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Equivalent fractions are fractions that have different numerators and denominators but are equal to the same value. For example, 6/14 and 9/27 both are equivalent fractions as their decimal value (0.429) are the same. 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, their examples, and others in detail in this article. Table of Content What are Equivalent Fractions?Equivalent fractions are defined as fractions that have the same value but have different numerators and denominators. For instance, 3/9, 4/12, 5/15, and 6/18 are equivalent fractions as their values in the simplest form is 1/3. Equivalent fractions indicate the same portion of the whole value. We can find an equivalent fraction for every fraction by multiplying or dividing both the numerator and the denominator with the same number. Equivalent Fractions Definition
Equivalent Fractions ExamplesWe represent the equivalent fraction as the fraction which results in the same value but it is interesting to note that they represent the same value when represented graphically. We can understand with the help of the following example. Suppose we have to distribute a chapatti in two equal parts then each part is represented using a 1/2 fraction. Now, we distribute the similar chapatti into four parts a take two out of them which is represented as 2/4, similarly if the chapati is broken into six parts and out of which three parts are taken which is represented as 3/6 and lastly if it is broken into eight parts and out of which four parts are taken then we represent this fraction as 4/8. Here in the above example, we see that all the fraction represents half of all the values, and thus all are equivalent fractions. The image added below represent the equivalent fraction of 1/2. Equivalent Fractions Examples Here, 1/2 = 2/4 = 3/6 = 4/8 all are equivalent fractions and their simplest form is 1/2. How to Find Equivalent Fractions?For every fraction, we can determine an equivalent fraction either by multiplying or dividing both the numerator and the denominator with the same number. That’s why when all equivalent fractions are simplified, they are reduced to the same fraction. We have two ways of finding the equivalent fraction of any number,
Multiplying Numerator and Denominator by Same NumberFor every fraction, we can determine an equivalent fraction by multiplying both the numerator and the denominator with the same number. For instance, to determine the equivalent fraction of 2/3, multiply both the numerator and the denominator with the same number, i.e., 2. Thus, the equivalent fraction of 2/3 is 4/6. Similarly, we can find some other equivalent fractions by repeating the same process. Equivalent fractions of 2/3
Hence, we can conclude that equivalent fractions of 2/3 are 4/6, 8/12, and 10/15 Dividing Numerator and Denominator by Same NumberFor every fraction, we can determine an equivalent fraction by dividing both the numerator and the denominator by the same number. For instance, to find the equivalent fraction of 45/300, first, we have to find their common factors. Here, 3 is a common factor of both 45 and 300. So, the equivalent fraction of 45/300 can be found by dividing its numerator and denominator by 3. Thus, the equivalent fraction of 45/300 is 15/100. Let us simplify the fraction further. 5 is a common factor of 15 and 100. So, 15/100 = (15÷5)/(100÷5) = 3/20 Hence, the equivalent fractions of 45/300 are 15/100 and 3/20. As there are no common factors for 3 and 20 other than 1, 3/20 is the simplified form of 45/300. Equivalent Fractions ChartThe chart that represents the equivalent fraction of any quantity is called the equivalent fraction chart. The chart added below represents the equivalent fraction of 1, 1/3, 1/6, etc.  Equivalent Fractions Chart From the given chart, we can observe that the equivalent fractions of 1/3 are 2/6, 4/12, 8/24,… Now, let us see the equivalent fractions of some unit fractions.
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,
Making Denominators EqualWe 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:
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 FractionsBy 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:
Cross Multiplication MethodTo 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:
Visual MethodUsing 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.  Visual Method We simply observe the shaded portion of the given fractions and if they are equal our fraction is equivalent. Read More, Equivalent Fractions ExamplesExample 1: Find “a” if 10/21 and a/16 are equivalent fractions. Solution:
Example 2: Find the value of “x” if 5/36 and x/9 are equivalent fractions. Solution:
Example 3: Find if 5/9 and 11/15 are equivalent fractions or not. Solution:
Example 4: What are the equivalent fractions of 7/8? Solution:
Example 5: What is its denominator, if the numerator of a fraction equivalent to 6/24 is 14? Solution:
Practice Questions on Equivalent FractionsQ1. Find an equivalent fraction for 3/4 by multiplying the numerator and the denominator by 2. Q2. Determine if 2/3 and 8/12 are equivalent fractions. Q3. Simplify the fraction 18/24 to its simplest form. Q4. Find an equivalent fraction for 5/6 by multiplying the numerator and the denominator by 3. Q5. Determine if 7/8 and 21/24 are equivalent fractions. Q6. Find two equivalent fractions for 4/5. FAQs on Equivalent FractionsWhat are Equivalent Fractions?
What are Examples of Equivalent Fractions?
How to Find Equivalent Fractions?
How to Determine whether Fractions are Equivalent?
What are Equivalent Fractions of 1/7?
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Reffered: https://www.geeksforgeeks.org
| School Chemistry |
Type: | Geek |
Category: | Coding |
Sub Category: | Tutorial |
Uploaded by: | Admin |
Views: | 11 |