Equivalent fractions can be identified as fractions that may have different numerators and also denominators but they represent the very same value. Because that example, 9/12 and 6/8 are tantamount fractions since both room equal come 3/4.
All tantamount fractions get decreased to the same portion in their simplest form as checked out in the over example. Explorethe givenlesson to get a far better idea of just how to find equivalent fractions and how to inspect if the given fractions are equivalent.
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|1.||What Are equivalent Fractions?|
|2.||How To uncover Equivalent Fractions?|
|3.||How to determine if 2 Fractions room Equivalent?|
|4.||Equivalent fountain Chart|
|5.||FAQs onEquivalent Fractions|
What Are identical Fractions?
Two or an ext fractions are said to be equivalent if they are equal come the same fraction when simplified. For example, the identical fractions the 1/5are5/25, 6/30, and also 4/20, which on simplification, an outcome inthe exact same fraction, that is, 1/5.
Equivalent fountain Definition:
Equivalent fractions are defined as those fractions which room equal to the same value irrespective of your numerators and denominators. Because that example, both 6/12 and 4/8 room equal come 1/2, as soon as simplified, which way they are indistinguishable in nature.
Examples of identical Fractions
Here space some instances of indistinguishable fractions.
Example:1/2, 2/4, 3/6, and also 4/8 are identical fractions.
Let us see just how their values room equal. Us will stand for each of the fractions as circles v shaded parts.
Here, we can see the the amount of shaded portion is the exact same in all the circles. Hence,1/2, 2/4, 3/6, and also 4/8are tantamount fractions.
Equivalent fractions deserve to be written by multiply or dividing both the numerator and also the denominator by the very same number. This is the factor why these fractions get reduced to the very same number once they space simplified. Let us know the two means in i m sorry we can make tantamount fractions:
Multiply the numerator and the denominator through the same number.Divide the numerator and the denominator by the same number.
1. Multiplythe Numerator and Denominator by the same Number
To discover the equivalent fractions for any kind of given fraction, multiply the numerator and the denominator by the exact same number. For example, to uncover an equivalentfraction the 3/4, multiplythe molecule 3 and the denominator 4by the exact same number, say, 2. Thus, 6/8 is an equivalent portion of 3/4. We can discover some other equivalent fractions by multiply the numerator and also the denominator that the given fraction by samenumber.3/4= (dfrac3 imes 34 imes 3) =9/123/4=(dfrac3 imes 44 imes 4) =12/163/4=(dfrac3 imes 54 imes 5) =15/20
Thus, the identical fractions the 3/4are 6/8, 9/12, 12/16, and also 15/20.
2. Dividethe Numerator and Denominator through the exact same Number
To find the tantamount fractions for any kind of given fraction, dividethe numerator and the denominator through the exact same number. Because that example, to uncover an equivalent fraction of 72/108, us will very first find their typical factors. We understand that 2is a common factor of both 72 and also 108. Hence, one equivalent fraction of 72/108 have the right to be found by dividing its numerator and also denominator by 2. Thus, 36/54 is an equivalent portion of 72/108. Let united state see exactly how the fraction is more simplified:2is a common factor the 36 and also 54. Thus, 36/54= (dfrac36 div 254 div 2)= 18/27Again, 3 is a common factor of 18 and 27. Thus, 18/27= (dfrac18 div 327 div 3)=6/9Again, 3 is a common factor of 6 and also 9. Thus, 6/9=(dfrac6 div 39 div 3)=2/3
Therefore, a fewequivalent fractions of 72/108 room 36/54, 18/27, 6/9, and also 2/3. Here, 2/3is the simplified type of 72/108 together there is no common factor (other than 1) the 2 and 3.
We have to simplify the given fractions to discover whether lock are identical or not. Leveling to gain equivalent numbers have the right to be excellent toa point where both the numerator and denominator have to still be totality numbers. There room various methods to recognize if the offered fractions are equivalent. Several of them are:
Making the platform the sameFinding the decimal type of both the fractionsCross multiplication methodVisual method
Let us determine whether 2/6 and 3/9 are equivalent fractions by each of these methods.
1. Making the denominators the Same
The platform of the fractions, 2/6 and 3/9are 6 and also 9. The LCM the the denominators 6 and 9 is 18. Let us make the denominators of both fractions 18, by multiplying them with perfect numbers.2/6=(dfrac2 imes 36 imes 3)= 6/183/9=(dfrac3 imes 29 imes 2)= 6/18
We have the right to observe thatboth the fountain are equivalent to the same portion 6/18.Thus, the offered fractions are equivalent.
Note:If the fractions space NOT equivalent, us can examine the greater or smaller fraction by looking in ~ the numerator of both the result fractions. Hence,this technique can likewise be offered for comparing fractions.
2. Detect the Decimal kind of Both the Fractions
Let us uncover the decimal type of both the fountain 2/6 and 3/9 to view if they offer the same value.2/6= 0.3333333...3/9= 0.3333333...
The decimal worths of both the fractions are the same and hence, they are equivalent.
3. Overcome Multiplication Method
To identify whether 2/6 and also 3/9 are equivalent, we cross main point them.If both the assets are the same, the fractions are equivalent.
Since both the assets here space 18, thegiven fractions room equivalent.
3. Intuitive Method
Let us represent each of the fountain 2/6 and also 3/9 pictorially on identical shapes and check if the shaded portions of both are equal.
We have the right to see that the shaded sections of both circles are equal. Hence, the given fractions space equivalent.
Charts and tables are regularly used come represent ideas in a far better way because they offer as a handy recommendation for calculations and also are simpler to understand. Anchor charts and also tables, likethe one offered below, makeit much easier for the students to understand equivalent fractions. Let united state use the adhering to chart to uncover the equivalent fractions the 1/4.
From this chart, we have the right to observe that the tantamount fractions that 1/4 are: 2/8, 3/12, 4/16,...
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