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E:\Working\Focus_Learning\Math_Genius_5_(05-10-2023)\Open_Files\CHAP_04
\\November 22, 2023 3:12 PM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

example 2: Compare the following.
3
2
7
(a) and (b) and 4
5 4 9 27
Solution: (a) First, we have to change the given fractions into their respective
equivalent fractions having the same denominator equal to the LCM of

the denominators of the given fractions.
Now, find the LCM of the denominators 5 and 4.

LCM of 5 and 4 is 20.
3
2
Therefore, = 2 × 4 = 8 and = 3 × 5 = 15
5 5 × 4 20 4 4 × 5 20
Since, 15 > 8

So, 15 > 8
20 20
3
Thus, > 2
4 5

(b) Change the given fractions into their respective equivalent fractions having
the same denominator equal to the LCM of the denominators of the given
fractions.
Now, find the LCM of the denominators 9 and 27.

LCM of the denominators 9 and 27 is 27.
7
Then, = 7 × 3 = 21 and 4 = 4 × 1 = 4
9 9 × 3 27 27 27 × 1 27

Since, 21 > 4
So, 21 > 4
27 27
7
Thus, > 4 .
9 27

example 3: Which is greater 3 5 or 3 3 ?
6 4 2 6, 4

Solution: We have, 3 5 = 3 × 6 + 5 = 18 + 5 = 23 2 3, 2
6 6 6 6 3 3, 1

and 3 3 = 3 × 4 + 3 = 12 + 3 = 15 1, 1
4 4 4 4 LCM = 2 × 2 × 3 = 12

LCM of 6 and 4 is 12.

Now, 23 = 23 × 2 = 46 and 15 = 15 × 3 = 45
6 6 × 2 12 4 4 × 3 12 Remember
46 45 23 15 To compare mixed fractions,
Clearly, 46 > 45, so 12 > 12 i.e., 6 > 4 first convert them into

Thus, 3 5 > 3 3 . improper fractions and then
compare them as usual.
6 4

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