The document summarizes key concepts about ratios and proportions. It defines a ratio as the comparison of two quantities of the same kind by division. It provides three ways to write a ratio and lists five properties of ratios. A proportion is defined as an equation that says one ratio is equal to another. The rule of proportion states that the product of extremes is equal to the product of means. Direct proportion and inverse proportion are defined as two quantities increasing or decreasing together in the same or opposite ratios, respectively. Continued proportion is defined as the ratio of the first and second numbers being equal to the ratio of the second and third numbers. An example verifies that 2, 4, 8 are in continued proportion.

1. Sri Dharmasthala Manjunatheswara
College( Autonomous ) Ujire
Ratio and Proportions.
Department of
Statistics
Presenter :-
Ganesh Gouda
2nd BBA
R.No : 201011
Venue :
Classroom
Date of Presentation
08-02-2022
-: Topic :-

3. Ratio :
The comparison of two quantities of the same
kind by division is called ratio.
 A ratio has “no units”.

4. Compare the number of boys to girls in the class.

8. Three ways to write a Ratio
The ratio of a to b , can be written as :
1. a to b
2. a:b
3. ab

9. Properties of Ratio:
1. Ratio is not changed by multiplying or dividing the antecedent and consequent by the same
number.
2. Ratio is independent of units of measurement, that is, it is an abstract number.
3. Quantities of different kind cannot be expressed as ratio.
4. If the product of two ratios is 1, each is said to be the inverse or reciprocal of the other. Thus a : b
is the inverse or reciprocal of b : a and vice versa.
5. In the ratio a : b, if
(i) a = b, then a : b is the ratio of quantity, e.g. 3:3.
(ii) If a > b, then a : b is said to be the ratio of greater inequality, e.g. 6:5.
(iii) If a < b, then a : b is said to be the ratio of lesser inequality, e.g. 3:4.

11. 3:2
Examples :

12. Proportion

13. A Proportion is an equation
that says one ratio is equal to another.
Meaning
Ratio
Ratio

15. Rule of Proportion:
In any proportion, the product of extremes is
equal to the product of means.
i.e, if a : b = c : d, then a × d = b × c
If a : b = c : d or a b = c d then a,b,c and d are in proportion.
Example if 2 : 3 = 4 : 6 then 2,3,4,6 are in proportion

16. If two quantities are so related to each other that an
increase or decrease in the magnitude of one, results in the increase or
decrease in the magnitude of the other in the same ratio, then the two
quantities are in direct proportion.
Direct Proportion

17. Answer

18. When two quantities are so related that as one
increases the other decreases and as one decreases the other
increases, then we say that the two quantities are in inverse
proportion.
Inverse Proportion

19. C = 5 Candies

20. Continued Proportion
Three numbers are said to be in continued
Proportion if the ratio of first and second number is equal to the
ratio of second and third number.

21. Verify whether 2, 4, 8 are in continued proportion.
Solution:
Continued proportion=a : b :: b : c
a × c = b2
2 : 4 :: 4 : 8
2 × 8 = 4 × 4
16=16
Therefore 2, 4, 8 are in continued proportion.