what are motebel answers to 1/2 equivalent t
Equivalent fractions are the fractions that have different numerators and denominators just are equal to the same value. For example, 2/4 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 proportion of the whole.
For each fraction, we can detect its equivalent fraction by multiplying both numerator and denominator with the same number. For case, nosotros have to find the tertiary equivalent fraction of ⅔; then we accept to multiply ii/3 by 3/3. Hence, 2/3 ten (3/3) = six/nine, is the fraction equivalent to ii/iii.
What are Equivalent Fractions?
Equivalent fractions state that two or more than than two fractions are said to be equal if both results are the aforementioned fraction afterward simplification. Let us say, a/b and c/d are two fractions, after the simplification of these fractions, both upshot in equivalent fractions, say e/f, so they are equal to each other.
For example, the equivalent fraction of 1/iii is five/xv, because if we simplify 5/xv, so the resulted fraction is the same.
The biggest question here can be, why practise they take equal values in spite of having different 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 partitioning gives exactly the same value.
Case of Equivalent Fraction
Take for an example:
1/two = 2/4 = 4/eight
Merely, information technology is clearly seen that the in a higher place fractions have different numerators and denominators.
Dividing both numerator and denominator by their common factor, we take:
\(\begin{array}{l}\large \frac{4 \div 4}{8 \div four}\terminate{array} \)
=one/ii
In the aforementioned way, if we simplify 2/four, again get 1/two.
\(\brainstorm{array}{50}\big \frac{2\div 2}{iv\div 2}\terminate{array} \)
= 1/2
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, convert this fraction into an improper fraction.
1 ½ = (ane × two + 1)/2 = (2 + 1)/ii = 3/2
The equivalent fractions for the above fraction are:
three/ii = (iii × 2)/(2 × 2) = half dozen/4
3/two = (3 × iii)/(two × three) = nine/6
iii/ii = (3 × iv)/(ii × 4) = 12/8 and 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 same.
Multiplying numerator and denominator past the same number
For example, consider the fraction 1/5
- Multiplying numerator and denominator with two, we get 1/v ten 2/two = 2/10
- Multiplying numerator and denominator with 3, we go ane/v x 3/3 = three/15
- Multiplying numerator and denominator with iv, we get one/five 10 4/4 = iv/20
Therefore, we can conclude that,
i/5 = 2/x = 3/fifteen = 4/20
Dividing numerator and denominator by the aforementioned number
For example, nosotros need to detect the equivalent fraction of 18/32.
Find the Highest common factor of 18 and 32.
HCF (xviii, 32) = 2
Now divide the numerator and denominator by 2, to get the equivalent fraction of xviii/32.
(18÷ii)/(32÷2) = nine/xvi
Hence, 9/sixteen is equivalent to 18/32.
Note:Nosotros can but multiply or divide by the aforementioned numbers to become an equivalent fraction and not addition or subtraction. Simplification to go equivalent numbers tin be done to a signal where both the numerator and denominator should notwithstanding be whole numbers.
Equivalent Fractions Chart
Let us see the equivalent fractions for unit fractions.
| Unit Fraction | Equivalent Fractions |
| 1/two | ii/4, 3/half-dozen, 4/8.. |
| i/three | 2/6, iii/9, iv/12.. |
| 1/4 | ii/8, 3/12, iv/16.. |
| 1/5 | 2/x, 3/15, four/20,.. |
| ane/6 | 2/12, three/18, iv/24,.. |
| i/7 | 2/fourteen, 3/21, 4/28,.. |
| 1/8 | two/xvi, three/24, 4/32,.. |
| 1/ix | 2/18, 3/27, 4/36,.. |
Methods to Determine Equivalent Fractions
How tin can we determine if two fractions are equivalent or non? It is possible by these methods:
- Method 1: Make the Denominators the aforementioned
- Method 2: Cross Multiply
- Method 3: Catechumen to decimals
Method ane:
Past making the denominators the same, we can evaluate if two fractions are equivalent.
For example, notice if 2/3 and 6/ix are equivalent.
LCM of 3 and ix = ix
Multiply ii/3 by iii/3 to brand the denominator equal to ix.
2/three x 3/iii = half dozen/9
Hence, by making the denominators the same, nosotros can see, 2/3 and 6/9 are equivalent fractions.
Method 2:
Given, two fractions 1/2 and 3/6
Cantankerous multiply both the fractions to go:
ane x 6 = 6
two x three = 6
Since, both the values are equal, therefore, 1/2 and three/6 are equivalent fractions.
Method iii:
If two fractions are given, nosotros can simply notice their decimals to check if they are equivalent fractions.
Allow us check if one/4 and 3/12 are equivalent fractions by converting them in decimal form.
1/4 = 0.25
3/12 = 0.25
Since, both the fractions results in the same decimal, thus they are equivalent.
Solved Examples
Case 1: The given fractions 5/xvi and x/12 are equivalent fractions, then discover the value of x.
Solution:
Given:5/xvi = x/12
x = (five x 12)/16
x = 60/16
10 =15/iv
Therefore, the value of ten is 15/4.
Instance 2: Ii fractions 3/5 and 4/x are equivalent. Discover the value of x.
Solution: Given,
iii/five = 4/x
x = (4 x 5)/3
x = xx/3
Case 3: What fractions are the same equally ¼?
Solution: To find equivalent fractions of ¼ we need to multiply the numerator and denominator past the same numbers. Hence,
¼ 10 (2/two) = 2/eight
¼ x (3/3) = iii/12
¼ 10 (4/four) = 4/xvi
¼ x (five/five) = 5/xx
And then on.
Have persisting doubts on any topic? Effort reaching out to our mentors but with BYJU'South – The Learning App.
Exercise Questions
- Notice the equivalent fraction of 8/10
- What is the simplest form of 9/81?
- Write the fraction iii-sevenths as an equivalent fraction with a denominator of 21.
- Write the fraction v-eighth as an equivalent fraction with a denominator of 24.
Related Articles
- Equivalent Fractions Calculator
- Types of Fractions
- Like Fractions And Different Fractions
- How to Simplify Fractions?
- Comparing Fractions
- Fractions Worksheets
Often Asked Questions – FAQs
What are equivalent fractions?
Two or more fractions that have different numerators and denominators but event in the aforementioned 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/nine
⅕ and 5/25
¾ and 12/16
How to make up one's mind whether fractions are equivalent?
Nosotros need to simplify the given fractions to detect whether they are equivalent or not. Suppose three/ix and ⅔ are two fractions. 3/ix tin be further simplified to ⅓, but ⅓ is not equal to ⅔. Therefore, they are not equivalent.
Merely, 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, we demand to multiply both numerator and denominator past the same number. Hence,
⅗ 10 (2/2) = 6/10
What are the equivalent fractions of 5/10?
five/10 is equal to ½ afterward simplification. Hence, the equivalent fractions of v/ten are:
½, 2/iv, 3/6, 4/8 and so on.
Source: https://byjus.com/maths/equivalent-fractions/
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