Therefore, when setting up a direct proportion problem, make sure that the ratio is stated correctly.
Failure to do so may result in another type of proportion known as an inverse proportion, which will
give you the wrong answer.
2-2. Defining Inverse Proportions
. The term "inverse proportion"
to those problems where
an increase in the value of one term will cause a decrease in the value of another term. The same would
hold true if a decrease in one term would cause an increase in another term. For example, the ratio 3:2 is
the inverse of the ratio 2:3, thus when the two ratios are equated, the terms, or elements, are said to be
inversely proportional. In this example, the product of each ratio is equal.
3:2 :: 2:3 or 2:3 :: 3:2
a. Another example is where the means of a proportion can be changed in an inverse manner
while the extremes are held constant (the same can be done with the extremes and the means held
constant). For example, in the proportion 2:5 :: 8:20, the means' product (5 x 8) is 40. If the first mean
is doubled and the second mean is halved, the proportion becomes 2:10 :: 4:20. The means' product is
still 40 even through the means were inversely changed. You will note that the means' product of both
proportions is equal to the extremes' product; thus, the proportional relationship between the ratios
remains the same. A similar situation exists if the extremes are changed.
2:5 :: 8:20
Doubling the first extreme and halving the remaining extreme changes the proportion but not the
relationship between ratios.
4:5 :: 8:10
Any of the three proportion rules may be applied to the examples above to determine an unknown value
and to prove that a proportion is true.
b. Proportion problems can be used effectively in determining the manpower needed on a
proposed survey project For example, it is necessary to estimate the number of days needed to survey a
pipeline right-of-way in a tropical country. Although the line is long, this assignment normally takes
252 days for 2 survey teams to complete. However, adverse weather conditions are expected in about
60 days; therefore, can 12 survey teams complete the assignment before day 60?
c. Your analysis should indicate that if the number of survey teams increases, the number of
days to complete the assignment will decrease. Therefore, in order to solve this problem, use an inverse
proportion, whereby one term decreases as another term increases. The best way to set up an inverse
proportion is to equate like terms, such as 2 teams:12 teams and 252 days:x days. You infer that the
time involved with 12 survey teams is less than that required with 2 teams therefore, you can invert the