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Welcome to our Math lesson on Direct Proportion, this is the second lesson of our suite of math lessons covering the topic of Proportion, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
There are two main types of proportion: direct and inverse proportion. In direct proportion, the quantities a and c change in the same way as well as b and d.
In the example given earlier, the number of kilometres travelled is proportional to the amount of gasoline consumption. From the numbers, it is clear that if the number of kilometres triples, the gasoline consumption triples too. This type of proportion is known as direct proportion.
By definition, direct proportion is the relation between quantities whose ratio (or rate) is constant.
(We will see later that two quantities that are in inverse proportion behave in the opposite way, i.e. when one increases, the other decreases).
In the example with fuel consumption, this constant was the unit rate of gas consumption expressed in km/L (in both cases this number was 30 km/L). Let's see another example involving quantities that are in direct proportion with each other.
Five workers can carry a 200 kg load from the point A to the point B. How many workers are needed to carry 760 kg load in the same route?
This is a direct proportion example where any increase by a certain factor of the load brings the necessity to increase the number of workers by the same factor. Hence, we can use two approaches to find the missing quantity:
Thus, using the first method, we have:
Load carried by a single worker = Reference load/Reference number of workers
Thus, we have
Since the actual load to be carried is 760 kg, we obtain for the number of workers needed for this work:
The second method is shorter. We write
Thus,
As you see, the result obtained is the same with either method used.
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