a riddle

[Kai Vanuffelen]

Now,
My eleven year old son and I had a difference of opinion this moring about how to work out a seemingly simple mathematical equation. We both came to different answers.

How much is 1 + 2 x 2 = ?

Is it
a) 5 or
b) 6

Five was my answer, because first you do multiplication, then addition, so it becomes 2 x 2 = 4 and one is added makes five.
At school I was always taught to do calculations in a certain order.
Powers first, multiplication second, division third, square root fourth, addition fifth and subtraction last.

n^, x, /, V, +, -

If you know what I mean, as this is not a mathematical keyboard.

Of course 1 + 2 x 2 = 2 x 2 + 1

Dylan worked it out from left to right and came to the conclusion
1 + 2 = 3 and multiply this 3 by 2 makes six

Who is correct? Surely in mathematics there can only be one correct answer.

 

[Cliff Wilson MCPF]

Now,
My eleven year old son and I had a difference of opinion this moring about how to work out a seemingly simple mathematical equation. We both came to different answers.

How much is 1 + 2 x 2 = ?

Is it
a) 5 or
b) 6

Five was my answer, because first you do multiplication, then addition, so it becomes 2 x 2 = 4 and one is added makes five.
At school I was always taught to do calculations in a certain order.
Powers first, multiplication second, division third, square root fourth, addition fifth and subtraction last.

n^, x, /, V, +, -

If you know what I mean, as this is not a mathematical keyboard.

Of course 1 + 2 x 2 = 2 x 2 + 1

Dylan worked it out from left to right and came to the conclusion
1 + 2 = 3 and multiply this 3 by 2 makes six

Who is correct? Surely in mathematics there can only be one correct answer.

You are. Order of Operations is a mathematical principal.

http://en.wikipedia.org/wiki/Order_of_operations

 

[Gregory K. Norris CPF]

I knew that, but couldn't have explained why you do it that way. But I knew instantly and remember the class where I learned it when I saw Cliff's response. (Which is pretty good under any circumstance since I am no spring chick).

I wonder if this is still being taught. I was taught by a math teacher so mean that she frequently shook her ruler at me and threatened to rap my knuckles. Though that may be why it was so ingrained in me.:smile:

 

[John Ranes II CPF GCF]

Kai,

Distributive Law at work here...

(1+2) x 2 = 6 which is the same as (1x2) + (2x2) = 6

I'm pretty sure that is what this is about. :madgrin: Math used to be so easy! :livid:

Darn it Cliff....I guess I'm wrong! Order of Operations... don't even recall that!

John

 

[Kai Vanuffelen]

Thanks for replying Cliff.
Had a look at this site and was confused by the following equation

10 - 3 + 2 = 9 and not 5

Apparently subtraction and addition have the same presedence and it becomes

10 + ( - 3 ) + 2 = 9

In other words, multiplication and division have the same presedence and so do parenthesis and exponents. They are all opposites of each other ( groups of two).

 

[Cliff Wilson MCPF]

Thanks for replkying Cliff.
Had a look at this site and was confused by the following equation

10 - 3 + 2 = 9 and not 5

Apparently subtraction and addition have the same presedence and it becomes

10 + ( - 3 ) + 2 = 9

In other words, multiplication and division have the same presedence and so do parenthesis and exponents. They are all opposites of each other ( groups of two).

yep, So, I would parse the equation you have as (10 - 3) + 2 = 9

You can sort out the operator precedence by applying parenthesis with equal operator ( * / ) and (+ - ) for example being applied left to right.

guess my Mathematics/Computer Science BS comes in handy sometimes.

 

[Kai Vanuffelen]

It also depends upon which calculator you use. Simple ones will get it wrong, so best to avoid calculators as much as possible and let the brain do all the hard work.

John is also correct in alluding, that 1 + 2 x 2 is actually two equations crammed into one.
1 x 2 = 2
and
2 x 2 = 4

Add these answers together becomes 2 + 4 = 4 + 2 = 6

Then there is this

2 ++ 3 = 5
2 + - 3 = 2 - 3 = - 1
2 - - 3 = 2 + 3 = 5

This makes me wonder, if subtraction has presedence over addition, division has presedence over multiplication and square roots have presedence over powers.

Are there any others apart from these six?

 

[David Lantrip MCPF GCF]

I see these little puzzles all over Facebook and they're just annoying and meaningless. Mainly because nobody who knows anything about math would ever write a problem out as

7+2x3-4+1-2= ?

That's why we have parentheses, brackets and so on.

 

[Rick Granick]

...shook her ruler at me and threatened to rap my knuckles. Though that may be why it was so ingrained in me.

Must have been a wooden ruler.
op2: Rick

 

[Gregory K. Norris CPF]

...with one of those sharp little steel edges. You and I are the only ones who caught that, Rick.