4 3/5 As A Fraction
Equivalent fractions are the fractions that have different numerators and denominators but are equal to the aforementioned value. For example, 2/4 and 3/6 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 find its equivalent fraction past multiplying both numerator and denominator with the aforementioned number. For example, we have to find the 3rd equivalent fraction of ⅔; then we have to multiply 2/3 by three/3. Hence, 2/three × (3/3) = 6/9, is the fraction equivalent to 2/3.
What are Equivalent Fractions?
Equivalent fractions state that ii or more than two fractions are said to be equal if both results the same fraction later on simplification. Permit us say, a/b and c/d are 2 fractions, afterwards the simplification of these fractions, both result in equivalent fractions, say east/f, and so they are equal to each other.
For example, the equivalent fraction of 1/three is 5/15, because if we simplify 5/15, then the resulted fraction is the same.
The biggest question hither can exist, why practice they have equal values in spite of having different numbers?
The reply to this question is that, as the numerator and denominator are not co-prime numbers, therefore they have a common multiple, which on partitioning gives exactly the same value.
Case of Equivalent Fraction
Take for an case:
ane/ii = 2/4 = four/8
Only, information technology is conspicuously seen that the above fractions take dissimilar numerators and denominators.
Dividing both numerator and denominator past their common factor, we have:
\(\brainstorm{array}{l}\frac{4 \div iv}{8 \div iv}=\frac{i}{2}\end{array} \)
In the same style, if we simplify 2/4, once again get 1/two.
\(\brainstorm{array}{l}\frac{2\div 2}{4\div 2}=\frac{one}{2}\finish{array} \)
Equivalent fractions of a mixed fraction:
Permit united states of america consider a mixed fraction to find its equivalent fraction.
Mixed fraction = 1 ½
Now, catechumen this fraction into an improper fraction.
1 ½ = (1 × 2 + 1)/2 = (2 + ane)/2 = three/2
The equivalent fractions for the above fraction are:
iii/2 = (iii × 2)/(2 × ii) = 6/four
iii/ii = (3 × 3)/(2 × 3) = ix/half dozen
3/ii = (3 × 4)/(2 × 4) = 12/8 and so on.
How to Detect Equivalent Fractions?
Equivalent fractions are evaluated by multiplying or dividing both the numerator and the denominator by the aforementioned number. Therefore, equivalent fractions, when reduced to their simplified value, will all exist the same.
Multiplying numerator and denominator past the aforementioned number
For example, consider the fraction 1/5
- Multiplying numerator and denominator with two, we become one/v × 2/2 = ii/10
- Multiplying numerator and denominator with 3, we become 1/5 × 3/3 = 3/15
- Multiplying numerator and denominator with 4, we go 1/5 × 4/4 = 4/20
Therefore, we can conclude that,
1/v = 2/10 = 3/15 = iv/twenty
Dividing numerator and denominator by the aforementioned number
For case, we demand to find the equivalent fraction of 18/32.
Detect the Highest mutual cistron of 18 and 32.
HCF (18, 32) = 2
At present divide the numerator and denominator by 2, to get the equivalent fraction of 18/32.
(eighteen÷2)/(32÷2) = 9/16
Hence, 9/xvi is equivalent to xviii/32.
Note:We can only multiply or split up by the same numbers to get an equivalent fraction and not improver or subtraction. Simplification to get equivalent numbers can be done to a point where both the numerator and denominator should still be whole numbers.
Equivalent Fractions Chart
Let us come across the equivalent fractions for unit fractions.
| Unit Fraction | Equivalent Fractions |
| 1/two | two/4, 3/vi, 4/8.. |
| 1/3 | 2/6, iii/ix, four/12.. |
| 1/4 | 2/8, three/12, 4/16.. |
| one/5 | 2/x, 3/xv, iv/20,.. |
| one/6 | 2/12, iii/18, 4/24,.. |
| ane/7 | ii/14, 3/21, 4/28,.. |
| 1/8 | ii/16, 3/24, 4/32,.. |
| i/ix | 2/18, 3/27, 4/36,.. |
Methods to Determine Equivalent Fractions
How tin we decide if two fractions are equivalent or not? It is possible by these methods:
- Method 1: Brand the Denominators the aforementioned
- Method 2: Cross Multiply
- Method 3: Convert to decimals
Method 1:
By making the denominators the same, we tin can evaluate if 2 fractions are equivalent.
For example, notice if 2/3 and 6/9 are equivalent.
LCM of 3 and ix = nine
Multiply 2/3 by 3/three to make the denominator equal to 9.
two/three × 3/three = six/9
Hence, by making the denominators the aforementioned, we tin see, 2/3 and 6/9 are equivalent fractions.
Method 2:
Given, two fractions 1/2 and 3/6
Cross multiply both the fractions to become:
one 10 half-dozen = half dozen
2 x three = 6
Since, both the values are equal, therefore, 1/ii and 3/vi are equivalent fractions.
Method 3:
If two fractions are given, we can just find their decimals to bank check if they are equivalent fractions.
Let united states cheque if one/4 and 3/12 are equivalent fractions past converting them in decimal form.
1/four = 0.25
iii/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 ten/12 are equivalent fractions, then find the value of x.
Solution:
Given:v/sixteen = x/12
ten = (5 × 12)/16
10 = 60/16
x =fifteen/4
Therefore, the value of 10 is 15/4.
Instance ii: 2 fractions 3/5 and 4/x are equivalent. Observe the value of x.
Solution: Given,
three/five = 4/x
x = (iv × five)/3
10 = 20/3
Example 3: What fractions are the aforementioned equally ¼?
Solution: To detect equivalent fractions of ¼ we need to multiply the numerator and denominator by the same numbers. Hence,
¼ × (2/ii) = 2/8
¼ × (three/3) = 3/12
¼ × (4/4) = 4/16
¼ × (5/5) = five/20
And and so on.
Video Lesson on Fractions
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Practice Questions
- Find the equivalent fraction of 8/10
- What is the simplest course of 9/81?
- Write the fraction iii-sevenths as an equivalent fraction with a denominator of 21.
- Write the fraction five-eighth as an equivalent fraction with a denominator of 24.
Related Manufactures
- Equivalent Fractions Calculator
- Types of Fractions
- Like Fractions And Unlike Fractions
- How to Simplify Fractions?
- Comparing Fractions
- Fractions Worksheets
Frequently Asked Questions on Equivalent Fractions
What are equivalent fractions?
Two or more than fractions that accept different numerators and denominators just result in the same value after simplification are said to exist equivalent fractions.
What are the examples of equivalent fractions?
The examples of equivalent fractions are:
2/iv and 3/half dozen
⅓ and three/9
⅕ and v/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/nine can be farther simplified to ⅓, only ⅓ is not equal to ⅔. Therefore, they are not equivalent.
But, ⅚ and 10/12 are equivalent fractions because 10/12 = ⅚.
What is the equivalent fraction of ⅗?
To discover the equivalent fraction of ⅗, we demand to multiply both numerator and denominator past the same number. Hence,
⅗ × (2/ii) = 6/10
What are the equivalent fractions of 5/x?
5/x is equal to ½ later on simplification. Hence, the equivalent fractions of 5/ten are:
½, 2/4, 3/6, iv/eight so on.
4 3/5 As A Fraction,
Source: https://byjus.com/maths/equivalent-fractions/
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