2:3 and 5:9 into equivalent
Answers
Answer:
Hope it helped u :)
Step-by-step explanation:
Equivalent fractions state that two or more than two fractions are said to be equal if both results are the same fraction after simplification. Let us say, a/b and c/d are two fractions, after the simplification of these fractions, both result in equivalent fraction, say e/f, then they are equal to each other.
For example, the equivalent fraction of 1/3 is 5/15, because if we simplify 5/15, then the resulted fraction is the same.
The biggest question here can be, why do they have equal values in spite of having different number?
The answer to this question is that, as the numerator and denominator are not co-prime numbers, therefore they have a common multiple, which on division gives exactly the same value.
Take for an example:
1/2 = 2/4 = 4/8
But, it is clearly seen that the above fractions have different numerators and denominators.
Dividing both numerator and denominator by their common factor, we have:
4÷48÷4
=1/2
In the same way, if we simplify 2/4, again get 1/2.
2÷24÷2
= 1/2
How to Find Equivalent Fractions
These fractions are actually the same because when we multiply or divide both the numerator and the denominator by the same number, the value of the fraction actually doesn’t change. Therefore, equivalent fractions, when reduced to their simplified value, will all be the same.
For example, consider the fraction 1/5
Multiplying numerator and denominator with 2, we get 1/5 = 2/10
Multiplying numerator and denominator with 3, we get 1/5 = 3/15
Multiplying numerator and denominator with 4, we get 1/5 = 4/20
Therefore, we can conclude that,
1/5 = 2/10 = 3/15 = 4/20
Keep in mind that we can only multiply or divide by the same numbers to get an equivalent fraction and not addition or subtraction. Simplification to get equivalent numbers can be done till a point where both the numerator and denominator should still be whole numbers.
Try the following question to check your understanding of the concept of equivalent fractions.
Unit Fraction Equivalent Fractions
1/2 2/4, 3/6, 4/8..
1/3 2/6, 3/9, 4/12..
1/4 2/8, 3/12, 4/16..
1/5 2/10, 3/15, 4/20,..
1/6 2/12, 3/18, 4/24,..
1/7 2/14, 3/21, 4/28,..
1/8 2/16, 3/24, 4/32,..
1/9 2/18, 3/27, 4/36,..
Questions and Answers
Example 1: The given fractions 5/16 and x/12 are equivalent fractions, then find the value of x.
Solution:
Given: 5/16 = x/12
x = (5 x 12)/16
x = 60/16
x =15/4
Therefore, the value of x is 15/4.
Example 2: Two fractions 3/5 and 4/x are equivalent. Find the value of x.
Solution: Given,
3/5 = 4/x
x = (4 x 5)/3
x = 20/3
Example 3: What fractions are same as ¼?
Solution: To find equivalent fractions of ¼ we need to multiply the numerator and denominator by the same numbers. Hence,
¼ x (2/2) = 2/8
¼ x (3/3) = 3/12
¼ x (4/4) = 4/16
¼ x (5/5) = 5/20
And so on.
Example 4: What is the fourth equivalent fraction of ¾?
Answer: To find the fourth equivalent fraction of ¾, we need to multiply numerator and denominator by 4. Hence,
¾ x (4/4) = 12/16
2/3×3/3=6/9
5/9×1/1=5/9
6/9=5/9