Question

How do you know if the pair \[\dfrac{4}{3}\] and \[\dfrac{8}{6}\] form a proportion?

Answer 1

Hint: Proportion validates if the two ratios are equivalent to each other. We use ratios to compare two things that share the same units; we represent the ratio in \[a:b\] or \[\dfrac{a}{b}\] . We have two ratios and if the product of the means is equal to the product of extremes then the given pair form a proportion.

Complete step-by-step answer:
Proportion is a statement that equates two ratios or rates.
Given, \[\dfrac{4}{3}\] and \[\dfrac{8}{6}\] .
Now we know that the proportion is represented as \[\dfrac{a}{b} = \dfrac{c}{d}\] or \[a:b::c:d\] . Where ‘a’ and ‘d’ is called extremes and ‘b’ and ‘c’ is called means.
If \[a \times d = b \times c\] then the given pair form a proportion.
Now,
 \[\dfrac{4}{3} = \dfrac{8}{6}\]
We can see that ‘4’ and ‘6’ is called extremes and ‘8’ and ‘3’ is called means.
 \[4 \times 6 = 8 \times 3\]
 \[ \Rightarrow 24 = 24\]
Hence the given pair forms a proportion. That is a true proportion.

Note: The ratio and proportions are different. A fraction is a number that names part of a whole or a part of a group. The denominator represents the total number of equal parts the whole is divided into. A ratio is a comparison of two quantities. The ratio is an expression while the proportion is an equation.