Arrange the given fractions in descending order by making numerators equal : (i) 5/6, 4/15, 8/9 and 1/3 (ii) … /11 (iii) 1/10,…
Answers:
(i) 5/6, 4/15, 8/9 and 1/3
L.C.M. of numerators 5, 4, 8 and 1 = 40
∴ 5/6 = (5 × 8)/(6 × 8) = 40/48
4/15 = (4 × 10)/(15 × 10) = 40/150
8/9 = (8 × 5)/(9 × 5) = 40/45
1/3 = (1 × 40)/(3 × 40) = 40/120
From above see that 40/45 > 40/48 > 40/120 > 40/150
∴ 8/9 > 5/6 > 1/3 > 4/15
Hence, 8/9, 5/6, 1/3, 4/15 are in descending order.
(ii) 3/7, 4/9, 5/7 and 8/11
L.C.M. of numerator 3, 4, 5 and 8 = 120
∴ 3/7 = (3 × 40)/(7 × 40) = 120/280
4/9 = (4 × 30)/(9 × 30) = 120/270
5/7 = (5 × 24)/(7 × 24) = 120/168
8/11 = (8 × 15)/(11 × 15) = 120/165
It is clear that from the above that
120/165 > 120/168 > 120/270 > 120/280
Or 8/11 > 5/7 > 4/9 > 3/7
Hence, 8/11, 5/7, 4/9 and 3/7 are in ascending order.
(iii) 1/10, 6/11, 8/11 and 3/5
L.C.M. of 1, 6, 8 and 3 = 24
∴ 1/10 = (1 × 24)/(10 × 24) = 24/240
6/11 = (6 × 4)/(11 × 4) = 24/44
8/11 = (8 × 3)/(11 × 3) = 24/33
3/5 = (3 × 8)/(5 × 8) = 24/40
It is clear from the above that 24/33 > 24/40 > 24/44 > 24/240
Or 8/11 > 3/5 > 6/11 1/10
Hence, 8/11, 3/5, 6/11 and 1/10 are in ascending order.a