Why Do You Multiply The Reciprocal Of The 2nd Fraction, By The First When Dividing Fractions?

Question: Why do you multiply the reciprocal of the 2nd fraction, by the first when dividing fractions?

Explanation: Let`s use an analogy here where divide means share/split.

If you share 1 pizza between a couple of 2 people, they will each end up with a half.

Now lets try picture the reverse slowly. You have a couple of of 2 people and you share 1 pizza between half the couple, this means each half of the couple (1 person) is getting one pizza and this is only possible if there are 2 pizzas all together.

Now this can be done with halves, thirds, quarters .. it really does not matter. This is why dividing by a number is the same as multiplying by the reciprocal as if you was to divide by a fraction you are basically saying a fraction of the set gets "a value" and so what does the set get all together.

This is why dividing anything whether it`s a whole number or a fraction, by a fraction is the same as multiplying by the reciprocal of the fraction.

This is an example way of how I will be explaining to the student. That said, I will use different approaches if the student is struggling and some students learn better vocally so this example is not for everyone. That said, I do hope this piece helps at least the majority.