Riya Hansen

2022-07-14

Most students asked why is that $\frac{a}{b}÷\frac{c}{d}=\frac{ad}{bc}$
I just told them: inverse the second fraction and multiply. Why? They ask me. I have no idea.
Any logical answers to them kids?
These day teachers just told students at secondary to memorise and no why is allowed in lessons. I think that is wrong. Putting people of studying maths.

amanhantmk

Expert

By definition, $x÷y$ should be a number $z$ such that $x=yz$
So you just verify:
$\frac{ad}{bc}×\frac{c}{d}=\frac{a}{b}$
Ultimately this works because of the associative and commutative laws of multiplication, but you don't have to tell the students that.
"Why" should always be allowed.

Frederick Kramer

Expert

When you divide $x÷y$, it is the same as $\frac{x}{y}=x×\frac{1}{y}$. Students familiar with fractions should be able to understand this. This is true no matter what $x$ or $y$ are, even if they're fractions. Therefore, $\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}×\frac{d}{c}=\frac{ad}{bc}$