The fractions which are equivalent have the same value, even though they may look different. These fractions are really the same.
For example,
3/4 = 6/8 = 12/16
Why are they the same ?
Because, when we multiply or divide both the numerator and denominator by the same number, the fraction keeps it's value.
Let us divide a rectangle into two equal parts and shade one of the parts.
In the above rectangle, the shaded part is 1/2.
That is, in total of 2 parts, one part is shaded.
Let us divide the same rectangle into four equal parts and shade 2 parts.
In the above rectangle, the shaded part is 2/4.
That is, in total of 4 parts, two parts are shaded.
Let us divide the same rectangle into six equal parts and shade 3 parts.
In the above rectangle, the shaded part is 3/6.
That is, in total of 6 parts, three parts are shaded.
In all the above figures, the shaded portion are equal but they can be represented by different fractions.
1/2 = 2/4 = 3//6
When two or more fractions represent the same part of a whole, the fractions are called equivalent.
Change both numerator and denominator using multiplication or division by the same number.
Example :
Using multiplication :
1/2, 2/4 and 4/8 are equivalent fractions.
Using division :
18/36, 6/12 and 1/2 are equivalent fractions.
Problem 1 :
Write 4 fractions which are equivalent to 5/6.
Solution :
5/6 = (5 ⋅ 2)/(6 ⋅ 2) = 10/12
5/6 = (5 ⋅ 3)/(6 ⋅ 3) = 15/18
5/6 = (5 ⋅ 4)/(6 ⋅ 4) = 20/24
5/6 = (5 ⋅ 5)/(6 ⋅ 5) = 25/30
The four fractions which are equivalent to 5/6 are
10/12, 15/18, 20/24 and 25/30
Problem 2 :
Write 3 fractions which are equivalent to 3/7.
Solution :
3/7 = (3 ⋅ 2)/(7 ⋅ 2) = 6/14
3/7 = (3 ⋅ 3)/(7 ⋅ 3) = 9/21
3/7 = (3 ⋅ 4)/(7 ⋅ 4) = 12/28
The four fractions which are equivalent to 5/6 are
6/14, 9/21 and 12/28
Problem 3 :
Pick out the fractions which are equivalent :
2/5, 12/16, 1/3, 5/15, 16/40, 3/4, 9/12
Solution :
The fractions 2/5 and 16/40 are equivalent.
Because, 2/5 = (2 ⋅ 8) / (5 ⋅ 8) = 16/40
The fractions 12/16, 3/4 and 9/12 are equivalent.
Because, 12/16 = (12 ÷ 4) / (16 ÷ 4) = 3/4
and 9/12 = (9 ÷ 3) / (12 ÷ 3) = 3/4
The fractions 1/3 and 5/15 are equivalent.
Because, 1/3 = (1 ⋅ 5) / (3 ⋅ 5) = 5/15
Problem 4 :
Find the missing numbers :
Solution :
The numerator of the first two fractions are 5 and 35. And 5 will become 35, when we multiply by 7.
So, we have to multiply the denominator of the first fraction 9 by 7 in order to get the denominator of the second fraction.
Hence, the denominator of the second fraction is 63.
The denominator of the first and third fraction are 9 and 72. And 9 will become 72, when we multiply by 8.
So, we have to multiply the numerator of the first fraction 5 by 8 in order to get the numerator of the third fraction.
Hence, the numerator of the third fraction is 40.
Problem 5 :
Find the missing numbers :
Solution :
The numerator of the first two fractions are 3 and 21. And 3 will become 21, when we multiply by 7.
So, we have to multiply the denominator of the first fraction 5 by 7 in order to get the denominator of the second fraction.
Hence, the denominator of the second fraction is 35.
The denominator of the first and third fraction are 5 and 20. And 5 will become 20, when we multiply by 4.
So, we have to multiply the numerator of the first fraction 3 by 4 in order to get the numerator of the third fraction.
Hence, the numerator of the third fraction is 12.
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