Question

The equality of two ratios is known as _____________.

Answer 1

Hint: We are asked to fill in the blank with the most appropriate answer. When we have two ratios \[a:b\] and \[c:d\], and we say that these ratios are equal, we will call them proportions. These ratios though it may look different outwardly but when we reduce it to the simplest form these ratios are the same only. And when four numbers are in proportion, we write the expression as, \[a:b::c:d\] which is read as, ‘a’ is to ‘b’ as ‘c’ is to ‘d’. Hence, we will have the required answer for the blank.

Complete step by step answer:
According to the given question, we are asked to fill the given blank with the most appropriate answer.
We are asked about the equality of ratios.
Suppose we have two ratios, say \[a:b\] and \[c:d\]. And let’s say we are also given that these ratios are equal. So, when we say that two ratios are equal, they are no longer two different ratios rather both are the same. They just look different outwardly as one of them would be a multiple, but if we are to reduce them into the simplest form, then they are alike.
If two ratios are equal, then those ratios are proportional. And we can write the proportionality of two ratios as,
\[a:b::c:d\] which is read as, ‘a’ is to ‘b’ as ‘c’ is to ‘d’

Therefore, the equality of two ratios is known as proportion.

Note: The two ratios need not be similar looking at first, we can check if the ratios are equal by first reducing the given ratios into the simplest forms first and then carrying out the comparison.
For example – if we have \[1:2\] and \[5:10\], they may seem different but when they are reduced they are similar to \[1:2\].