Equivalent fractions space the fractions that have various numerators and denominators yet are equal to the exact same value. For example, 2/4 and also 3/6 are identical fractions, because they both room equal to the ½. A fraction is a component of a whole. Identical fractions represent the same proportion the the whole. 

For every fraction, us can uncover its equivalent portion by multiplying both numerator and also denominator through the very same number. For example, we have actually to discover the third equivalent portion of ⅔; climate we have to multiply 2/3 through 3/3. Hence, 2/3 x (3/3) = 6/9, is the portion equivalent to 2/3. 


Table of contents:Definition

What are tantamount Fractions?

Equivalent fractions state that 2 or much more than 2 fractions are claimed to be same if both results are the same portion after simplification. Let united state say, a/b and also c/d space two fractions, after the leveling of these fractions, both result in tantamount fractions, to speak e/f, climate they space equal to each other.

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For example, the equivalent portion of 1/3 is 5/15, because if we simplify 5/15, climate the resulted portion is the same.

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The best question here have the right to be, why carry out they have actually equal values despite having different numbers?

The answer to this question is that, as the numerator and also denominator are not co-prime numbers, because of this they have actually a common multiple, i beg your pardon on division gives specifically the exact same value.

Example of identical Fraction

Take for an example:

1/2 = 2/4 = 4/8

But, that is plainly seen that the over fractions have different numerators and denominators.

Dividing both numerator and denominator through their common factor, us have:

(large frac4 div 48 div 4)

=1/2

In the very same way, if we leveling 2/4, again obtain 1/2.

(large frac2div 24div 2)

= 1/2

How to discover Equivalent Fractions?

Equivalent fractions space evaluated by multiplying or dividing both the numerator and the denominator through the very same number. Therefore, equivalent fractions, when reduced to their simplified value, will all it is in the same.

Multiplying numerator and denominator by exact same number

For example, take into consideration the portion 1/5

Multiplying numerator and denominator with 2, we obtain 1/5 x 2/2 = 2/10Multiplying numerator and also denominator through 3, we get 1/5 x 3/3 = 3/15Multiplying numerator and also denominator v 4, we get 1/5 x 4/4 = 4/20

Therefore, we can conclude that,

1/5 = 2/10 = 3/15 = 4/20

Dividing numerator and also denominator by very same number

For example, we require to discover the equivalent portion of 18/32.

Find the Highest typical factor of 18 and 32.

HCF (18, 32) = 2

Now division the numerator and also denominator by 2, to get the equivalent portion of 18/32.

(18÷2)/(32÷2) = 9/16

Hence, 9/16 is identical to 18/32.

Note: We deserve to only main point or division by the exact same numbers to obtain an equivalent portion and not enhancement or subtraction. Simplification to acquire equivalent numbers can be excellent to a point where both the numerator and denominator should still be whole numbers.

Equivalent fountain Chart

Let united state see the equivalent fractions for unit fractions.


Unit FractionEquivalent Fractions
1/22/4, 3/6, 4/8..
1/32/6, 3/9, 4/12..
1/42/8, 3/12, 4/16..
1/52/10, 3/15, 4/20,..
1/62/12, 3/18, 4/24,..
1/72/14, 3/21, 4/28,..
1/82/16, 3/24, 4/32,..
1/92/18, 3/27, 4/36,..

Methods to recognize Equivalent Fractions

How deserve to we recognize if 2 fractions are indistinguishable or not? the is feasible by this methods:

Method 1: make the platform sameMethod 2: cross MultiplyMethod 3: convert to decimals

Method 1:

By make the platform same, we have the right to evaluate if 2 fractions room equivalent.

For example, uncover if 2/3 and 6/9 room equivalent.

LCM of 3 and also 9 = 9

Multiply 2/3 by 3/3 to make the denominator equal to 9.

2/3 x 3/3 = 6/9

Hence, by do the denominators same, we have the right to see, 2/3 and also 6/9 are indistinguishable fractions.

Method 2: 

Given, two fractions 1/2 and also 3/6

Cross main point both the fountain to get:

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1 x 6 = 6

2 x 3 = 6

Since, both the values space equal, therefore, 1/2 and 3/6 are identical fractions.

Method 3: 

If two fractions are given, we have the right to simply discover their decimals to check if lock are equivalent fractions.

Let us examine if 1/4 and also 3/12 are indistinguishable fractions by convert them in decimal form.

1/4 = 0.25

3/12 = 0.25

Since, both the fractions outcomes in the same decimal, for this reason they space equivalent.

Solved Examples

Example 1: The given fractions 5/16 and x/12 are identical fractions, then discover the value of x.

Solution:

Given: 5/16 = x/12

x = (5 x 12)/16

x = 60/16

x =15/4

Therefore, the value of x is 15/4.

Example 2: 2 fractions 3/5 and also 4/x room equivalent. Uncover the worth of x.

Solution: Given,

3/5 = 4/x

x = (4 x 5)/3

x = 20/3

Example 3: What fractions are very same as ¼?

Solution: To find equivalent fountain of ¼ we must multiply the numerator and denominator through the same numbers. Hence,

¼ x (2/2) = 2/8

¼ x (3/3) = 3/12

¼ x (4/4) = 4/16

¼ x (5/5) = 5/20

And so on.

Example 4: What is the fourth equivalent portion of ¾?

Answer: To discover the fourth equivalent fraction of ¾, we must multiply numerator and also denominator by 4. Hence,

¾ x (4/4) = 12/16

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Practice Questions

Find the equivalent fraction of 8/10What is the simplest type of 9/81?Write the portion three-sevenths as an equivalent fraction with a denominator of 21.Write the portion five-eighth together an equivalent fraction with a denominator the 24.

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