Whatever we do in life, we manipulate fractions on a daily basis. This is done for example when we cut a pie, read a percentage on a label or play LEGO.

Fractions are also the first abstract concept taught in mathematics and more often what confuses students with mathematics. Although these may seem tricky at first, it becomes much simpler once we visualize what a fraction is and how it works.

Taking a Fraction

The number above, at the numerator, represents the number of shares we take.
The number below, at the denominator, represents the number of total shares.

If we take 1/4 (a quarter) of a pie, we cut it into 4 equal parts and take 1 share.

A quarter, 1/4, of a (spinach) pie.

A quarter, 1 / 4, of a (pistachio) cake.

Other concrete examples:
- If in a class of 16 students 9 are girls, then 9/16 of them are girls.
- To advance 3/4 of a meter, we divide it into 4 equal steps (of 25cm) then advance of 3 times this distance (75cm).
- To take 3/5 of a number, we divide by 5 and multiply by 3.

Two main rules

We never divide by 0!

If we multiply or divide the numerator and the denominator of a fraction by the same number: we get an equivalent fraction (equal).

Objectives

To know how to simplify a fraction will allow us, among others, to:
- Better visualize and compare quantities.
- Transform a fraction to an equivalent one.
- Manipulate smaller numbers.
- Simplify calculations.
- Understand percentages (%).

Multiplying and dividing fractions
How to proceed?
Why is the solution a smaller number than the fractions involved when we multiply?
It becomes childish once we get the insight ;)

Adding and subtracting fractions
Adding and subtracting fractions may seem tricky at first, but if we follow a few simple steps, we will have the hang of it in no time.

We may want to visualize and manipulate fractions first. Let's use the H.urna Explorer