how to find equivalent decimal for a fraction

Equivalent fractions are the fractions that have dissimilar numerators and denominators just are equal to the same value. For case, 2/four and 3/six are equivalent fractions, because they both are equal to the ½. A fraction is a part of a whole. Equivalent fractions represent the same portion of the whole.

For each fraction, nosotros can notice its equivalent fraction by multiplying both numerator and denominator with the same number. For example, we take to observe the 3rd equivalent fraction of ⅔; and then nosotros have to multiply 2/3 by 3/3. Hence, 2/3 × (iii/three) = 6/nine, is the fraction equivalent to 2/three.

What are Equivalent Fractions?

Equivalent fractions land that ii or more than two fractions are said to be equal if both results the same fraction subsequently simplification. Allow us say, a/b and c/d are ii fractions, afterward 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/3 is v/15, because if we simplify v/xv, and so the resulted fraction is the aforementioned.

Equivalent Fractions example

The biggest question here tin be, why do they have equal values in spite of having different numbers?

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

Example of Equivalent Fraction

Take for an example:

i/2 = two/4 = 4/8

Simply, information technology is clearly seen that the above fractions have different numerators and denominators.

Dividing both numerator and denominator by their common gene, we take:

$\brainstorm{array}{l}\large \frac{4 \div 4}{8 \div four}\finish{assortment} $

=1/2

In the same fashion, if we simplify ii/4, once again get one/two.

$\begin{assortment}{l}\large \frac{ii\div 2}{four\div two}\end{array} $

= 1/ii

Equivalent fractions of a mixed fraction:

Permit us consider a mixed fraction to notice its equivalent fraction.

Mixed fraction = 1 ½

At present, convert this fraction into an improper fraction.

1 ½ = (i × 2 + 1)/2 = (ii + ane)/ii = iii/ii

The equivalent fractions for the higher up fraction are:

iii/2 = (iii × 2)/(2 × 2) = half dozen/4

3/ii = (iii × 3)/(2 × 3) = 9/six

iii/2 = (3 × 4)/(2 × 4) = 12/8 and so on.

How to Observe Equivalent Fractions?

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

Multiplying numerator and denominator by the aforementioned number

For case, consider the fraction 1/5

Multiplying numerator and denominator with two, we get one/5 × two/2 = 2/ten
Multiplying numerator and denominator with 3, we get 1/5 × 3/3 = 3/15
Multiplying numerator and denominator with 4, we go 1/5 × four/4 = 4/20

Therefore, we can conclude that,

1/5 = ii/10 = 3/fifteen = 4/xx

Dividing numerator and denominator by the same number

For case, nosotros need to observe the equivalent fraction of 18/32.

Find the Highest common cistron of eighteen and 32.

HCF (18, 32) = 2

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

(xviii÷2)/(32÷ii) = 9/xvi

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

Note:Nosotros can only multiply or dissever by the aforementioned numbers to get an equivalent fraction and non addition or subtraction. Simplification to get equivalent numbers can be done to a point where both the numerator and denominator should yet be whole numbers.

Equivalent Fractions Chart

Permit u.s. see the equivalent fractions for unit of measurement fractions.

Unit Fraction	Equivalent Fractions
1/2	2/four, 3/6, 4/8..
1/3	2/6, 3/ix, 4/12..
1/4	2/viii, 3/12, 4/16..
1/5	ii/10, three/fifteen, 4/twenty,..
ane/half-dozen	2/12, 3/18, 4/24,..
1/7	two/fourteen, three/21, 4/28,..
1/8	two/16, 3/24, 4/32,..
1/9	2/xviii, three/27, 4/36,..

Methods to Determine Equivalent Fractions

How tin we determine if two fractions are equivalent or not? Information technology is possible by these methods:

Method ane: Make the Denominators the same
Method 2: Cantankerous Multiply
Method 3: Convert to decimals

Method 1:

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

For case, find if 2/three and 6/ix are equivalent.

LCM of 3 and ix = 9

Multiply 2/3 past iii/3 to make the denominator equal to 9.

ii/3 × three/3 = 6/9

Hence, past making the denominators the same, we tin can run across, 2/3 and 6/nine are equivalent fractions.

Method 2:

Given, two fractions 1/ii and three/six

Cross multiply both the fractions to become:

$Equivalent fraction - Cross multiplication method$

one x 6 = vi

ii x 3 = 6

Since, both the values are equal, therefore, 1/two and three/6 are equivalent fractions.

Method iii:

If two fractions are given, we tin can simply observe their decimals to check if they are equivalent fractions.

Let united states bank check if i/iv and 3/12 are equivalent fractions by converting them in decimal form.

1/4 = 0.25

3/12 = 0.25

Since, both the fractions result in the same decimal, thus they are equivalent.

Solved Examples

Example ane: The given fractions v/xvi and 10/12 are equivalent fractions, then notice the value of ten.

Solution:

Given:5/xvi = 10/12

ten = (5 × 12)/sixteen

x = 60/16

10 =15/iv

Therefore, the value of x is 15/iv.

Example 2: Two fractions 3/5 and four/x are equivalent. Find the value of x.

Solution: Given,

three/5 = 4/x

x = (iv × 5)/iii

ten = 20/3

Example three: What fractions are the same equally ¼?

Solution: To find equivalent fractions of ¼ we need to multiply the numerator and denominator by the same numbers. Hence,

¼ × (2/2) = ii/8

¼ × (3/three) = three/12

¼ × (4/iv) = 4/sixteen

¼ × (5/5) = 5/20

And so on.

Video Lesson on Fractions

Accept persisting doubts on any topic? Try reaching out to our mentors but with BYJU'Southward – The Learning App.

Do Questions

Find the equivalent fraction of viii/10
What is the simplest class of nine/81?
Write the fraction three-sevenths equally an equivalent fraction with a denominator of 21.
Write the fraction 5-eighth equally an equivalent fraction with a denominator of 24.

Equivalent Fractions Calculator
Types of Fractions
Similar Fractions And Unlike Fractions
How to Simplify Fractions?
Comparing Fractions
Fractions Worksheets

Frequently Asked Questions on Equivalent Fractions

What are equivalent fractions?

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

What are the examples of equivalent fractions?

The examples of equivalent fractions are:
two/4 and iii/6
⅓ and iii/9
⅕ and 5/25
¾ and 12/xvi

How to decide whether fractions are equivalent?

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

What is the equivalent fraction of ⅗?

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

What are the equivalent fractions of five/10?

five/10 is equal to ½ after simplification. Hence, the equivalent fractions of 5/ten are:
½, two/4, 3/6, 4/8 and so on.

Source: https://byjus.com/maths/equivalent-fractions/

Posted by: davisinscurs36.blogspot.com