What are Ratios?
In certain circumstances, the comparison by the process of division makes good sense when compared to performing their difference. Hence the comparison of two quantities by the process of division method is called as ‘Ratio’ between two numbers.
The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things. The sign used to denote a ratio is ‘:‘.
A ratio can be written as a fraction, say \(\frac{2}{5}\). Or can write it by using “to,” as “2 to 5.”We happen to see various comparisons or say ratios in our daily life.
Take the example of a comparison between the number of girls to number of boys in a classroom. Out of the total students in class, if the number of boys is 5 and the number of girls being 3, then the ratio between girls and boys can be written as 3:5( Girls: Boys). The ratio can also be written in the form of factor like \(\frac{3}{5}\).
Proportions :-
What is a Proportion? Ratio and proportions are said to be faces of the same coin. When two ratios are equal in value, then they are said to be in proportion. In simple words, it compares two ratios. Proportions are denoted by the symbol ‘::’ or ‘=’.
Let us assume that, in proportion the two ratios are a:b & c:d. The two terms ‘b’ and ‘c’ are called as ‘means or mean term,’ whereas the terms ‘a’ and ‘d’ are known as ‘extremes or extreme terms.’
a/b = c/d or a : b :: c : d |
Let us consider one more example of a number of students in a classroom. Our first ratio of number of girls to boys is 3:5 and that of the other is 4:8, then the proportion can be written as
3 : 5 :: 4 : 8 or 3/5 = 4/8
Here 3 & 8 are the extremes, while 5 & 4 are the means.
Ratio and Proportion Problems:-
Example 1. Are the ratios 4:5 and 8:10 said to be in Proportion?
Solution- 4:5= 4/5 = 0.8 and 8: 10= 8/10= 0.8
Since both the ratios are equal, they are said to be in proportion.
Example 2. Are the two ratios 8:10 and 7:10 in proportion?
Solution- 8:10= 8/10= 0.8 and 7:10= 7/10= 0.7
Since both the ratios are not equal, they are not in proportion.
Continued Proportion:
Consider two ratios to be a:b and c:d.
Then in order to find the continued proportion for the two given ratio terms, we convert the means to a single term/number. This would in general be the LCM of means.
Fo the given ratio, the LCM of b & c will be bc.
Thus multiplying the first ratio by c and second ratio by b, we have
First ratio- ca:bc
Second ratio- bc: bd
Thus the continued proportion can be written in the form of
ca:bc:bd
Example: Given ratio are-
a:b = 2:3
b:c = 5:2
c:d = 1:4
Find a:b:c.
Solution: Multiplying the first ratio by 5, second by 3 and third by 6, we have
a:b = 10: 15
b:c = 15 : 6
c:d = 6 : 24
In the ratio’s above, all the mean terms are equal, thus
a:b:c:d = 10:15:6:24
Likewise, ratio and proportion are used to solve many real world problems. Now get model solutions for chapter Ratios and Proportion in detail and step-by-step procedure to all questions in an NCERT textbooks only at BYJU’S.