# Arrange Given Fractions In Descending Order By Making Numerators Equal

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,…

(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