-3

1) $ 36 ÷ 6( 9 – 3) = ?$ $1$ or $36$

2) $36 ÷ 6^{ (5 – 3)} \times 6 = ?$ $6$ or $216$

My Attempt : I used "VBODMAS" rule to solve the problem.

1) $ 36 ÷ 6( 9 – 3) =36 ÷ 6$ of $6$ $= 1$

2) $36 ÷ 6^{ (5 – 3)} \times 6$ = $36 ÷ 6^2 \times 6$ = $1 \times 6 = 6$

Actually I am confused about the use of 'OF' in 'VBODMAS' rule.. Can anyone please help me out?

cmi
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    As an aside, using $a\div b$ and $a/b$ leads to such ambiguity in these situations. If you were to use the far superior $\frac{a}{b}$ to denote division it would have been clear what the intention was as it would either have been written as $\frac{36}{6}(9-3)$ or as $\frac{36}{6(9-3)}$ and it would have been clear whether $(9-3)$ is a factor of the top or of the bottom. In any event, with practice one recognizes which notations are potentially ambiguous and so learns to avoid them, much like how using $\sin^{-1}$ means different things depending where you are making $\arcsin$ superior. – JMoravitz May 08 '19 at 12:02

2 Answers2

4

There is no solution for these, it is simply a matter of definition.

The operations $/$ and $*$ are usually equally strong (not sure if that is the right term, sorry), so $$36/6(9-3)$$ could be both

$$\frac{36}{6(9-3)}$$

or

$$\frac{36}{6} \cdot (9-3).$$

Some say that in such a case, you should evaluate from left to right, so the second solution is right, others say that if we leave out the dot in a multiplication, it is stronger than a multiplication or division with symbol, thus the second one would be correct.

Again, there is no "right" answer, it all boils down to how you define these things.

Therefore, such questions are often used to generate heated discussions in the "only 7.93% of people are clever enough to solve this!" type of posts.
As mathematicians, we should try to avoid writing something like that.

Dirk
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1

First evaluate the terms in brackets and do the operations as per the BODMAS rule Here,

1) $36\div6(9-3) = 36\div6(6) = 6(6) = 36$

[However if you perform $36\div(6(9-3))$ the answer will be $36\div36 = 1$]

2) $36\div6^{(5-3)}$x$6 = 36\div6^2.6 = 1.6 = 6$

Google calculator for verification

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19aksh
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  • All that using google calculator here shows is that for this specific program and these specific numbers the result is interpreted in that specific way. However, if you were to see someone write $360/2\pi$ from context you would likely assume that this is intended to be interpreted as $360/(2\pi)$ and is being used to convert an angle from radians to degrees rather than $(360/2)\pi$ which has little to no meaning, going against your proposed answer. Context is highly important. In some contexts it makes more sense for $a/bc$ to be $a/(bc)$ while in others it may make more sense as $(a/b)c$. – JMoravitz May 09 '19 at 01:23