Is 4/8 Greater Than 1/3

Equivalent fractions are the fractions that have unlike numerators and denominators merely are equal to the aforementioned value. For case, 2/4 and 3/vi are equivalent fractions, because they both are equal to the ½. A fraction is a part of a whole. Equivalent fractions stand for the same portion of the whole.

For each fraction, we can find its equivalent fraction by multiplying both numerator and denominator with the same number. For example, we have to observe the third equivalent fraction of ⅔; so we take to multiply two/3 by 3/3. Hence, 2/3 × (iii/3) = 6/ix, is the fraction equivalent to 2/3.

What are Equivalent Fractions?

Equivalent fractions state that ii or more than 2 fractions are said to be equal if both results the aforementioned fraction afterward simplification. Let us say, a/b and c/d are two fractions, afterwards the simplification of these fractions, both result in equivalent fractions, say e/f, then they are equal to each other.

For example, the equivalent fraction of ane/iii is v/fifteen, because if nosotros simplify 5/15, and so the resulted fraction is the same.

Equivalent Fractions example

The biggest question hither can be, why exercise they accept equal values in spite of having different numbers?

The reply to this question is that, every bit the numerator and denominator are not co-prime number numbers, therefore they have a common multiple, which on segmentation gives exactly the same value.

Instance of Equivalent Fraction

Have for an case:

1/two = 2/4 = 4/8

But, information technology is conspicuously seen that the above fractions have different numerators and denominators.

Dividing both numerator and denominator by their mutual factor, nosotros have:

$\begin{array}{l}\frac{4 \div 4}{viii \div 4}=\frac{one}{2}\end{array} $

In the same manner, if we simplify 2/4, again get one/2.

$\begin{assortment}{l}\frac{2\div 2}{iv\div ii}=\frac{1}{ii}\stop{array} $

Equivalent fractions of a mixed fraction:

Let united states of america consider a mixed fraction to detect its equivalent fraction.

Mixed fraction = 1 ½

Now, convert this fraction into an improper fraction.

1 ½ = (one × 2 + 1)/2 = (ii + one)/2 = 3/2

The equivalent fractions for the in a higher place fraction are:

3/ii = (three × 2)/(2 × 2) = six/4

3/two = (three × 3)/(2 × 3) = 9/vi

three/2 = (3 × 4)/(two × four) = 12/8 and so on.

How to Find Equivalent Fractions?

Equivalent fractions are evaluated past multiplying or dividing both the numerator and the denominator past the same number. Therefore, equivalent fractions, when reduced to their simplified value, will all be the same.

Multiplying numerator and denominator by the aforementioned number

For example, consider the fraction 1/5

Multiplying numerator and denominator with 2, we get 1/5 × 2/2 = 2/10
Multiplying numerator and denominator with 3, nosotros get 1/5 × 3/3 = three/15
Multiplying numerator and denominator with 4, we become i/5 × 4/4 = 4/20

Therefore, we can conclude that,

ane/five = 2/x = 3/15 = four/20

Dividing numerator and denominator by the same number

For case, we demand to discover the equivalent fraction of 18/32.

Find the Highest common cistron of xviii and 32.

HCF (18, 32) = 2

Now divide the numerator and denominator past 2, to become the equivalent fraction of xviii/32.

(18÷ii)/(32÷2) = 9/16

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

Annotation:We can only multiply or divide past the same numbers to get an equivalent fraction and not addition or subtraction. Simplification to get equivalent numbers tin can be done to a indicate where both the numerator and denominator should still be whole numbers.

Equivalent Fractions Nautical chart

Let u.s. run across the equivalent fractions for unit fractions.

Unit Fraction	Equivalent Fractions
i/2	2/iv, 3/half dozen, 4/8..
i/3	2/half-dozen, 3/9, 4/12..
1/4	two/viii, 3/12, four/sixteen..
1/v	2/ten, 3/15, 4/20,..
1/six	2/12, 3/18, 4/24,..
1/7	two/14, 3/21, 4/28,..
1/8	ii/16, 3/24, four/32,..
1/9	ii/18, three/27, four/36,..

Methods to Make up one's mind Equivalent Fractions

How tin can we determine if ii fractions are equivalent or not? It is possible by these methods:

Method 1: Make the Denominators the same
Method ii: Cross Multiply
Method three: Convert to decimals

Method one:

Past making the denominators the same, we can evaluate if two fractions are equivalent.

For example, discover if ii/three and 6/9 are equivalent.

LCM of 3 and nine = 9

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

2/three × 3/3 = 6/ix

Hence, by making the denominators the same, we can encounter, two/three and 6/9 are equivalent fractions.

Method 2:

Given, 2 fractions ane/2 and iii/6

Cantankerous multiply both the fractions to get:

$Equivalent fraction - Cross multiplication method$

one x 6 = half dozen

2 x 3 = half-dozen

Since, both the values are equal, therefore, 1/2 and 3/half dozen are equivalent fractions.

Method iii:

If 2 fractions are given, nosotros can simply find their decimals to check if they are equivalent fractions.

Let us check if 1/4 and three/12 are equivalent fractions by converting them in decimal form.

one/iv = 0.25

3/12 = 0.25

Since, both the fractions effect in the aforementioned decimal, thus they are equivalent.

Solved Examples

Example 1: The given fractions v/16 and x/12 are equivalent fractions, so find the value of x.

Solution:

Given:5/xvi = 10/12

ten = (five × 12)/xvi

x = 60/16

x =15/four

Therefore, the value of x is fifteen/4.

Example two: Two fractions 3/5 and 4/x are equivalent. Discover the value of x.

Solution: Given,

3/v = 4/ten

x = (4 × 5)/3

x = xx/iii

Example 3: What fractions are the same equally ¼?

Solution: To notice equivalent fractions of ¼ we demand to multiply the numerator and denominator past the same numbers. Hence,

¼ × (2/2) = 2/8

¼ × (iii/3) = 3/12

¼ × (4/4) = iv/sixteen

¼ × (5/v) = five/20

And so on.

Video Lesson on Fractions

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Practice Questions

Discover the equivalent fraction of 8/10
What is the simplest grade of 9/81?
Write the fraction three-sevenths every bit an equivalent fraction with a denominator of 21.
Write the fraction five-eighth as an equivalent fraction with a denominator of 24.

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Frequently Asked Questions on Equivalent Fractions

What are equivalent fractions?

Ii or more fractions that have different numerators and denominators but consequence in the same value later on simplification are said to be equivalent fractions.

What are the examples of equivalent fractions?

The examples of equivalent fractions are:
2/four and 3/6
⅓ and 3/9
⅕ and five/25
¾ and 12/16

How to determine whether fractions are equivalent?

We demand to simplify the given fractions to find whether they are equivalent or not. Suppose 3/nine and ⅔ are two fractions. 3/9 tin can exist further simplified to ⅓, just ⅓ is non equal to ⅔. Therefore, they are not equivalent.
But, ⅚ and ten/12 are equivalent fractions because 10/12 = ⅚.

What is the equivalent fraction of ⅗?

To observe the equivalent fraction of ⅗, we demand to multiply both numerator and denominator by the aforementioned number. Hence,
⅗ × (ii/2) = 6/10

What are the equivalent fractions of 5/10?

v/x is equal to ½ after simplification. Hence, the equivalent fractions of 5/x are:
½, ii/4, three/6, 4/eight and so on.