Equivalent Ratios

In mathematics, a ratio is a phrase used to compare two or more numbers. It’s a metric for determining how large or little a quantity is in contrast to another. In a ratio, two quantities are compared by dividing them.The dividend is referred to as the ‘antecedent,’ whereas the divisor is referred to as the ‘consequent.’

The term “equivalent ratio” refers to a ratio that can be simplified to the same value. In other words, if one ratio can be stated as a multiple of the other, they are deemed comparable.

Equivalent Ratios:-

“Two or more ratios that reflect the same relation or comparison of numbers are known as equivalent ratios,” according to the definition of the equivalent ratio in arithmetic. It works in a similar way to equivalent fractions. Proportion refers to the equality of two ratios. Althohe antecedent and consequent values differ, when reduced to their most basic form, they yield the same result.

For example, To determine whether 2:3 and 16:24 are equal ratios,  we must reduce both ratios to their most basic form. Because the HCF of 2 and 3 = 1, 2:3 is already in its simplest form. 16 and 24 have an HCF of 8. To determine the reduced version, divide both of these numbers by 8. This means that (16/8):(24/8) = 2:3. It is obvious that 2:3 and 16:24 provide the same effect, hence they are similar ratios.

Equivalent Ratios Evaluation :-

When it comes to finding equivalent ratios, you may encounter two scenarios. The first is to examine and identify whether or not the given ratios are equivalent, and the second is to find equivalent ratios of a particular ratio. Let’s take each one in turn.

To find a ratio that is comparable to a given ratio, we must first represent it in fraction form. The equivalent fraction can then be obtained by multiplying or dividing the first and second terms by the same non-zero value. Finally, we represent it as a ratio.

There are two approaches for determining whether or not the given ratios are equivalent: the cross multiplication method and the HCF method. To find analogous ratios using the cross multiplication approach, follow the steps below:

Step 1 :- Writing the given ratio in the fractional form. ( Numerator over denominator)

Step 2 :- Do the cross multiplication.

Step 3 :- When both the products are same, then it means that they are in equivalent ratio.

Using the another process, let’s look at the HCF approach for determining equivalent ratios.

Step 1 :- Calculate the HCF of both the antecedent and consequent ratios.

Step 2 :- Divide each ratios’ terms by their respective HCF.

Step 3 :- If both ratios have the same reduced form, they are equivalent.

Equivalence Ratio Table :-

We can multiply any natural number to both components of a ratio to find its equivalents, hence there are an endless number of equivalent ratios for a given ratio. An equivalent ratio table is a table that shows some of the equivalent ratios of a particular ratio in a format that is easy to grasp. 

We can also create a table of equivalent ratios for any ratio. Let’s take the ratio 2:3 and multiply it by several natural integers starting at 2 to get its corresponding ratios. It’s worth noting that, whenever possible, we can split the terms of a ratio by their common factor to discover analogous ratios.

  2:3 = (2×2):(3×2) = 4:6

  2:3 = (2×3):(3×3) = 6:9

  2:3 = (2×4):(3×4) = 8:12

  2:3 = (2×5):(3×5) = 10:15

And so on…..

Example:- The relationship between the two halves of the ratios did not change, the ratios 40/1 and 80/2 are equivalent. You drive 40 miles for every hour you drive, according to the 40/1 ratio. When we write 80/2, the connection between the two numbers remains the same. You’re still averaging 40 miles per hour on the road. However, since you’ve been driving for 2 hours, you’ve covered 80 miles. Even if the numbers in 80/2 are different from those in 40/1, they nevertheless express the same distance-time connection.

Conclusion:-

Equivalent-ratios is a ratio formed by multiplying or dividing the numerator and denominator of a given ratio by the same number. Equivalent ratios are those that may be reduced to the same value by dividing both antecedent and consequent values by a common fraction. 

To put it another way, two ratios are deemed comparable if the larger one can be stated as a multiple of the smaller one. As a result, all we have to do to acquire the equivalent ratio of another ratio is multiply the two quantities by the same number. Comparable ratios and equivalent fractions are two concepts that are related.

We’ve learnt that in order to determine equivalent ratios for a given ratio, we must first put it in fraction form. The numerator and denominator of a fraction will then be multiplied by the same non-zero value. The equivalent ratio of a particular ratio has no effect on the ratio’s value.