A DIDACTIC PROPOSAL TO TEACH TO DIVIDE FRACTIONS. PART II

LEARNING TO DIVIDE A FRACTION BETWEEN ANOTHER FRACTION

Maigualida is on a diet and is in the dilemma of how to consume half a bar of chocolate without gaining weight. Her friend Yaneth suggests consuming it fractionally, at a rate of a third part every certain time, during the day. How many servings equivalent to the 3rd part of the chocolate bar represent half of it?

The previous approach suggests the following questions:

How many times is 1/3 contained in 1/2?
How many times does 1/3 fit in 1/2?
How much is ½ divided by 1/3?

Graphically, this is the situation:

When superimposing bars 1 and 2, it is observed that the yellow strip that represents half of the unit, in this case of the chocolate bar, coincides with the middle of the 2nd strip, green in this case, that is, 1 / 3 plus half of the next third, that is, 1/3 plus 1/6, as illustrated in the last bar.

So, 1/3 fits 1.5 times in a ½. That is, ½ between 1/3 is equal to 1 ½.
How does Maigualida distribute half of the chocolate bar between each of the three thirds of the day?

This question involves dividing half of the chocolate bar into three equal parts. This is, ½ between 3. According to what is explained in part I of this tutorial, we divide the unit into two equal parts and then divide each half into three parts. Therefore, during the day, Maigualida should consume 1/6 of the half chocolate bar on three different occasions, that is, 1/6 + 1/6 + 1/6 = ½, as illustrated when comparing bars 1 and 3.

SOURCE: VILLALOBOS (2014), A DIDACTIC PROPOSAL TO TEACH TO DIVIDE FRACTIONS.