Proportionality: 4th grade math course PDF download.

A math course on proportionality in the fourth grade. In this lesson, the student should be able to demonstrate whether a table is proportional and know how to calculate the proportionality coefficient. In addition, they will be able to develop skills in using the cross product rule to determine a fourth proportional. Proportionality in math is very important for student progress. You will learn physical science through compound quantities like average speed. You should also be able to recognize a proportional situation graphically.

We will end this lesson by solving problems from everyday life in the eighth grade.

I. The fourth proportional


We consider two proportional quantities and three given values a,b and c.

The value of x can be determined using the rule of three (or the cross product).

Definition of the fourth proportional

Example 1:

Six jars of honey cost 21€. It is assumed that the price paid is proportional to the number of pots purchased. How much are five pots?

  • The data are grouped in a proportionality table:

Proportionality table 1

  • We determine x by calculation using the cross product rule.

x=\frac{21\times  \,5}{6}=\frac{105}{6}=17,5 €.

  • We deduce that five pots of honey cost 17.5 €.

Example 2:

A 225 MB file is downloaded in 54 seconds.

How long does it take to download a 850 MB file under the same conditions?

  • It is assumed that the connection speed is constant, i.e. the download time is proportional to the file size.
  • The data are grouped in a proportionality table.

Proportionality table 2

  • We determine the value of x using the cross product rule seen in seventh grade: x=\frac{54\times  \,850}{225}=\frac{45900}{225}=204\,s.
  • We deduce that the download time for a file with a capacity of 850 MB is 204 seconds.


Example 1 can also be solved by determining the price of a pot: 21\,:\,6\,=3,50 € so a pot costs 3.50 euros.

Then, we determine the price of 5 pots: 5\times  \,3,50=17,50 €.

On the other hand, this transition to unity is more delicate in example 2.

II. Apply proportionality in math

1. percentages


In a middle school with 475 students, there are 323 half-boarders.

What is the percentage of half boarders at this college?

We are looking for the number of half boarders per 100 students in which the proportion of half boarders would be the same.

  • The data are grouped in a proportionality table.

Proportionality table 3

  • We determine x by the calculation: x=\frac{323\times  ,100}{475}=68.
  • This means that 68% of the students are half-boarders at this college.

2. average speed


The average speed v is defined as a function of time t and speed d.



During a hike in the mountains, we covered 12.6 km in 4h 30 min.

What was our average speed?

  • Here, d = 12.6 km and t = 4h 30 min=4.5 h.
  • So we have v=\frac{d}{t}=\frac{12,6}{4,5}=2,8\,km/h.


  • Care must be taken to ensure consistency of units in applications.
  • One passes from a speed in m/s in km/h by multiplying by 3,6.

3. Compound quantities


Gold is one of the densest metals. Its density is 19,3\,kg/dm^3.

The Bank of France keeps this metal in the form of blocks, called ingots, 2.65 dm high and whose base has an area of 0.244 dm².

How much does such an ingot weigh?

  • To say that the density of gold is 19,3\,kg/dm^3 means that 1\,dm^3 of gold weighs 19.3 kg.
  • The mass of an ingot of volume V=2,65\times  \,0,244=0,6466\,dm^3 is sought.

composite sizes 2

  • x=\frac{19,3\times  \,0,6466}{1}=12,48\,kg
  • A gold bar weighs 12.48 kg.

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

Télécharger puis imprimer cette fiche en PDF

Télécharger ou imprimer cette fiche «proportionality: 4th grade math course PDF download.» au format PDF afin de pouvoir travailler en totale autonomie.

D'autres fiches dans la section 4th grade math class

Télécharger nos applications gratuites Mathématiques Web avec tous les cours,exercices corrigés.

Application Mathématiques Web sur Google Play Store.    Application Mathématiques Web sur Apple Store.    Suivez-nous sur YouTube.

D'autres articles analogues à proportionality: 4th grade math course PDF download.

  • 96
    Pyramid and cone: 4th grade math course download PDF.The pyramid and the cone are a very important chapter in eighth grade math. The student will need to know all the definitions as well as the different vocabulary regarding faces, vertex, base and height. Thus, it must also develop skills in calculations with the formulas of volume: I. The…
  • 96
    Equations: 4th grade math lessons for download PDF.The course on equations of the first degree with one unknown with the definition and the properties of solving an equation and then the method of solving problems in the fourth grade (4e) is to be understood completely. The student should be able to solve an equation with the various…
  • 95
    Powers: 4th grade math course download PDF.A math course on powers in the fourth grade. The student must have assimilated the definition of a power but also know the different formulas such as the product of two powers, the quotient of powers or the power of a power. Develop computational skills with scientific writing (or scientific…
Les dernières fiches mises à jour

Voici la liste des derniers cours et exercices ajoutés au site ou mis à jour et similaire à proportionality: 4th grade math course PDF download. .

  1. Integrals : corrected high school math exercises in PDF.
  2. Intégrales : exercices de maths en terminale corrigés en PDF.
  3. الوظائف والحدود: تمارين الرياضيات في السنة النهائية مصححة بتنسيق PDF.
  4. Functions and limits: senior math exercises corrected in PDF.
  5. Fonctions et limites : exercices de maths en terminale corrigés en PDF.

Inscription gratuite à Mathématiques Web. Mathématiques Web c'est 2 146 113 fiches de cours et d'exercices téléchargées.

Copyright © 2008 - 2023 Mathématiques Web Tous droits réservés | Mentions légales | Signaler une Erreur | Contact

Scroll to Top
Mathématiques Web