Math Lesson 4.3.2 - Direct Proportion

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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.

Direct Proportion

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.

Example 2

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?

Solution 2

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:

  1. To find the unit rate first (which in this specific example corresponds to the amount of load a single worker can carry) and then divide the total load to this number in order to find the number of workers needed, and
  2. To write the proportion in the form a/b = c/d where d is 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

L1 = Ltot/N1
= 200 kg/5 workers
= 40 kg/worker

Since the actual load to be carried is 760 kg, we obtain for the number of workers needed for this work:

Nactual = Lactual/L1
= 760 kg/40 kg/worker
= 19 workers

The second method is shorter. We write

Reference load/Reference number of workers = Actual load/Actual number of workers

Thus,

200 kg/5 workers = 760 kg/Actual number of workers
Actual number of workers = 760 kg × 5 workers/200 kg
= 19 workers

As you see, the result obtained is the same with either method used.

More Proportion Lessons and Learning Resources

Ratio and Proportion Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
4.3Proportion
Lesson IDMath Lesson TitleLessonVideo
Lesson
4.3.1Definition of Proportion
4.3.2Direct Proportion
4.3.3Graph of Direct Proportion
4.3.4Cross Product in Direct Proportion
4.3.5Inverse (Indirect) Proportion
4.3.6Graph of Inverse Proportion

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  7. Continuing learning ratio and proportion - read our next math tutorial: Properties of Proportion. Geometric Mean

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