Solved Example based on Equivalent Fractions
Example 1: Find “a” if 10/21 and a/16 are equivalent fractions.
Solution:
Given,
10/21 = a/16
Using Cross Multiplication
a×21 = 10×42
a = 10×42 / 21
a = 20
Hence, the required value of “a” is 20
Example 2: Find the value of “x” if 5/36 and x/9 are equivalent fractions.
Solution:
Given,
5/36 and x/9 are equivalent fraction
Using Cross Multiplication Method
5/36 = x/9
x = (5 × 9)/36
x = 5/4
Hence, the required value of “x” is 5/4
Example 3: Find if 5/9 and 11/15 are equivalent fractions or not.
Solution:
Let us use Cross Multiplication Method to check whether 5/9 and 11/15 are equivalent fractions or not.
Now, by Cross Multiplication of the given fractions we get,
5 × 15 = 75
9 × 11 = 99.
Here, both products are not equal, i.e., 75 ≠ 99.
Hence, 5/9 and 11/15 are not equivalent fractions.
Example 4: What are the equivalent fractions of 7/8?
Solution:
To find equivalent fractions of 7/8, multiply the numerator and denominator by the same numbers.
7/8 × (2/2) = 14/16
7/8 × (3/3) = 21/24
7/8 × (4/4) = 28/32
7/8 × (5/5) = 35/40
7/8 × (6/6) = 42/48
Hence, the equivalent fractions of 7/8 are 14/16, 21/24, 28/32, 35/40, 42/48, and so on.
Example 5: What is its denominator, if the numerator of a fraction equivalent to 6/24 is 14?
Solution:
Let the unknown denominator be “x”.
Given,
6/24 = 14/x
We know that, if two fractions are equivalent their products when they are cross-multiplied are equal, i.e.
6 × x = 24 × 14
x = (24 × 14)/6 = 56.
Hence, the value of x is 56.
Equivalent Fractions
Equivalent Fractions are the fractions that represent the same value and by simplifying the fraction in simplest form we always get the same fraction. We define the fraction as a way of representing a part of some quantity. Suppose we have one pizza with six equal sizes and Shiv takes two slices from it then the remaining pizza is represented as, 4/6 which is equivalent fraction to 2/3. The various other examples of equivalent fractions are 1/3, 2/6, 3/9, and others.
The simplest form of all the equivalent fractions is the same, i.e. if all the equivalent fraction is reduced to the simplest term then they all are the same. For example, the simplest form of 1/3, 2/6, and 3/9 is 1/3. Let’s learn more about equivalent fractions, its example, and others in detail in this article.
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