This course with the definition and properties of linearity proportionality as well as the proportionality table in the 5th grade will be beneficial to you.
In this lesson we will see:
- the definition of proportionality between two quantities;
- the proportionality table
- the property of linearity
- the percentages.
The student should be able to use all the properties by the end of this chapter. Then, to develop skills on the use of the cross product property. We will end this lesson with problem solving in fifth grade.
I. Situation of proportionality
1. proportional quantities
Two quantities are proportional when we can pass from one to the other
by always multiplying by a unique non-zero number.
If this is the case, this number, noted a, is called the proportionality coefficient.
- The side length and perimeter of a square are proportional because the perimeter of a square is obtained by multiplying its side length by 4.
- Here is the distance covered by a balloon in free fall. In 1 s, it covers 5 m and in 2 s, it covers 20 m. To go from the fall time to the distance covered, we do not multiply by the same number, so the fall time and the distance covered by the balloon are not proportional.
When we summarize the different values taken by two quantities in a table, this table is called a proportionality table.
In a proportionality table, we go from the values of the first quantity to those of the second by multiplying by the proportionality coefficient.
At a speed of 70 km/h, a car consumes 5 L per 100 km.
- Fuel consumption and distance traveled are proportional.
- At this speed, when the car travels a distance of 1 km, it consumes 0.05 L. These results can be grouped in a proportionality table.
- At this speed, the consumption, in liters of fuel, is equal to the product of the number of kilometers traveled by 0.05 which is the proportionality coefficient.
- In this situation of proportionality, the coefficient makes it possible to calculate the consumption from the number of kilometers travelled. For example, at this speed and for 15 km, the consumption will be L.
II. Applications of proportionality
1.apply to a percentage
During sales, a 15% discount is given on items in a store.
This means that:
- the discount and the initial price of an item are proportional;
- if the initial price of an item is 100 € then the discount is 15 €.
We are looking for the reduction of an article costing 80 €. These data are grouped in a proportionality table.
Therefore the reduction sought is equal to €.
To calculate x% of a quantity, multiply the quantity by x and then divide by 100.
25% of 350 is equal to .
The scale of a map or plan is the proportionality coefficient that allows you to go from real lengths to lengths on the map or plan.
This drawing represents the plan of a SA365 Dauphin helicopter.
In reality, it is 3.9 m high, so the scale is :
This means that 1 cm on the plan corresponds to 150 cm in reality.
The actual length of the device is therefore .
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