what is an equivalent fractions
Answers
Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same 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 represent the same proportion of the whole.
For each fraction, we can find its equivalent fraction by multiplying both numerator and denominator with the same number. For example, we have to find the third equivalent fraction of ⅔; then we have to multiply 2/3 by 3/3. Hence, 2/3 x (3/3) = 6/9, is the fraction equivalent to 2/3.
ake 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
÷
4
8
÷
4
4÷48÷4
=1/2
In the same way, if we simplify 2/4, again get 1/2.
2
÷
2
4
÷
2
2÷24÷2
= 1/2
Equivalent fractions of a mixed fraction:
Let us consider a mixed fraction to find its equivalent fraction.
Mixed fraction = 1 ½
Now, convert this fraction into an improper fraction.
1 ½ = (1 × 2 + 1)/2 = (2 + 1)/2 = 3/2
The equivalent fractions for the above fraction are:
3/2 = (3 × 2)/(2 × 2) = 6/4
3/2 = (3 × 3)/(2 × 3) = 9/6
3/2 = (3 × 4)/(2 × 4) = 12/8 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 1/5
Multiplying numerator and denominator with 2, we get 1/5 x 2/2 = 2/10
Multiplying numerator and denominator with 3, we get 1/5 x 3/3 = 3/15
Multiplying numerator and denominator with 4, we get 1/5 x 4/4 = 4/20
Therefore, we can conclude that,
1/5 = 2/10 = 3/15 = 4/20
Dividing numerator and denominator by the same number
For example, we need to find the equivalent fraction of 18/32.
Find the Highest common factor of 18 and 32.
HCF (18, 32) = 2
Now divide the numerator and denominator by 2, to get the equivalent fraction of 18/32.
(18÷2)/(32÷2) = 9/16
Hence, 9/16 is equivalent to 18/32.
Note: 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 to a point where both the numerator and denominator should still be whole numbers. I did a lot of typing pls rate my work