Slide 1 : What is Ratio? The comparison between two quantities of the same unit is a ratio. It shows how many times one quantity is bigger or smaller than the other. Example 1:
Distance between Delhi and Jaipur : Distance between Delhi and Agra
Can compare and can express by ratio. Example 2:
Density of Mercury : Density or Iron
Can compare and can express by ratio. Example 3:
Height of Sachin Tendulkar : Weight of Sachin Tendulkar
Can NOT compare and can NOT express by ratio.
Slide 2 : How to express or write Ratio? The ratio between two quantities (for example 3 and 8) can be written as: 3 : 8 3 / 8 37.5% 0.375 This is read as “3 is to 8”
Slide 3 : Antecedent and Consequent The first term in a ratio is called the “antecedent” and the second term is called “consequent”. Example:
In the ratio 3 : 8 , the antecedent is 3 and the consequent is 8.
Slide 4 : A ratio remains unchanged when both the terms are multiplied or divided by the same number. Example 1:
3 : 5 = (3x4) : (5x4) = 12 : 20 Example 2:
Slide 5 : A ratio is said to be in its simplest form if both the integers are co-prime (co-prime are the numbers which have no common positive divisor other than 1). For Example:
3 : 4
14 : 15
7 : 8 are the simplest form of ratio because both the integers are co-prime in above examples. But,
25 : 50 is not in its simplest form, because it can reduce as follows: Hence, simplest form of 25 : 50 is 1 : 2
Slide 6 : A ratio has NO units. It can NOT be expressed in terms of any units of measurement. For Example:
20 minutes : 30 minutes = 20 : 30
5 cm : 12 cm = 5 : 12
3 liter : 7 liter = 3 : 7
Slide 7 : In order to find the ratio between two given quantities, they should be expressed in the same unit and simplified. Example 1:
25 cm : 2 m = 25 cm : 200 cm = 25 : 200 = 1 : 8 Example 2:
1 kg : 500 gm = 1000 gm : 500 gm = 1000 : 500 = 2 : 1
Slide 8 : Exercise 1: Divide Rs. 700 among A, B, C in the ratio 2: 5 : 7 respectively. Solution: A : B : C
2 : 5 : 7 It means, if we have to divide Rs. (2+5+7) = Rs. 14 among A, B, C; then A’s share will be Rs. 2, B’s Share will be Rs. 5 and C’s share will be Rs. 7 out of Rs. 14. A will get = 700 x 2 14 = Rs. 100 B will get = 700 x 5 14 = Rs. 250 C will get = 700 x 7 14 = Rs. 350
Slide 9 : Exercise 2: Divide Rs. 588 among Mary, Bharat, Nichole in the ratio Solution: Mary : Bharat : Nichole It means, if we have to divide Rs. (15+25+44) = Rs. 84 among Mary, Bharat and Nichole; then Mary’s share will be Rs. 15, Bharat’s Share will be Rs. 25 and Nichole’s share will be Rs. 44 out of Rs. 84. Mary will get = 588 x 15 84 = Rs. 105 Bharat will get = 588 x 25 84 = Rs. 175 Nichole will get = 588 x 44 84 = Rs. 308 = 15 : 25 : 44