How to check if Two Fractions are Equivalent?
We can check whether two fractions are equivalent or not by using the three methods that include,
- Make Denominators of both fraction Equal
- Determining decimal form of both Fractions
- Cross Multiplication Method
Now let’s learn about each method in detail.
Making Denominators Equal
We can check whether the given fractions are equivalent by just making their denominator equal. And if they have an equal denominator along with an equal numerator they are equivalent fractions.
Example: Find if 4/10 and 6/15 are equivalent fractions or not.
Solution:
LCM of 10 and 15 is 30.
Multiply 4/10 by 3/3 and 6/15 by 2/2 to make their denominators equal to 30.
4/10 Ă— 3/3 = 12/30
6/15 Ă— 2/2 = 12/30
Now comparing two fractions we get that the denominator and the numerator of both the fractions are equal and hence, they are equivalent fratcion.
Note: If the fractions are NOT equivalent, we can check the greater or smaller fraction by looking at the numerator of both the resultant fractions in which denominators are equal. Hence, this method can also be used for comparing fractions.
Determining Decimal form of both Fractions
By finding the decimals of the given fractions, we can check whether they are equivalent or not. If the decimal form of both fractions is equal they are equivalent fractions and if the decimal form of both the fraction is not equal they are not equivalent fractions.
Example: Find if 3/4, 6/8, and 12/16 are equivalent fractions or not.
Solution:
Decimal form of all the fractions is,
3/4 = 0.25
6/8 = 0.25
12/16 = 0.25
As the decimal values of the given fractions are the same, the given fractions are equivalent.
Cross Multiplication method
To identify whether two fractions are equivalent or not, cross-multiplication is also used. The fractions are equivalent if both the products of the cross multiplication are the same.
Example: Find if 3/6 and 4/8 are equivalent fractions or not.
Solution:
The given fractions are equivalent as both the products of cross multiplication are 24.
Visual Method
Using the visual method we can easily find whether two fractions are equivalent or not as equivalent fractions represent the same shaded value in their visual structure. Such as 1/2 and 2/4 as shown in the image below both represent half of the value of any disc and thus they are equivalent fractions.
We simply observe the shaded portion of the given fractions and if they are equal our fraction is equivalent.
Read More,
Equivalent Fractions
Equivalent Fractions are the fractions that represent the same value and by simplifying the fraction in simplest form we always get the same fraction. We define the fraction as a way of representing a part of some quantity. Suppose we have one pizza with six equal sizes and Shiv takes two slices from it then the remaining pizza is represented as, 4/6 which is equivalent fraction to 2/3. The various other examples of equivalent fractions are 1/3, 2/6, 3/9, and others.
The simplest form of all the equivalent fractions is the same, i.e. if all the equivalent fraction is reduced to the simplest term then they all are the same. For example, the simplest form of 1/3, 2/6, and 3/9 is 1/3. Let’s learn more about equivalent fractions, its example, and others in detail in this article.