Riya Hansen

Answered

2022-07-14

Most students asked why is that $\frac{a}{b}\xf7\frac{c}{d}=\frac{ad}{bc}$

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.

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.

Answer & Explanation

amanhantmk

Expert

2022-07-15Added 17 answers

By definition, $x\xf7y$ should be a number $z$ such that $x=yz$

So you just verify:

$\frac{ad}{bc}}\times {\displaystyle \frac{c}{d}}={\displaystyle \frac{a}{b}$

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.

So you just verify:

$\frac{ad}{bc}}\times {\displaystyle \frac{c}{d}}={\displaystyle \frac{a}{b}$

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

2022-07-16Added 7 answers

When you divide $x\xf7y$, it is the same as $\frac{x}{y}=x\times \frac{1}{y}$. 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, $\frac{a}{b}\xf7\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}=\frac{ad}{bc}$

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