Basic Mathematical Facts about Inverse Proportion

Basic Mathematical Facts about Inverse Proportion

Today we will explore some basic math facts about inverse proportion.

Before that we always remember that direct proportion is in fraction form and inverse proportion is in multiplicative form. So we call the inverse proportion elements as factors. That is to say that it is the product of two multiplying factors.

Let us take the number 48. How can we write its multiple factors?

1 × 48 = 48

2 × 24 = 48

3 × 16 = 48

4 × 12 = 48

6 × 8 = 48

8 × 6 = 48

12 × 4 = 48

16 × 3 = 48

24 × 2 = 48

48 × 1 = 48

You seem to be wondering if there are so many ways to write. Yes, can you write in so many ways?

Now we are going to tabulate these for inverse proportion just as we tabulated them for direct proportion. While tabulating in such a way, let us refer to factor 1 for numerator and factor 2 for denominator. Because in inverse proportion we have to set the fraction system as a multiplier. That is also the inverse proportion. That is, even the method of writing against the direct proportion.

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

 

Did you notice the table?

When looking from left to right i.e. from here to there, the factors in factor 1 are increasing and decreasing presence in factor 2. That is, as the factor 1 increases, the factor 2 decreases.

If we look at this from right to left i.e. from there to here, the factors in factor 1 are decreasing and the factors in factor 2 are increasing, aren't they? We already know that this is the property of inverse proportion.

As far as the inverse proportion is concerned, if the factors of one element increases, the factors of the other element must decrease. Or if the factors of one element decreases, the factors of another element must increase. The reason I repeat this trait in different sentences is because you should always keep this trait in mind. You mean the trait you already have in mind? That's right too.

Now we need to put the table in multiplicative form instead of fractional form.

That is

1 × 48

 2 × 24.

Any two pairs of factors you now multiply will yield the answer 48. Yes, you mean that's because we set up this table by making factors of 48? Yes that's right. But this is the basic math fact you need to know about inverse proportion.

Also, any two pairs taken and equated will have the same product.

1 × 48 = 2 × 24 = 48. Yes, you mean to come like that? That's right too.

If this is to be expressed in terms of variables then x × y = a constant should be expressed as a constant.

So a direct proportion means that x / y = a constant and an inverse proportion means that x × y = a constant, have you seen? You should always keep this basic distinction in mind.

That's all we need to know about inverse proportion. Shall we summarize what we have learned so far?

1. Inverse proportion means that when one of two factors increases, the other decreases. Or when one of the two factors decreases the other increases.

2. The product of any two factors in inverse proportion is a constant.

3. Equating any two products in inverse proportions are equal.

Tomorrow we will look at the life applications of inverse proportion.

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