WHAT IS THE PROPORTIONALITY FACTOR? (EXERCISES SOLVED) - MATHS - 2024

The proportionality factor or constant of proportionality is a number that will indicate how much the second object changes in relation to the change suffered by the first object.

For example, if it is said that the length of a ladder is 2 meters and that the shadow it casts is 1 meter (the proportionality factor is 1/2), then if the ladder is reduced to a length of 1 meter, the shadow will reduce its length proportionally, therefore the length of the shadow will be 1/2 meter.

If instead the ladder is increased to 2.3 meters then the length of the shadow will be 2.3 * 1/2 = 1.15 meters.

Proportionality is a constant relationship that can be established between two or more objects such that if one of the objects undergoes some change then the other objects will also undergo a change.

For example, if it is said that two objects are proportional in terms of their length, then if one object increases or decreases its length, then the other object will also increase or decrease its length in a proportional way.

Proportionality factor

The proportionality factor is, as shown in the example above, a constant by which one quantity must be multiplied to obtain the other quantity.

In the previous case, the proportionality factor was 1/2, since the ladder «x» measured 2 meters and the shadow «y» measured 1 meter (half). Therefore, we have that y = (1/2) * x.

So when "x" changes, then "y" changes as well. If it is "y" that changes then "x" will also change but the proportionality factor is different, in that case it would be 2.

Proportionality exercises

First exercise

Juan wants to make a cake for 6 people. The recipe that Juan has says that the cake has 250 grams of flour, 100 grams of butter, 80 grams of sugar, 4 eggs and 200 milliliters of milk.

Before starting to prepare the cake, Juan realized that the recipe he has is for a cake for 4 people. What should be the magnitudes that Juan should use?

Solution

Here the proportionality is as follows:

4 people - 250g flour - 100g butter - 80g sugar - 4 eggs - 200ml milk

6 persons -?

The proportionality factor in this case is 6/4 = 3/2, which could be understood as first dividing by 4 to get the ingredients per person, and then multiplying by 6 to make the cake for 6 people.

By multiplying all the quantities by 3/2, the ingredients for 6 people are:

6 people - 375g flour - 150g butter - 120g sugar - 6 eggs - 300ml milk.

Second exercise

Two vehicles are identical except for their tires. The radius of the tires of one vehicle is equal to 60cm and the radius of the tires of the second vehicle is equal to 90cm.

If, after doing a tour, the number of laps made by the tires with a smaller radius was 300 laps. How many laps did the larger radius tires make?

Solution

In this exercise the constant of proportionality is equal to 60/90 = 2/3. So if the smaller radius tires made 300 turns, then the larger radius tires made 2/3 * 300 = 200 turns.

Third exercise

3 workers are known to have painted a 15 square meter wall in 5 hours. How much can 7 workers paint in 8 hours?

Solution

The data provided in this exercise are:

3 workers - 5 hours - 15 m² of wall

and what is asked is:

7 workers - 8 hours ---? m² of wall.

First you might ask how much 3 workers would paint in 8 hours? To find out this, the row of data supplied is multiplied by the ratio factor 8/5. This results in:

3 workers - 8 hours - 15 * (8/5) = 24 m² of wall.

Now you want to know what happens if the number of workers is increased to 7. To know what effect it produces, multiply the amount of painted wall by the factor 7/3. This gives the final solution:

7 workers -– 8 hours - 24 * (7/3) = 56 m² of wall.

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