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A rule of three sum is possibly the most common of mathematical procedures. Using rules of three sum, in three simple steps, it is possible to determine an unknown variable if we have three other given values.

A simple, direct rule of three sum enables us to calculate a value in relation to direct proportion. What this means is that, if we half one value, the other value is also halved. The given task could, in this case, appear as follow:

If three cars consume 150 litres of gas, how much gasoline would be consumed by 5 cars?

As is evident from our function, we have three known values (3 cars, 150l, and 5 cars) and one unknown (the amount of gasoline consumed by 5 cars). According to the basic task, we have a direct proportion because an increasing number of cars leads to an increasing amount of gasoline consumed. Let us resolve this function:

1. step one: three cars consume 150 l of gas / : 3

2. step two 1 car consumes 50 l of gas / . 5

3. step three 5 cars consume 250 l of gas

The response therefore is that 5 cars consume 250 l of gas.

Using the simple rule of sums, we can also resolve calculations of percentage. One such problem appears as follows:

If a bag weighs 35g, how much does 25% of that bag weigh?

With the help of the rule of three sums, we can resolve this problem very
quickly:

1. step one: 100% corresponds to 35 kg /
:100

2. step two: 1%
corresponds to 0,35 kg / . 25

3. step three 25% corresponds to 8,75 kg

The response is that 25% of 35 kg is 8.75 kg.

With the help of indirect proportion, we can solve problems in which values are indirectly proportional. This would be like saying: if we have a half of one value, then we have to double a second value. An example of such a problem may be:

If three workers need 7 hours to fulfill a certain job, how long would it take 7 workers to accomplish the same task?

In this case, we also have three knowns and one unknown. With this problem, we have a simple indirect proportion because, with a larger number of workers, the time required is less. The solution looks as follows:

1. step one: 3 workers accomplish a certain job within 7 hours / :3
/ . 3

2. step two 1 worker accomplishes the same job within 21 hours / . 7 / : 7

3. step three 7 workers accomplish the same job within 3 hours.

In this case then, the response is that seven workers need 3 hours to accomplish the same task.

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