Problem Statement
The question asks us why the quotient of the division of two fractions is greater than the dividing fractions.
Solution
The reasons for this is that:
1. A number in the denominator is the same as multiplying by the reciprocal of that number.
That is,
[tex]\begin{gathered} \frac{3}{4}=3\times\frac{1}{4} \\ \\ \text{where,} \\ \frac{1}{4}\text{ is the reciprocal of 4} \end{gathered}[/tex]
2. Multiplying by the reciprocal of a fraction makes the fraction become greater than 1. That is,
[tex]\begin{gathered} \frac{3}{\frac{3}{4}}=3\times\frac{4}{3} \\ \\ \text{where,} \\ \frac{4}{3}\text{ is the reciprocal of }\frac{3}{4} \end{gathered}[/tex]
3. This, therefore, has the effect of multiplying a fraction by a number bigger than 1 to give a larger answer because of the multiplication operation rather than the lower value as expected in a division operation.
