In this article, you will learn about Equivalent Ratios. In order to understand more, you need to look at the equivalent ratios examples that would help you in getting the right idea on how to find equivalent ratios. Equivalent ratios are ratios that can be simplified or reduced to the same value. In other words, two ratios are equivalent if one can be expressed as a multiple of the other. Some of the equivalent ratios examples are 1:2 and 4:8, 3:5 and 12:20, 9:4 and 18:8, etc.
On this page, we will learn about the definition of Equivalent Ratios, how to find equivalent ratios, some solved example problems on equivalent ratios, and so on.
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Equivalent Ratios – Definition
A ratio that is obtained by dividing or multiplying the numerator and denominator of a ratio by the same number is known as an Equivalent Ratio. The equivalent ratio is similar to the concept of Equivalent Fractions. The equivalence of two ratios is also known as proportion. If the antecedent and consequent values are different, but still, if we reduce them to the simplest form, we will get the same value.
Consider an 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. So, the value 2:3 is already in simplest form and the HCF of 2 and 3 is 1. Next, the HCF of 16 and 24 is 8. Now, divide both these numbers by 8 to get the reduced form. This implies (16÷8):(24÷8) = 2:3. It says that 2:3 and 16:24 result in the same value, therefore they are equivalent ratios.
Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities that are antecedent and consequent by the same number. This Equivalent ratio method is similar to the method of finding equivalent fractions.
How to Find Equivalent Ratios?
In order to find equivalent ratios, we need to make a multiplication or division of both the terms of the given ratio which needs to be done by the same non-zero number. It is important to learn how to determine the equivalent ratios of a ratio by writing the ratio in the form of fractions. When it comes to finding equivalent ratios, two cases might come up. 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.
We have two methods to check whether the given ratios are equivalent are not. The two methods are the cross multiplication method and the HCF method.
Follow the steps given below to find equivalent ratios using the cross multiplication method:
(i) Find whether the ratios 10:8 and 30:24 are equivalent ratios or not.
- Step 1:Â Write both the ratios in the form of fractional that is numerator over the denominator.
- Step 2: Next, perform the cross multiplication. So, multiply 10 by 24 and 8 by 30.
- Step 3: Then if both the products are equal, it means they are equivalent ratios. Here 10 × 24 = 240 and 8 × 30 = 240.
Therefore, they are equivalent ratios.
(ii) Now, let us observe the HCF method for identifying equivalent ratios using the same example.
- Step 1: First, find the HCF of the antecedent and consequent of both ratios. Here, the HCF (10, 8) is 2, and the HCF (30, 24) is 6.
- Step 2: Now, Divide both the terms in 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 are equivalent ratios.
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Equivalent Ratios Examples with Solutions
Problem 1: Find the value of x and y using the ratio value of 12:20.
Solution:
As given in the question the ratio value is 12:20.
Now, we need to find the values of x and y.
First, let us consider the two ratios that are,
12/20 = x/5Â = 12×5 = 20x x
60 = 20 x
x = 60/20 = 30.
Hence, the value of x is 30.
Next, in order to find the value of y. We have to consider the 1st and 3rd ratios.
Here it will be, 12/20 = 9/y
12y = 20×9 = 12y = 180
y= 180/12 = 15
Therefore, the value of y is 15.
Problem 2: What are the two equivalent ratios of 10: 11?
Solution:
Given in the question, the ratio value is 10:11.
Now, we need to find the two equivalent values.
To write the equivalent ratios of a given ratio, we can multiply the terms by any natural number starting from 2.
So, we can divide as well if the terms are not co-prime numbers. Here 10 and 11 are co-primes.
Let us multiply them by 2 and 3 to find their equivalents.
The values are,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.
Problem 3: The ratios are 15:10 and 30:15. Check whether the given ratios are equivalent or not?
Solution:
As given in the question, the ratios are 15:10 and 30:15.
Now, we need to find whether the given ratios are equivalent or not.
Let us use the cross multiplication method, we can write these ratios are 15/10 and 30.15.
Now, we will multiply 15 by 15 and 10 by 30. We get,
15 × 15 = 225
10 × 30 = 300.
Here, 225 is not equal to 300.
Therefore, the ratios 15:10 and 30:15 are not equivalent ratios.
Problem 4: What will be the value of x. If 2:3 is equivalent to 10:x?
Solution:
In the given question, the ratios are 2:3 and 10:x.
Now, we will find the value of x.
It says that we have to multiply 2:3 with a natural number such that the answer will be in the form of 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. That means we will have to multiply 3 with 15.
So, it will be 2:3 = (2×5):(3×5) = 10:15.
Then the value of x is 15.
Therefore, 2:3 and 10:15 are equivalent ratios, and the required value of x is 15.
Problem 5: Are the ratios 1:2 and 2:3 are Equivalent?
Solution:Â
As given in the question, the ratios are 1:2 and 2:3.
Now, to check the given ratios are equivalent or not.
The values 1:2 and 2:3 are rewritten as 1/2 = 2/3.
So, we have 1/2 = 1×3/ 2×3 = 3/6. ​
Next, the value 2/3 = 2×2/3×2 = 4/6.​
We will find that 3/6<4/6 2 which means 1/2 is less than 2/3.​
Thus, the ratio of 1/2 is not equivalent to the ratio of 2/3.
FAQs on Equivalent Ratios
1. What are Equivalent Ratios?
The Equivalent Ratios states that when the comparison of two different ratios is the same, then such ratios are called Equivalent Ratios.
2. How do we find the Equivalent Ratio?
In order to find equivalent ratios, we need to make a multiplication or division of both the terms of the given ratio which needs to be done by the same non-zero number. It is important to learn how to determine the equivalent ratios of a ratio by writing the ratio in the form of fractions. It again needs to be compared by using multiplication and division.
3. What is the difference between Equivalent Ratios and Equivalent Fractions?
Equivalent ratios means are ratios that are express the same relationship between two numbers. Equivalent Fractions are two fractions that are equivalent they have the same value.
4. How can we find the Equivalent Ratio of 6:4?
To find the equivalent ratio of 6:4, first, convert the ratio into a fraction and then multiply and divide the fraction by a common factor.
So, it is 6:4 = 6/4 x (2/2) = 12/8
Thus, 12/8 is equivalent to 6:4.