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
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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.
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:
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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.
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
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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 1:3 2:6 3:9 4:12 5:15
Related Articles on Equivalent Ratios
Check these interesting articles related to the concept of equivalent ratios.
- Comparison of Ratios
- Simplifying Ratios Calculator
- Equivalent Ratio Calculator
- Ratio
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