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\ 08-Oct-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

For Fractions Having different numerators

Change the fractions into their respective equivalent fractions with the same denominator
by finding the LCM of the denominators. Compare them as like fractions.

Example 2: Compare the following. Think Tank Critical Thinking
7
( a) and 2 3 ( b) and 4
5 4 9 27 Three friends are running
Solution: ( a) First, we have to change the given a race. After 10 minutes, Sam has
3
fractions into their respective completed 5 of the race, Ali has

equivalent fractions having the completed 3 of the race, and David
same denominator equal to the 4 5
LCM of the denominators of the has completed 8 of the race. Who is
given fractions. winning the race?

Now, find the LCM of the denominators 5 and 4.
The LCM of 5 and 4 is 20.
2
3
Therefore, = 2 × 4 = 8 and = 3 × 5 = 15
5 5 × 4 20 4 4 × 5 20
2
3
15 > 8, so 15 > 8 . Thus, > .
20 20 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.

The 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
7
21 > 4, so 21 > 4 . Thus, > 4 .
27 27 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

The LCM of 6 and 4 is 12.
23 23 × 2 46 15 15 × 3 45
Now, = = and = =
6 6 × 2 12 4 4 × 3 12 Math Insight
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
6 4 compare them as usual.

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