Hello friends, today we are going to start with the session called properties of ratio, which
comes under Introduction to Ratio and Proportion. What is ratio? Ratio I can say comparison
of quantities having similar units. For example, if I consider age of A is 12 years and age of B
is 18 years. Can I say the ratio of the age is 12 is to 18. Yes, that is the simplified form is 2:3.
2 and 3 are not actual terms there has to be a multiplying factor. Here the multiplying factor
is 6. That is 6 into 2 and 6 into 3 will give me their actual ages.
Let’s now proceed with one more example. I am considering there is a solution of milk and
water where milk is 24 litres and water is 60 litres. Can I say the ratio of 24 and 60 is 2 and
5? It means what, that the ratio of milk is to water is 2 is to 5 or the ratio water is to milk is 5
is to 2. What is fraction of milk here? Out of 2 plus 5, 7 parts, 2 parts are milk. So, I can say
the fraction of milk is 2 by 7 and the fraction of water is 5 by 7.
Now, let’s proceed. I am considering a situation that is A upon 7 is equal to B upon 5 is equal
to C upon 4. Using this relation, I need to find the relation of A, B and C. To understand this if
I consider, A has 7 parts of pizza, B has 5 parts of pizza and C has 4 parts of pizza. But each
part of A, B, C is equal. Can I say, 1/7th of A, will be equal to 1/5th of B, will be equal to 1/4th
of C, that is A is to B is to C is 7 is to 5 is to 4. To understand this, let us consider the alternate
method. The alternate method is A upon 7 is equal to B upon 5 is equal to C upon 4. So,
during equal relation you can equate them to a constant value let’s say K. So, if I consider A
upon 7 is equal to B upon 5 is equal to C upon 4 is equal to K. So, can I say A is 7K, B is 5K, C
is 4K. And hence again I can say A is to B is to C, is 7 is to 5 is to 4. Let’s consider the case as A
is to B is to C is 1 upon 7 is to 1 upon 5 is to 1 upon 4, again you need to find the ratio of
ABC, but this is also a ratio given to you. This is a fractional form given to you. You need to
convert them into an integral form. To convert them into an integral form.