Equivalent fractions space the fractions that have different numerators and denominators but are equal to the same value. For example, 2/4 and 3/6 are identical fractions, because they both space equal to the ½. A portion is a component of a whole. Indistinguishable fractions stand for the very same proportion the the whole. 

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


Table of contents:Definition

What are equivalent Fractions?

Equivalent fountain state that two or more than 2 fractions are claimed to be equal if both outcomes are the same portion after simplification. Let us say, a/b and also c/d room two fractions, after ~ the leveling of this fractions, both an outcome in tantamount fractions, say e/f, then they room equal to every other.

You are watching: What fraction is equivalent to 2/3

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

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The best question here can be, why do they have actually equal values regardless of having different numbers?

The answer come this inquiry is that, together the numerator and also denominator are not co-prime numbers, because of this they have actually a common multiple, i m sorry on department gives precisely the exact same value.

Example of indistinguishable Fraction

Take for an example:

1/2 = 2/4 = 4/8

But, the is clearly seen the the above fractions have various numerators and denominators.

Dividing both numerator and also denominator by their common factor, we have:

(large frac4 div 48 div 4)

=1/2

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

(large frac2div 24div 2)

= 1/2

How to find Equivalent Fractions?

Equivalent fractions room evaluated by multiply or splitting both the numerator and also the denominator by the very same number. Therefore, indistinguishable fractions, when decreased to their simplified value, will certainly all be the same.

Multiplying numerator and also denominator by exact same number

For example, consider the portion 1/5

Multiplying numerator and also denominator v 2, we obtain 1/5 x 2/2 = 2/10Multiplying numerator and denominator v 3, we acquire 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 need to discover the equivalent portion of 18/32.

Find the Highest typical factor that 18 and 32.

HCF (18, 32) = 2

Now division the numerator and denominator by 2, to acquire the equivalent fraction of 18/32.

(18÷2)/(32÷2) = 9/16

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

Note: We can only multiply or division by the very same numbers to acquire an equivalent portion and not enhancement or subtraction. Leveling to acquire equivalent numbers can be done to a suggest where both the numerator and denominator have to still be entirety numbers.

Equivalent fractions Chart

Let us see the indistinguishable fractions because that 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 identify Equivalent Fractions

How can we recognize if 2 fractions are identical or not? that is feasible by these methods:

Method 1: do the denominators sameMethod 2: cross MultiplyMethod 3: transform to decimals

Method 1:

By make the denominators same, we can evaluate if two fractions are equivalent.

For example, find if 2/3 and also 6/9 are equivalent.

LCM that 3 and 9 = 9

Multiply 2/3 by 3/3 to do the denominator same to 9.

2/3 x 3/3 = 6/9

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

Method 2: 

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

Cross multiply both the fractions to get:

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1 x 6 = 6

2 x 3 = 6

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

Method 3: 

If two fractions are given, we can simply discover their decimals to check if castle are equivalent fractions.

Let us examine if 1/4 and 3/12 are identical fractions by converting them in decimal form.

1/4 = 0.25

3/12 = 0.25

Since, both the fractions results in the exact same decimal, thus they space equivalent.

Solved Examples

Example 1: The provided fractions 5/16 and x/12 are equivalent fractions, then uncover the value of x.

Solution:

Given: 5/16 = x/12

x = (5 x 12)/16

x = 60/16

x =15/4

Therefore, the worth of x is 15/4.

Example 2: two fractions 3/5 and 4/x space equivalent. Find the value 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 uncover equivalent fractions of ¼ we should multiply the numerator and also denominator by 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 therefore on.

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

Answer: To uncover the 4th equivalent portion of ¾, we have to multiply numerator and also denominator through 4. Hence,

¾ x (4/4) = 12/16

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Practice Questions

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

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