DESCRIBING PROPORTIONS | GRADE 9 Q3

A proportion is a statement of equality of two ratios.
In symbols: 𝑎/𝑏=𝑐/𝑑 𝑜𝑟 𝑎:𝑏=𝑐:𝑑 where 𝑏≠0 and 𝑑≠0.
Each number in a proportion is called a term.
𝑎(first term)/𝑏(second term)=𝑐(third term)/𝑑(fourth term)
The second and third terms are called the means and the first and fourth terms are called the extremes of the proportion.
Note that the above proportion is read as “a is to b as c is to d”.
To illustrate, in the proportion 3 : 4 = 9 : 12, the extremes are 3 and 12 while the means are 4 and 9. In the proportion 5 : 6 = 50 : 60, can you name the extremes? How about the means?
Consider each of the two proportions above. Let us multiply the extremes and then multiply the means. What do you observe? We get the product 3 x 12 = 4 x 9 for the first proportion, and the product 5 x 60 = 6 x 50 for the second proportion. Does this equality hold true for all proportions? This equality is generalized in the Fundamental Law of Proportionality which states that:
In any proportion, the product of the means is equal to the product of the extremes.