A Fraction Equivalent To 1/2

Equivalent fractions are the fractions that have unlike numerators and denominators merely are equal to the aforementioned value. For instance, 2/iv and 3/half dozen 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 tin observe its equivalent fraction by multiplying both numerator and denominator with the same number. For example, we accept to observe the third equivalent fraction of ⅔; then we accept to multiply 2/3 by 3/iii. Hence, 2/3 × (three/3) = vi/9, is the fraction equivalent to two/3.

What are Equivalent Fractions?

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

For example, the equivalent fraction of 1/three is 5/xv, because if nosotros simplify five/xv, then 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, every bit the numerator and denominator are not co-prime numbers, therefore they take a common multiple, which on partition gives exactly the aforementioned value.

Example of Equivalent Fraction

Have for an example:

1/2 = ii/4 = 4/8

Only, it is clearly seen that the above fractions have unlike numerators and denominators.

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

$\begin{array}{l}\frac{four \div 4}{eight \div 4}=\frac{ane}{2}\end{assortment} $

In the aforementioned way, if we simplify 2/4, again go ane/2.

$\brainstorm{assortment}{fifty}\frac{ii\div 2}{4\div 2}=\frac{1}{ii}\end{array} $

Equivalent fractions of a mixed fraction:

Allow us consider a mixed fraction to find its equivalent fraction.

Mixed fraction = 1 ½

At present, convert this fraction into an improper fraction.

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

The equivalent fractions for the above fraction are:

iii/2 = (3 × 2)/(2 × 2) = half dozen/4

3/2 = (3 × 3)/(2 × 3) = 9/vi

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

How to Find Equivalent Fractions?

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

Multiplying numerator and denominator past the same number

For case, consider the fraction ane/5

Multiplying numerator and denominator with 2, we get i/5 × 2/two = 2/ten
Multiplying numerator and denominator with iii, we get 1/five × 3/3 = 3/xv
Multiplying numerator and denominator with four, we go 1/5 × 4/4 = iv/20

Therefore, we can conclude that,

i/5 = 2/ten = three/15 = four/20

Dividing numerator and denominator by the same number

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

Discover the Highest common cistron of 18 and 32.

HCF (eighteen, 32) = 2

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

(18÷2)/(32÷two) = ix/sixteen

Hence, ix/sixteen is equivalent to 18/32.

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

Equivalent Fractions Chart

Let us see the equivalent fractions for unit fractions.

Unit Fraction	Equivalent Fractions
1/2	ii/4, iii/vi, 4/8..
1/3	ii/half-dozen, 3/9, iv/12..
ane/4	2/8, 3/12, 4/16..
1/v	2/10, iii/15, 4/twenty,..
1/half dozen	2/12, 3/18, four/24,..
1/7	2/14, 3/21, 4/28,..
1/8	2/16, 3/24, four/32,..
1/nine	2/18, 3/27, four/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 same
Method 2: Cross Multiply
Method 3: Convert to decimals

Method 1:

By making the denominators the aforementioned, nosotros can evaluate if ii fractions are equivalent.

For example, notice if two/3 and 6/9 are equivalent.

LCM of 3 and 9 = 9

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

2/iii × 3/iii = 6/nine

Hence, by making the denominators the same, we can see, 2/3 and half dozen/ix are equivalent fractions.

Method 2:

Given, 2 fractions i/two and 3/vi

Cross multiply both the fractions to get:

$Equivalent fraction - Cross multiplication method$

ane ten six = 6

2 x 3 = 6

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

Method 3:

If two fractions are given, nosotros can only notice their decimals to check if they are equivalent fractions.

Let us check if i/4 and 3/12 are equivalent fractions by converting them in decimal form.

ane/4 = 0.25

3/12 = 0.25

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

Solved Examples

Instance one: The given fractions 5/16 and x/12 are equivalent fractions, and then notice the value of x.

Solution:

Given:5/16 = 10/12

x = (five × 12)/16

x = 60/16

x =15/4

Therefore, the value of x is 15/4.

Example 2: Two fractions 3/v and 4/ten are equivalent. Find the value of x.

Solution: Given,

3/five = 4/x

x = (four × 5)/three

10 = twenty/3

Example 3: What fractions are the same as ¼?

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

¼ × (two/2) = two/8

¼ × (three/3) = three/12

¼ × (iv/4) = 4/xvi

¼ × (5/5) = five/20

And so on.

Video Lesson on Fractions

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Practice Questions

Find the equivalent fraction of 8/ten
What is the simplest grade of 9/81?
Write the fraction three-sevenths as an equivalent fraction with a denominator of 21.
Write the fraction v-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 than fractions that take different numerators and denominators just 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 three/half-dozen
⅓ and three/9
⅕ and 5/25
¾ and 12/xvi

How to decide whether fractions are equivalent?

We need to simplify the given fractions to find whether they are equivalent or not. Suppose 3/9 and ⅔ are ii fractions. iii/9 can be further simplified to ⅓, but ⅓ is not equal to ⅔. Therefore, they are not equivalent.
Simply, ⅚ and 10/12 are equivalent fractions considering 10/12 = ⅚.

What is the equivalent fraction of ⅗?

To find the equivalent fraction of ⅗, nosotros need to multiply both numerator and denominator by the same number. Hence,
⅗ × (2/ii) = 6/10

What are the equivalent fractions of 5/10?

5/10 is equal to ½ after simplification. Hence, the equivalent fractions of 5/10 are:
½, 2/four, 3/6, 4/8 and then on.