That Section introduces the fractions, or rationals, and shows the decimal numbers as particular case of rationals.
This Lecture introduces the fractions, that are with the integers the rational numbers. The rational numbers are the exact results of the division of relative integers. The fractions are the way to manage sharing a quantity into portions.
The added pdf file examines the notions of multiple representations of a rational number as fractions and optionally as a relative integer. It introduces the notion of "canonical" representation.
That quiz assesses the new knoledges about fractions… and shows an example of fraction that is not a decimal number!
We explain here how to 'set to the same denominator' two fractions in order to add or subtract them to one another.
As that lecture contains many formulae, not only numerical examples are given in the video, but an additional pdf file called ‘FractionsAddSubtractExercises’ is given with all the formulae set and exercises, with the solutions at the end.
Another pdf file, called ‘RationalNumbersAddSubtract’ shows that the different formulae given are equivalent for the different representations of the same rational numbers.
As fractions set divisions, their multiplication and division is more straightforward than their adddition and subtraction!
That lecture contains also many formulae, so numerical examples are given in the video, and an additional pdf file called ‘FractionsMultDivExercises’ is given with all the formulae set and exercises, with the solutions at the end.
The rational numbers set Q has, together with the addition and the multiplication, a so called structure of "field". This lecture explains the characteristic properties of a field, always beginning with examples on fractions.
There is one additional pdf files, "QplusMultField", that explains more completely the structure of field and its consequences, in particular the definition and properties of the division between 2 rational numbers.
We end this course with three additional matters related to rational numbers: proportionality calculations (the so-called ‘rule of 3’ for French scholars), the decimal approximations, and the percentages calculation.
All these matters are driven by examples, with a Scilab session for the decimal approximations.