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\\November 22, 2023 3:12 PM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

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example 4: Arrange the following fractions in ascending order: , , , .
6 9 2 3
Solution: Change the given fractions into their respective equivalent fractions having
the same denominator equal to the LCM of the denominators of the given
fractions. LCM of the denominators 6, 9, 2 and 3 is 18.
5 5 × 3 15 7 7 × 2 14
Then, = = ; = = 2 6, 9, 2, 3
6 6 × 3 18 9 9 × 2 18 3 3, 9, 1, 3
1 = 1 × 9 = 9 ; = 2 × 6 = 12 3 1, 3, 1, 1
2
2 2 × 9 18 3 3 × 6 18
Since, 9 < 12 < 14 < 15 1, 1, 1, 1
Therefore, 9 < 12 < 14 < 15 LCM = 2 × 3 × 3 = 18
18 18 18 18
1 2 7 5
Thus, < < < .
2 3 9 6

, , , .
example 5: Arrange the following fractions in descending order: 3 5 2 1
10 8 5 3
Solution: Change the given fractions into their respective equivalent fractions having
the same denominator equal to the LCM of the denominators of the given
fractions. LCM of the denominators 10, 8, 5 and 3 is 120.

Then, 3 = 3 × 12 = 36 5 5 × 15 = 75
; =
10 10 × 12 120 8 8 × 15 120 2 10, 8, 5, 3
2 = 2 × 24 = 48 1 1 × 40 = 40 2 5, 4, 5, 3
; =
5 5 × 24 120 3 3 × 40 120 5 5, 2, 5, 3
Since, 75 > 48 > 40 > 36 1, 2, 1, 3
75 48 40 36
Therefore, > > > LCM = 2 × 2 × 2 × 3 × 5 = 120
120 120 120 120
2
1
Thus, 5 > > > 3 .
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Method of cross Multiplication

We can also compare two fractions by cross-multiplication method.

In this method, the numerator of the first fraction is multiplied by the denominator of the
second fraction and the numerator of the second fraction is multiplied by the denominator
of the first fraction.
8
8
example: Let us compare and 5 . Cross-multiply the fractions and 5 .
9 11 9 11
8 5 9 × 5 = 45
9 11 8 × 11 = 88

The cross-products are 88 and 45. The first product is greater than
the second product.
Clearly, 88 > 45. So, the first fraction > the second
8
So, > 5 fraction.
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