How Many 1/4 Is 1/3

Equivalent fractions are the fractions that accept different numerators and denominators but are equal to the same value. For example, 2/4 and iii/vi 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, we can find its equivalent fraction by multiplying both numerator and denominator with the same number. For example, nosotros have to observe the tertiary equivalent fraction of ⅔; then nosotros have to multiply 2/3 by 3/3. Hence, 2/three × (3/3) = 6/9, is the fraction equivalent to two/3.

What are Equivalent Fractions?

Equivalent fractions state that two or more than two fractions are said to be equal if both results the aforementioned fraction after simplification. Let us say, a/b and c/d are two fractions, after 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 i/3 is 5/15, because if we simplify 5/15, and so the resulted fraction is the same.

Equivalent Fractions example

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

The answer to this question is that, equally the numerator and denominator are not co-prime numbers, therefore they have a mutual multiple, which on division gives exactly the same value.

Example of Equivalent Fraction

Take for an instance:

1/two = ii/four = 4/8

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

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

$\brainstorm{array}{fifty}\frac{four \div four}{viii \div 4}=\frac{1}{2}\cease{array} $

In the same way, if we simplify 2/4, again become 1/2.

$\begin{assortment}{fifty}\frac{2\div 2}{4\div two}=\frac{one}{2}\finish{assortment} $

Equivalent fractions of a mixed fraction:

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

Mixed fraction = 1 ½

At present, convert this fraction into an improper fraction.

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

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

3/two = (3 × 2)/(2 × 2) = 6/four

three/2 = (3 × 3)/(2 × iii) = 9/six

3/2 = (3 × iv)/(2 × iv) = 12/eight and so 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 same.

Multiplying numerator and denominator by the same number

For example, consider the fraction one/v

Multiplying numerator and denominator with 2, we get one/5 × 2/two = 2/10
Multiplying numerator and denominator with 3, we go one/v × 3/3 = iii/15
Multiplying numerator and denominator with 4, we go i/5 × 4/4 = 4/xx

Therefore, we tin can conclude that,

ane/5 = two/10 = 3/15 = 4/xx

Dividing numerator and denominator by the same number

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

Find the Highest common factor of 18 and 32.

HCF (18, 32) = ii

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

(18÷two)/(32÷2) = 9/16

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

Note:We can simply multiply or divide by the same 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 even so be whole numbers.

Equivalent Fractions Chart

Let us encounter the equivalent fractions for unit of measurement fractions.

Unit Fraction	Equivalent Fractions
1/two	2/4, 3/6, iv/eight..
ane/3	2/6, three/nine, 4/12..
1/4	two/8, three/12, 4/16..
1/5	2/10, three/15, iv/twenty,..
ane/vi	2/12, 3/18, four/24,..
1/7	2/14, 3/21, 4/28,..
1/8	2/16, iii/24, iv/32,..
1/9	two/eighteen, 3/27, four/36,..

Methods to Determine Equivalent Fractions

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

Method 1: Make the Denominators the same
Method ii: Cross Multiply
Method 3: Convert to decimals

Method one:

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

For case, find if two/3 and half dozen/nine are equivalent.

LCM of iii and nine = 9

Multiply two/3 by 3/3 to make the denominator equal to 9.

2/3 × iii/iii = 6/9

Hence, by making the denominators the same, we tin see, two/three and half dozen/nine are equivalent fractions.

Method 2:

Given, two fractions 1/2 and 3/6

Cross multiply both the fractions to go:

$Equivalent fraction - Cross multiplication method$

i x 6 = 6

ii 10 3 = 6

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

Method 3:

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

Let us check if 1/four and 3/12 are equivalent fractions by converting them in decimal course.

ane/4 = 0.25

3/12 = 0.25

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

Solved Examples

Instance 1: The given fractions 5/16 and 10/12 are equivalent fractions, then find the value of ten.

Solution:

Given:5/16 = x/12

x = (5 × 12)/16

x = 60/xvi

x =15/iv

Therefore, the value of x is xv/4.

Example ii: Two fractions 3/5 and 4/ten are equivalent. Detect the value of x.

Solution: Given,

3/5 = iv/10

10 = (4 × five)/3

x = 20/3

Case 3: What fractions are the same as ¼?

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

¼ × (2/2) = 2/8

¼ × (iii/3) = 3/12

¼ × (4/4) = four/16

¼ × (5/5) = five/20

And so on.

Video Lesson on Fractions

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Do Questions

Find the equivalent fraction of eight/10
What is the simplest class of 9/81?
Write the fraction three-sevenths equally 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 unlike numerators and denominators but result in the same value subsequently simplification are said to be equivalent fractions.

What are the examples of equivalent fractions?

The examples of equivalent fractions are:
two/4 and 3/half dozen
⅓ and 3/ix
⅕ and 5/25
¾ and 12/16

How to determine whether fractions are equivalent?

We need to simplify the given fractions to observe whether they are equivalent or not. Suppose 3/9 and ⅔ are two fractions. 3/9 can be further simplified to ⅓, merely ⅓ is not equal to ⅔. Therefore, they are not equivalent.
But, ⅚ and ten/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 × (2/2) = 6/10

What are the equivalent fractions of five/10?

v/ten is equal to ½ afterward simplification. Hence, the equivalent fractions of 5/10 are:
½, 2/4, 3/six, 4/eight and then on.

How Many 1/4 Is 1/3,

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

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