Answer:
3.5 : 7 > 1.2 : 2.5.
Step-by-step explanation:
1. Compare the ratios 4 : 5 and 2 : 3.
Solution:
Express the given ratios as fraction
4 : 5 = 4/5 and 2 : 3 =2/3
Now find the L.C.M (least common multiple) of 5 and 3
The L.C.M (least common multiple) of 5 and 3 is 15.
Making the denominator of each fraction equal to 15, we have
4/5 = (4 ×3)/(5 ×3) = 12/15 and 2/3 = (2 ×5)/(3 ×5) = 10/15
Clearly, 12 > 10
Now, 12/15 > 10/15
Therefore, 4 : 5 > 2 : 3.
2. Compare the ratios 5 : 6 and 7 : 9.
Solution:
Express the given ratios as fraction
5 : 6 = 5/6 and 7 : 9 =7/9
Now find the L.C.M (least common multiple) of 6 and 9
The L.C.M (least common multiple) of 6 and 9 is 18.
Making the denominator of each fraction equal to 18, we have
5/6 = (5 ×3)/(6 ×3) = 15/18 and 7/9 = (7 ×2)/(9 ×2) = 14/18
Clearly, 15 > 14
Now, 15/18 > 14/18
Therefore, 5 : 6 > 7 : 9.
3. Compare the ratios 1.2 : 2.5 and 3.5 : 7.
Solution:
1.2 : 2.5 = 1.2/2.5 and 3.5 : 7 =3.5/7
1.2/2.5 = (1.2 ×10)/(2.5 ×10 ) = 12/25 and 3.5/7 = (3.5 ×10)/(7 ×10) = 35/70 = 1/2
[We removed the decimal point from the ratios now, we will compare the ratio]
Now find the L.C.M (least common multiple) of 25 and 2
The L.C.M (least common multiple) of 25 and 2 is 50.
Making the denominator of each fraction equal to 50, we have
= 12/25 = (12 ×2)/(25 ×2) = 24/50 and 1/2 = (1 ×25)/(2 ×25) = 25/50
Now, 25/50 > 24/50
Therefore, 3.5 : 7 > 1.2 : 2.5.
