3:5 by 2, 3, and 4 respectively.
How are Unit Rates and Equivalent Ratios Related?
Unit rates and equivalent ratios are related to each other. Unit rates can be found by using the concept of equivalent ratios. For example, if it is given that a car covers 70 miles in 2 hours. In the ratio, it can be expressed as 70:2. We can find the unit rate (distance covered in 1 hour), by finding the equivalent ratio of 70:2 such that 2 will be reduced to 1. For that, we need to multiply both the terms by 2 to get 35:1. This is the required unit rate. Similarly, we can also find equivalent ratios from a given unit rate by multiplying the terms with a natural number. This is how unit rates and equivalent ratios are related to each other.
How are Proportional Quantities Described by Equivalent Ratios?
A set of equivalent ratios represent proportional quantities. For example, we can say that 2:3 and 4:6 are in proportion. Proportion is nothing but the equality of ratios. The proportional quantities are in direct variation with each other and are represented as equivalent ratios. This is how proportional quantities can be described by equivalent ratios.
How to Find Missing Numbers in Equivalent Ratios?
To find missing values in equivalent ratios, we have to first find the multiplying factor by equating the values of antecedents and consequents, and then we find the missing number. For example, if it is given that 1:4 and x:16 are equivalent ratios and we have to ding the missing value x. Here, the values of consequents are known to us, i.e 4 and 16. We multiply 4 by 4 to get 16. So, 4 us the multiplying factor in this case. So, we will multiply the antecedent of the first ratio 1 by 4 to find x. Therefore, the value of x is 4 such that 1:4 and 4:16 are equivalent ratios.