We are that taught you divide fractions by multipling the fraction to be divided by the reciprocal of the fraction we are dividing by. (NOTE: The PRODUCT of a number multiplied by its RECIPROCAL is 1.) In these exercises, the reason why this is done is stressed.
First we point out that there are three ways to express division. They are:
In each of these expressions, it is clear what is meant.
These exercises begin by expressing the division of two fractions with the second method.
Next we express it by the third method. This is done automatically. Notice that this expression is to be multiplied by another quotient of fractions.
To proceed we use the principles that any number divided by itself is 1 (for example 3 ÷ 3 = 1), and any number multiplied by 1 does not change its value (for example 3 × 1 = 3).
You are to choose a fraction to be divided by itself (which is 1). And multiply the given expression by it.
The object is to use the fraction that is the RECIPROCAL of the dividing fraction (that is, the one on the bottom).
If it is correct the next step is automatically set up.
Notice that the product of the dividing fraction and its reciprocal is replaced by "1", which is its product.
Finally, you need to multiply the remaining fractions to get your answer.