Direct proportionality indicates a situation in which, when one term is multiplied by a certain amount, the same exact thing happens to the second term.
In the same way, when one term is divided by a certain amount, the same exact thing happens to the second term.
The ratio between both magnitudes remains constant.
Let's observe an example that illustrates this concept.
Diana's credit card company charges a monthly fee of 2$, plus 1$ for each bank transaction.
Is the ratio of the amount Diana has to pay to the number of transactions she made during the month directly proportional?
Solution:
To answer this kind of question, it is convenient to draw a table:
X represents the number of transactions Diana made
Y represents the amount Diana has to pay
Notice, the question says that the credit card company applies a cost of 2$ each month, that is, even if Diana does not make any transactions, she will have to pay 2$.
Let's draw a table:
Now let's see:
Does the X multiply by a certain number and also the Y increase multiplied by the same number?
The answer is no.
We can see that when the X doubles and goes from 1 to 2
the Y does not double! From 3 to 4 what it does is 34.
Therefore, we can determine that the ratio of the amount Diana has to pay to the number of transactions she made during the month is not directly proportional.
Examples and exercises with solutions on direct proportion
Exercise #1
There are 18 balls in a box, 32 of which are white.
How many white balls are there in the box?
Video Solution
Answer
12
Exercise #2
In a box there are 28 balls, 41 of which are orange.
How many orange balls are there in the box?
Video Solution
Answer
7
Exercise #3
There are two circles.
One circle has a radius of 4 cm, while the other circle has a radius of 10 cm.
How many times greater is the area of the second circle than the area of the first circle?
Video Solution
Answer
641
Exercise #4
There are two circles.
The length of the radius of circle 1 is 6 cm.
The length of the diameter of circle 2 is 12 cm.
How many times greater is the area of circle 2 than the area of circle 1?
Video Solution
Answer
They are equal.
Exercise #5
There are two circles.
The length of the diameter of circle 1 is 4 cm.
The length of the diameter of circle 2 is 10 cm.
How many times larger is the area of circle 2 than the area of circle 1?
Video Solution
Answer
641
Check your understanding
Question 1
How many times longer is the radius of the red circle than the radius of the blue circle?