Proportionality and percentages: 6th grade math course in PDF.

Math course on proportionality and percentages This lesson covers the definition of proportionality and its additivity as well as the passage through the unit and percentages as well as the coefficient and the proportionality table. The student should be able to show if a table is proportional or not and also know how to calculate the value of the proportionality coefficient. Many skills will be developed in this chapter such as calculating the value of a fourth proportional knowing the value of the proportionality coefficient or solving problems in the sixth grade. We will end this chapter with the study of percentages.

I. Proportionality tables

1. coefficient of proportionality


At the market, the reason is sold 3,50€ the kilogram.

For 4 kg, we pay 4 times more than for 1 kg, i.e. 14 €.

Indeed, 4\times  \,3,50=14.

For 0.50 kg, you pay half as much as for 1 kg, i.e. 1.75 €.

Indeed, 0,5\times  \,3,50=1,75.

We say that the price, in euros, is proportional to the mass, in kilograms.

The price (in euros) is obtained by multiplying the mass (in kilograms) by 3.5.

proportionality table

In the table above, we go from a number in the first row to the corresponding number

of the second line by multiplying by the same number.

We say that this number (3.5) is a proportionality coefficient (it is the price of one kilogram of grapes).

2. multiplying a quantity by a number

Example 1:

The flow rate of a faucet is regular, i.e. the number of liters flowing is proportional to the duration of the flow. In 5 minutes, 8 liters of water flow out.

How long will it take for 20 L of water to flow out?

20=8\times  \,2,5

5\times  \,2,5=12,5

So 20 L of tap water will flow out in 12.5 min.

proportionality table
Example 2:

We take example 1 above. In 5 minutes, 8 L of water flows out.

If the tap is left on for 60 minutes, how many liters of water will flow out?

60=5\times  \,12

8\times  \,12=96

So in 60 minutes, 96 L of water will flow out.

proportionality table

3.additivity of proportionality


In 5 minutes, 8 L flows out and in 12.5 minutes, 20 L flows out.

5+12,5=17,5 min and 8+20=28 L.

So in 17.5 minutes, 28 liters of water will flow out.

Proportionality table

II. Passage through the unit and percentage

1. passing through the unit


With 5 kg of paint, you can cover 8 m² of facade.

  • To calculate the surface area of the façade covered with 9 kg of paint, proceed as follows

– with 1 kg of paint, you can cover 8 m²: 5 i.e. 1.6 m².

– with 9 kg of paint, you can cover 9\times  \,1,6=14,4\,m^2.

proportionality table

  • To calculate the mass of paint required for 30 m² of facade, we can proceed as follows:

-For 1m², you need 5 kg : 8 that is to say 0,625 kg of paint.

– for 30 m², it is necessary 30\times  \,0,625=18,75\,kg.

You can also use this proportionality table:

2.apply a percentage rate

To say that a fruit yogurt contains 14% fruit means that the mass of fruit is proportional to the mass of yogurt and that in 100 grams of yogurt there are 14 grams of fruit.

t is a number. To take t % of a quantity is to multiply that quantity by \frac{t}{100}.


A 125 g yogurt contains 14% fruit.

Calculating the mass of fruit in this yogurt is to take 14% of 125 g, i.e. to take

\frac{14}{100}\times  ,125=0,14\times  ,125=17,5\,g.

So there are 17.5 g of fruit in this 125 g yogurt.

Special cases:
  • Taking 50% of a quantity is taking half.
  • Taking 25% of a quantity is taking a quarter.
  • Taking 75% of a quantity is taking three-quarters.


25% of the 28 students in a sixth grade class wear glasses.

\frac{25\,}{100}\times  28=\frac{1}{4}\times  \,28=7 so 7 students in this class wear glasses.

Did you learn this course on proportionality and percentages in 6th grade?

La proportionnalité et les pourcentages

QCM de maths sur la proportionnalité et les pourcentages en 6ème.

Things to remember:

Skills to learn about proportionality:

what to remember

  • Know the definition;
  • Know how to calculate the proportionality coefficient;
  • Know how to calculate a fourth proportional;
  • Use the cross product;
  • Solve problems.

This course is in accordance with the official programs of thenational education.

In addition, you can consult the exercises on proportionality in the sixth grade.

Cette publication est également disponible en : Français (French) العربية (Arabic)

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