4
$\begingroup$

Recently I had this doubt about the order of precedence of mathematical operations multiplication and division. Given that we have a simple question like this

80 / 10 * 5

without parenthesis, what should be the answer?

Should it be 40 considering both multiplication and division has the same precedence and they should be operated in a left-to-right manner in this situation?

Or

Should it be 8/5 given that multiplication has precedence over division?

$\endgroup$
1
$\begingroup$

Think of it as $$ 80 \div 10 \cdot 5 $$ Since $\div$ and $\cdot$ have the same precedence. However, depending on the context is might also mean $\frac{80}{10 \cdot 5}$., but that is almost never the case unless you have brackets around $10 \cdot 5$.

$\endgroup$
  • $\begingroup$ Surprisingly I just met this particular case where ÷ have precedence over while calculating the taxes I have to pay in France as a freelancer. The formula is in a legal text (legifrance.gouv.fr/eli/decret/2017/3/8/ECFS1700138D/jo/texte/fr) and is Taux = T - 3,50 % × (1 - R/0,7 PSS). I could not make it work until I modified it to Taux = T - 3,50 % × (1 - R/ (0,7 PSS)). $\endgroup$ – Daishi Aug 22 '18 at 18:44
0
$\begingroup$

When you have multiple binary operators written in 'horizontal form' such as in $80\div 10\times 5$, that are of the same precedence, you perform them in left-to-right order. So in this case, $80\div 10\times 5=8\times 5=40$ (and yes, the order does matter in this case and others like it).

An alternative way of thinking about this, is to "treat the division sign like you do a negative sign (it comes with the number to it's right)" So we can think of $80\div 10\times 5$ as $80\times \frac{1}{10}\times 5$, and the we have associativity and commutativity since it's all multiplication.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.