Question

What is the difference between direct and inverse proportion and how do I know which to use? What are real life examples?

Answer 1

Hint: In this question we have to tell the difference between direct and inverse proportions. We know that these both are comparison quantities, so we will first understand the difference between the both and then also understand with examples.
The symbol of directly proportion is
$x\propto y$
And, inversely proportion is represented is represented with
$x\propto {\displaystyle \frac{1}{y}}$ .

Complete step-by-step answer:
Let us first understand the definition of Direct proportion. We know in direct proportion, when one quantity increases the other quantity increases too. Similarly when one quantity decreases, the other quantity decreases too. So we can say that the corresponding quantity always remains constant.
Some real life examples of direct proportion are:
If we buy more packets of milk, it will cost more money.
If we have to travel further to travel, it will take more time..
Bigger area of floor requires more tiles/paint.
We can see that if we use more packets, it will directly affect money, i.e. more money is needed.
So in direct proportion, the ratio between matching quantities stays the same if they are divided. We can represent it symbolic form:
$k={\displaystyle \frac{x}{y}}$ .

In inverse or indirect proportion, we can say that when one quantity increases the other quantity decreases too. When one quantity decreases the other quantity increases too.
Some of the examples of indirect proportion are:
If more people share a task, it will be completed in less time.
If we travel at a faster speed, it means that it will take less time.
If we pack sugar in smaller packets, then more packets will be needed for the same quantity.
Here we can see that if more people can work for a specified time, then time will be less consumed.
We can write the inverse proportion as follow:
$k=x\times y$ .
So we have to consider which quantities are being compared and we have to use our common sense to decide how to relate them .
Hence this is the difference between inverse and direct proportionality with examples.

Note: Let us take an example: The value of $f$ is directly proportional to $g$ . We have been given $f=20,g=10$ . Now we have to find an equation relating $f$ and $g$ .
We have been given
$f\propto g$, or we can write
 $f=kg$, where $k$ is the constant proportionality.
 By putting the values in expression we can write
$20=k\times 10$ .
It gives
 $k={\displaystyle \frac{20}{10}}=2$ .
So we will put this value in the expression:
$f=2g$ .
From this we can understand the relation between $f$ and $g$