Is 1/4 And 3/12 Equivalent

Equivalent fractions are the fractions that have different numerators and denominators merely are equal to the same value. For example, ii/4 and iii/6 are equivalent fractions, because they both are equal to the ½. A fraction is a part of a whole. Equivalent fractions correspond the same portion of the whole.

For each fraction, we tin can detect its equivalent fraction past multiplying both numerator and denominator with the same number. For case, we have to detect the third equivalent fraction of ⅔; then we have to multiply 2/3 past 3/iii. Hence, 2/three × (3/3) = 6/9, is the fraction equivalent to ii/3.

What are Equivalent Fractions?

Equivalent fractions state that two or more than than two fractions are said to be equal if both results the same fraction after simplification. Let usa say, a/b and c/d are two fractions, after the simplification of these fractions, both effect in equivalent fractions, say e/f, so they are equal to each other.

For example, the equivalent fraction of 1/three is 5/15, considering if nosotros simplify v/15, so the resulted fraction is the same.

Equivalent Fractions example

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

The answer to this question is that, as the numerator and denominator are non co-prime numbers, therefore they have a common multiple, which on segmentation gives exactly the aforementioned value.

Case of Equivalent Fraction

Take for an instance:

ane/2 = 2/4 = iv/8

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

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

$\brainstorm{array}{50}\frac{4 \div 4}{8 \div iv}=\frac{1}{2}\end{assortment} $

In the same way, if we simplify ii/four, once more get 1/two.

$\brainstorm{assortment}{l}\frac{2\div two}{4\div 2}=\frac{1}{2}\end{array} $

Equivalent fractions of a mixed fraction:

Let us consider a mixed fraction to discover its equivalent fraction.

Mixed fraction = i ½

Now, convert this fraction into an improper fraction.

1 ½ = (1 × 2 + 1)/2 = (two + 1)/2 = 3/2

The equivalent fractions for the above fraction are:

3/two = (three × two)/(2 × 2) = 6/4

3/2 = (3 × three)/(2 × 3) = 9/6

three/2 = (3 × iv)/(2 × iv) = 12/8 and so on.

How to Observe Equivalent Fractions?

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

Multiplying numerator and denominator by the aforementioned number

For example, consider the fraction i/v

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

Therefore, nosotros can conclude that,

one/v = ii/10 = 3/15 = 4/20

Dividing numerator and denominator past the same number

For example, we demand to find the equivalent fraction of 18/32.

Find the Highest common cistron of 18 and 32.

HCF (18, 32) = 2

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

(18÷2)/(32÷2) = ix/16

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

Notation:Nosotros can only multiply or split up by the aforementioned numbers to get an equivalent fraction and non improver or subtraction. Simplification to become equivalent numbers tin can be done to a point where both the numerator and denominator should still be whole numbers.

Equivalent Fractions Chart

Let united states see the equivalent fractions for unit fractions.

Unit Fraction	Equivalent Fractions
ane/2	2/4, 3/6, 4/8..
one/3	2/6, 3/9, 4/12..
1/iv	ii/8, 3/12, iv/16..
1/5	2/x, 3/15, 4/xx,..
1/6	2/12, iii/xviii, iv/24,..
1/7	2/xiv, three/21, 4/28,..
ane/eight	2/16, three/24, 4/32,..
1/9	two/xviii, three/27, 4/36,..

Methods to Determine Equivalent Fractions

How can we determine if two fractions are equivalent or not? It is possible past these methods:

Method 1: Make the Denominators the aforementioned
Method 2: Cantankerous Multiply
Method three: Catechumen to decimals

Method 1:

By making the denominators the same, we can evaluate if 2 fractions are equivalent.

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

LCM of iii and 9 = 9

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

2/3 × 3/3 = 6/9

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

Method 2:

Given, two fractions 1/ii and 3/6

Cantankerous multiply both the fractions to get:

$Equivalent fraction - Cross multiplication method$

1 x 6 = vi

2 x 3 = 6

Since, both the values are equal, therefore, 1/ii and 3/6 are equivalent fractions.

Method 3:

If two fractions are given, we can merely find their decimals to check if they are equivalent fractions.

Let united states of america check if ane/four and 3/12 are equivalent fractions by converting them in decimal form.

1/4 = 0.25

3/12 = 0.25

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

Solved Examples

Example 1: The given fractions 5/xvi and x/12 are equivalent fractions, and then find the value of x.

Solution:

Given:five/16 = x/12

10 = (5 × 12)/xvi

ten = 60/sixteen

ten =15/iv

Therefore, the value of x is 15/4.

Example ii: Two fractions three/five and iv/x are equivalent. Find the value of 10.

Solution: Given,

3/5 = four/ten

x = (4 × five)/3

x = 20/3

Example 3: What fractions are the same every bit ¼?

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

¼ × (2/two) = ii/eight

¼ × (3/3) = 3/12

¼ × (4/4) = 4/xvi

¼ × (5/v) = 5/20

And so on.

Video Lesson on Fractions

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Practice Questions

Find the equivalent fraction of eight/10
What is the simplest course 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?

Two or more fractions that have different numerators and denominators simply 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:
2/4 and 3/6
⅓ and 3/9
⅕ and five/25
¾ and 12/16

How to decide whether fractions are equivalent?

We need to simplify the given fractions to find whether they are equivalent or not. Suppose iii/ix and ⅔ are two fractions. 3/nine tin be further simplified to ⅓, but ⅓ is non equal to ⅔. Therefore, they are non equivalent.
But, ⅚ and 10/12 are equivalent fractions considering 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 same number. Hence,
⅗ × (2/2) = 6/ten

What are the equivalent fractions of 5/x?

5/x is equal to ½ later simplification. Hence, the equivalent fractions of 5/10 are:
½, ii/iv, 3/6, 4/8 and so on.