Equivalent Fractions
Definition
Equivalent fractions are different fractions that have the same value. The equivalent fractions of a given fraction are those fractions, whose numerators and denominators are in the same ratio as that of the original fraction.
Example: 1/3, 2/6, 3/9, 4/12..are equivalent fractions.
Finding equivalent fractions of a given fraction − Formula
Equivalent fraction of a given fraction is got by multiplying or dividing its numerator and denominator by the same whole number.
For example, if we multiply the numerator and denominator of 2/3 by 4 we get.
2/3 = (2 4) / (3 4) = 8/12 which is an equivalent fraction of 2/3.
Similarly, if we divide the numerator and denominator of 12/18 by 6 we get.
12/18 = (12 ÷ 6) / (18 ÷ 6) = 2/3. So 12/18 is an equivalent fraction of 2/3 as well.
Problem 1
Fill in the blank to make the fractions equivalent.
7/8 =? /40
Solution
Step 1:
To get an equivalent fraction, we multiply the numerator and the denominator by the same number
To go from 7/8 to ?/40, we multiply the denominator and numerator with 5 as follows.
7/8 = (7 5) / (8 5) = 35/40.
Step 2:
So we have filled the blank with 7 5 = 35.
So from 7/8 = 35/40, 35 is the answer.
7/8 and 35/40 are equivalent fractions.
Step 3:
We can check the answers with the pictures below
Below 7/8 parts are shaded. Splitting each part into 5 equal parts, we see that 35/40 of the smaller parts are shaded.
Problem 2
Fill in the blank to make the two fractions equivalent.
4/5 = ?/20
Solution
Step 1:
To go from 4/5 to ?/20, we multiply the denominator and numerator with 4 as follows.
4/5 = (4 4) / (5 4) = 16/20.
Step 2:
So we have filled the blank with 44 = 16.
So from 4/5 = 16/20, 16 is the answer
4/5 and 16/20 are equivalent fractions
Problem 3
Fill in the blank to make the two fractions equivalent.
?/28 = 3/4
Solution
Step 1:
To go from 3/4 to ?/28, we multiply the denominator and numerator with 7 as follows.
3/4 = (3 7) / (4 7) = 21/28.
Step 2:
So we have filled the blank with 37 = 21.
So from 21/28 = 3/4, 21 is the answer.
3/4 and 21/28 are equivalent fractions.