Inverse proportion animation

The heights of these two bars vary in When one gets large, the other gets small; when one gets
small, the other gets large -
When the blue bar grows so that it
its size.half (times 1/2)
If the green bar shrinks so that its height is cut to its
height.triple (times 3)
The height of one of the bars will Further explanations follow. |

It is probably best to understand direct proportions first.

If you are not familiar with direct proportions, perhaps it would help to see that material before going further here. You can find an explanation of direct proportions here.

Inverse proportions have reciprocal factor changes.

Probably better stated as a reciprocal proportion, the inverse proportions relates two quantities through factors that are multiplicative inverses. That is, through factors that are reciprocals, such as 3 and 1/3.

*Drive the same distance in twice (2) the
time at half (1/2) the speed.*

For example, let us say that you are driving a car and you are going to travel 60 miles. Consider this to be a constant distance throughout the following discussion.

Case #1:

Suppose that you spent 1 hour driving. Your average speed would be 60 mph.

Case #2:

Suppose that you spent 2 hours driving. Your average speed would be 30 mph.

So, changing the ** number of hours** that you drive will change the

Notice that the number of hours, the time, that is, changed by a factor of 2, since 1 hour times 2 is 2 hours.

Also, notice that the speed at which you were traveling changed by a factor of 1/2, since 60 mph times 1/2 is 30 mph.

The two quantities, ** time **and

Definition of Inverse Proportion

When quantities are related this way we say that they are in inverse proportion. That is, when two quantities change by reciprocal factors, they are inversely proportional.

In the above example the time is in inverse proportion to the average speed. One could also say that the average speed was in inverse proportion to the time.

The formal definition of inverse proportion:

Two quantities, A and B, are in inverse proportion if by whatever
A changes,
B changes by the factor.multiplicative inverse, or reciprocal, of that factor |