One greatness is a benchmark that can be used to compare measures diverse. At greatnessphysical most known and used in everyday life are the length, or the distance, a pasta (better known as weight), the velocity it's the volume. It is possible to build reasons between measurements of two distinct quantities, and when two of these reasons are equal, the quantities are called proportional. We say they are directly or inverselyproportional according to the behavior observed in one of them in relation to a variation in the measure of the other.
Directly proportional quantities
Two quantities are called directly proportional when the increase in the measure of one of them causes a increase in the measure of the other in the same proportion, or when one reduction in the measure of one of the magnitudes it causes a reduction in the measure of the other in the same proportion.
1ºANDexample: speed and distance covered are directlyproportional. This is because increasing the speed of an object causes the distance traveled by it (in the same amount of time) to increase as well.
Note that reducing the speed of an object causes the distance traveled by it, in a given period of time, to also decrease. That's why speed and distance covered are greatnessdirectlyproportional.
2nd Example: The number of employees in a factory and the number of products manufactured. Increasing the number of employees (under ideal production conditions) also increases the number of items produced.
Inversely proportional quantities
Two quantities are called inversely proportional when an increase in the measure of one of the quantities causes a reduction in the measure of the other, and vice versa.
Example: speed and time are inversely proportional. By increasing the speed of an object, it will take less time to travel a certain path.
It is important to remember that variations always occur in sameproportion, that is, if we double the object's speed, the time spent by it, in the same route, drops by half.
Rule of three
THE rule and three is a way of using the propertyfundamentalof theproportions to determine one of the four measures of two magnitudes, when the other three are known. The way to find this measure is not the same for directly proportional and inversely proportional quantities.
When two quantities are proportional, just apply this fundamental property over a proportion to find the missing measure.
Example: let's say a car is at 50 km/h and, in a given period of time, travels 250 km. How many kilometers would you travel if your speed were 75 km/h?
Assembling the proportion and applying the fundamental property of proportions, we will have:
250 = 50
x 75
50x = 75·250
50x = 18750
x = 18750
50
x = 375 km.
When the two magnitudes are inverselyproportional, you must set the proportion and inverter one of the reasons before applying the fundamental property of proportions.
Example: a vehicle, at 120 km/h, spends 2 hours on a given route. What would your speed be if the time spent on this route was 6 hours?
By increasing the time spent on the trip, the speed of the car decreases, so these greatness they are inverselyproportional. Assembling the proportion between them, we will have:
120 = 2
x 6
Before applying the fundamental property of proportions, it is necessary reverse one of the reasons. Note that each of them is related to one of the quantities. If the setting of the proportion is done differently, the solution will be wrong.
120 = 6
x 2
6x = 2·120
6x = 240
x = 240
6
x = 40 km/h
