Life Applications of Inverse Proportion

Life Applications of Inverse Proportion

Just like direct proportion is used in life, inverse proportion is also used in many ways in life.

Let's take the same table we took for the opposite ratio.

Factor 1	1	2	3	4	6	8	12	16	24	48
Factor 2	48	24	16	12	8	6	4	3	2	1

Now let's factor 1 as the length of the rectangle. So should I say take factor 2 as the width of the rectangle? If you take it like that, the table will change like this!

Length of the rectangle	1	2	3	4	6	8	12	16	24	48
Length of the rectangle	48	24	16	12	8	6	4	3	2	1

Now has a life application of the inverse proportion been found? That is, we know from the table how the length and width of a rectangle of 48 square units can be determined.

You can take factor 1 as workers and factor 2 as days. That means if one worker does a work it takes 48 days to complete the work and when two workers do the work it takes 24 days to complete the work. Similarly you can consistently understand that if three workers work it takes 16 days to complete the work and if four workers work it takes 12 days to complete the work. How will that table change then? That's how it is.

Workers	1	2	3	4	6	8	12	16	24	48
Days	48	24	16	12	8	6	4	3	2	1

Is that all? Factors can be taken speed and even over time. How do you say that?

Let's take factor 1 as speed i.e. kilometers traveled per minute and factor 2 as time i.e. minutes.

Suppose to reach a place. One km / minute speed will take 48 minutes and 2 km / minute speed will take 24 minutes. 3 km / minute speed will take 16 minutes. Oh you understand now? Now we have to take our table like this.

Speed (km/minute)	1	2	3	4	6	8	12	16	24	48
Time (minute)	48	24	16	12	8	6	4	3	2	1

 

Next you ask how the calculations are made in inverse proportion?

We can take the two factors as the length and breadth of the rectangle or as workers - days or speed - time as desired to make the calculation. Are these life applications we have created?

For example let us take workers – days. Will it take 8 days for 6 workers to complete a certain work according to the table? Assuming we don't know how many days it will take, do we substitute x for 8? Let us take the unknown value as such. Since we have to take the inverse proportion as a product, we have to take the inverse ratio as 6 × x instead of taking the ratio as a fraction.

By taking another pair from the inverse proportion table and equating this pair, we can find the value of x. Shall we assume that a particular works takes 12 days if four workers work on it? Shouldn't the inverse ratio be taken as 4 × 12 instead of as a fraction?

What we have taken is not the inverse proportion? If the number of workers increases here, the working days will decrease. Fewer workers mean longer working days. We have to take the opposite ratio rule as multiplication. Although we have seen this before, I am repeating it so that it is always in your mind. So shall we equate the two pairs of multiplications that we have just taken?

6 × x= 4 × 12

6 × x = 48

x = 48 / 6

x = 8

Did we find the answer we need to find is 8? If six workers work it will take only eight days to complete the work. So the answer is correct.

This is how inverse proportion calculations are created.

You can do the same calculation for the length-width of the rectangle and speed-time calculations of the particular work. You can also do a variety of calculations that create tables with different multipliers. The more you try, the more you practice!

Now that you have a good understanding of direct proportion and inverse proportion calculations.

Let's move on to the next mathematical topic after looking at some more concepts and a few calculations about ratio. What is right?

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