Determine if the following are in proportion.
15, 45, 40, 120

Hint: Take 15 and 45 find the ratio. Similarly, find the ratio of 40 and 120 and prove their ratio is the same.

“Complete step-by-step answer:”
Two varying quantities are said to be in relation of proportionality, if they are multiplicatively connected to a constant. i.e. when either their ratio or their product yields a constant. The value of this constant is called the coefficient of proportionality constant. The ratio is represented by the colon (:) sign between the quantities compared.
For example if \[\dfrac{a}{b}=\dfrac{c}{d}\]and is a proportion, then both \[\dfrac{d}{b}=\dfrac{c}{a}\]and \[\dfrac{a}{c}=\dfrac{b}{d}\]are in proportion.
We have to determine if 15, 45, 40 and 120 are in proportion.
Let’s take the ratio of 15 and 45 \[=\dfrac{15}{45}=\dfrac{1}{3}\]
\[\therefore \]Ratio of 15 and 45 = 1:3
Now take the ratio of 40 and 120 \[=\dfrac{40}{120}=\dfrac{1}{3}\]
\[\therefore \]Ratio of 40 and 120 = 1:3
\[\therefore 15:45=40:120\]
\[\therefore \]15, 45, 40 and 120 are in proportion.
Note: Take the values in another order i.e. 15, 40, 45 and 120.Changing the order will give the same ratio 8:3.