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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

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:

- 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
- To write the proportion in the form
=*a**/**b*where d is the missing quantity.*c**/**d*

Thus, using the first method, we have:

Load carried by a single worker = *Reference load**/**Reference number of workers*

Thus, we have

L_{1} = *L*_{tot}*/**N*_{1}

=*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:

N_{actual} = *L*_{actual}*/**L*_{1}

=*760 kg**/**40 kg**/**worker*

= 19 workers

=

= 19 workers

The second method is shorter. We write

Thus,

Actual number of workers =

= 19 workers

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

Enjoy the "Direct Proportion" math lesson? People who liked the "Proportion lesson found the following resources useful:

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- Ratio and Proportion Math tutorial: Proportion. Read the Proportion math tutorial and build your math knowledge of Ratio and Proportion
- Ratio and Proportion Video tutorial: Proportion. Watch or listen to the Proportion video tutorial, a useful way to help you revise when travelling to and from school/college
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- Ratio and Proportion Practice Questions: Proportion. Test and improve your knowledge of Proportion with example questins and answers
- Check your calculations for Ratio and Proportion questions with our excellent Ratio and Proportion calculators which contain full equations and calculations clearly displayed line by line. See the Ratio and Proportion Calculators by iCalculator™ below.
- Continuing learning ratio and proportion - read our next math tutorial: Properties of Proportion. Geometric Mean

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