0
$\begingroup$

Earlier I encountered $\frac{\frac{49}{4}}{3}$ and parsed it as $49$ divided by $\frac{4}{3}$. Using the knowledge that dividing by fraction is the same as multiplying by its reciprocal, I changed it to $\frac{147}{4}$.

It turns out this was wrong and I should've considered it as $\frac{49}{12}$. I understand the $3$ and the $4$ get multiplied together to get the $12$.

I'm almost embarrassed to ask this question as it seems too basic. Can someone explain why my original thinking didn't work. When you have two division bars, does it become ambiguous?

2 Answers 2

5

You have to distinguish $\frac{\frac{49}{4}}{3}$ from $\frac{49}{\frac{4}{3}}$ Unfortunately, the typeset difference my be subtle, so better think of it as $(49/4)/3$ vs. $49/(4/3)$. Division (like subtraction: $(49-4)-3=42\ne 48=49-(4-3)$, but unlike addition or multiplication) is not associative.

  • 0
    The note about associativity helps, thank you.2012-10-24
2

$\frac{49}{\frac{4}{3}} = \frac{147}{4}$

While,

$\frac{\frac{49}{4}}{3} = \frac{49}{12}$

I think you just misinterpreted the question...