Page 112 - ICSE Math 6

(c) The LCM of the denominators 9 and 1 is 9.
Multiply both the terms by 9 to get:
 5 
 ×9 : (2 × 9) = 5 : 18

 9 
To Divide a given quantity in a given ratio
Suppose a is to be divided in the ratio x : y, then

 x   y 
First part =   ×a and Second part =   ×a
 x + y   x + y 

Example 6: A rope of length 150 cm is divided into two pieces such that their lengths are in the
ratio 3 : 7. Find the length of each piece of the rope.

 3  3
Solution: Length of first piece =   ×150 cm = ×150 cm = 45 cm
 3 7+  10

 7  7
Length of second piece =   ×150 cm = ×150 cm = 105 cm
 3 7+  10

Example 7: If ` 1,500 is to be shared in the ratio 12 : 13, find the amount of each share.

12 12
Solution: First share = × ` 1,500 = × ` 1,500 = ` 720
12 + 13 25
13 13
Second share = × ` 1,500 = × ` 1,500 = ` 780
12 + 13 25

Example 8: The sides of a triangle are in the ratio 2 : 3 : 4. If the perimeter of the triangle is
180 cm, then find the sides of the triangle.

Solution: We know that, perimeter of a triangle is equal to the sum of its sides.
 2  2
\ First side =   ×180 cm = ×180 cm = 40 cm
 2 34++  9

 3  3
Second side =   ×180 cm = ×180 cm = 60 cm
 2 34++  9
 4  4
Third side =   ×180 cm = ×180 cm = 80 cm
 2 34++  9
Thus, the sides of the triangle are 40 cm, 60 cm and 80 cm.

Comparison of ratios
p r
To compare two or more ratios, we first express them as fractions. For any two ratios and , if:
p r q s
(a) p × s > q × r, then >
q s
p r
(b) p × s < q × r, then <
q s
p r
(c) p × s = q × r, then =
q s

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