How to solve Ascending and Descending of Fractions With steps and Method to do it with an examples?

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M e t h o d t o a r r a n g e f r a c t i o n s i n a s c e n d i n g o r d e s c e n d i n g o r d e r i s : 1 . L C M o f t h e d e n o m i n a t o r s o f t h e f r a c t i o n s b i s d e t e r m i n e d f i r s t . 2 . T h e n, c o n v e r s i o n o f t h e f r a c t i o n s i n t o i t s e q u i v a l e n t f r a c t i o n s a r e d o n e m a k i n g s u r e t h a t t h e r e s u l t i n g d e n o m i n a t o r i s e q u a l t o t h e o b t a i n e d L C M . 3 . T h e n, c o m p a r i s o n o f t h e n u m e r a t o r s o f e q u i v a l e n t f r a c t i o n s a r e d o n e t o d e t e r m i n e t h e a s c e n d i n g o r d e s c e n d i n g o r d e r o f t h e f r a c t i o n s . L e t u s c o n s i d e r a n e x a m p l e, \frac{2}{3}, \frac{3}{7} a n d \frac{5}{6} H e r e, L C M (3, 7, 6) = 42 s o, \frac{2}{3} = \frac{2 \times 14}{3 \times 14} = \frac{28}{42}, \frac{3}{7} = \frac{3 \times 6}{7 \times 6} = \frac{18}{42} a n d \frac{5}{6} = \frac{5 \times 7}{6 \times 7} = \frac{35}{42} N o w, 18 < 28 < 35, s o \frac{18}{42} < \frac{28}{42} < \frac{35}{42} H e n c e, i n a s c e n d i n g o r d e r t h e a r r a n g e m e n t o f t h e f r a c t i o n s w i l l b e : \frac{3}{7} < \frac{2}{3} < \frac{5}{6} R e g a r d s

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Arrange the following fractions 5/6, 8/9, 2/3 in ascending order.

First we find the L.C.M. of the denominators of the fractions to make the denominators same.

L.C.M. = 3 × 2 × 3 × 1 = 18

Now to make the fraction as like fractions divide the L.C.M. by the denominator of fractions, then multiply both the numerator and denominator of fraction with the number get after dividing L.C.M.

As in fraction 5/6 denominator is 6.

Divide 18 ÷ 6 = 3

Now, multiply both numerator and denominator by 3 = 5 × 3/6 × 3 = 15/18

Similarly, 8/9 = 8 × 2/9 × 2 = 16/18 (because 18 ÷ 9 = 2)

and 2/3 = 2 × 6/3 × 6 = 12/18 (because 18 ÷ 3 = 6)

Now, we compare the like fractions 15/18, 16/18 and 12/18

Comparing numerators, we find that 16 > 15 > 12

Therefore, 16/18 > 15/18 > 12/ 18

or 8/9 > 5/6 > 2/3

or 2/3 < 5/6 < 8/9

The ascending order of the fractions is 2/3, 5/6, 8/9.

Solved examples for arranging in descending order:

1. Arrange the following fractions 5/6, 7/10, 11/20 in descending order.

First we find the L.C.M. of the denominators of the fractions to make the denominators same.

L.C.M. of 6, 10 and 20 = 2 × 5 × 3 × 1 × 2 = 60

5/6 = 5 × 10/6 × 10 = 50/60 (because 60 ÷ 6 = 10)

7/10 = 7 × 6/10 × 6 = 42/60 (because 60 ÷ 10 = 6)

11/20 = 11 × 3/20 × 3 = 33/60 (because 60 ÷ 20 = 3)

Now we compare the like fractions 50/60, 42/60 and 33/60

Comparing numerators, we find that 50 > 42 > 33.

Therefore, 50/60 > 42/60 > 33/60 or 5/6 > 7/10 > 11/20

The descending order of the fractions is 5/6, 7/10, 11/20.

2. Arrange the following fractions 1/2, 3/4, 7/8, 5/12 in descending order.

First we find the L.C.M. of the denominators of the fractions to make the denominators same.

L.C.M. of 2, 4, 8 and 12 = 24

1/2 = 1 × 12/2 × 12 = 12/24 (because 24 ÷ 2 = 12)

3/4 = 3 × 6/4 × 6 = 18/24 (because 24 ÷ 10 = 6)

7/8 = 7 × 3/8 × 3 = 21/24 (because 24 ÷ 20 = 3)

5/12 = 5 × 2/12 × 2 = 10/24 (because 24 ÷ 20 = 3)

Now we compare the like fractions 12/24, 18/24, 21/24 and 10/24.

Comparing numerators, we find that 21 > 18 > 12 > 10.

Therefore, 21/24 > 18/24 > 12/24 > 10/24 or 7/8 > 3/4 > 1/2 > 5/12

The descending order of the fractions is 7/8 > 3/4 > 1/2 > 5/12.