I got a Grade A in O-Level maths and thought BOD was a charlton fan I feel cheated that my teachers failed me but I did attempt to do A level Maths and A level Super Maths or additional Maths but gave up after 3 months cos all the formula chuff was too much to take I thought the answer was 1 but I am 41 and now know I was robbed of a proper education
Just in case anyone's wondering whywe do multiplication before addition, one explanation is that it's because of algebraic notation. Algebra helps to shorten mathematical sentences. For example, if you have 5 apples and 3 bananas, you could call that "5a + 3b". Now bear in mind that the expression "5a" actually means "5 x a" (or "apple" multiplied by 5 if you like), so the whole expression really means "5 x a + 3 x b". Now, if you did these operations (adding, multiplying etc) from left to right, you would get, after each stage, running totals of; "5a", then "5a +3", then a final answer of "5ab +3b". Unfortunately, the "5ab" part doesn't make sense, because there is no such thing as "five applebananas". Everybody, whether mathematically minded or not, understands that if you say "I've got 5 apples and 3 bananas, you mean "five lots of apples PLUS 3 lots of bananas". This statement is translated mathematically as:
"5 x a + 3 x b"
and the multiplications are carried out first, the additions last.
Mathematicians realised centuries ago that algebraic notation required multiplying to be carried out before adding and decided that there should be standard rules of precedence in operations when performing arithmetic. It was a natural decision to make multiplication take precedence over addition because it is consistent with algebraic notation and therefore less confusing(!!!)
Now, if you consider the following situation:
A person is given 42 scratchcards. He wins £40 on the first one, he then loses the next 40, then he wins £1 on the last one. How much money has he won altogether?
Clearly, he has used all 42 scratchcards and his total winnings are £41. (1 lot of 40, 40 lots of 0 and 1 lot of 1)
Now in order to write this down algebraically, you could consider the letters f, z and o to represent occasions where he won forty, zero or one pound respectively.
This then becomes:
1f + 40z + 1o
but we don't need the "1" in front of f and o, so it simplifies to:
f + 40z + o
but now, putting the values of f =40, z = 0 and o = 1 into the expression gives:
40 + 40 x 0 + 1
which was the question posed in the original post.
The introduction of algebra to this situation may seem like it's making it even more complicated, but it's the best way I can think of to illustrate the reason why the answer can only be 41.
Also, the thing with brackets and language - it is possible to infer brackets with language, by saying things like:
"Add together 4 and 7, then multiply by 3".
This translates as:
(4 + 7) x 3
because the "then" has indicated precedence of the addition, and therefore implies brackets around that part of the expression.
Finally, if you're someone who thinks the answer is 1, it doesn't mean you're thick, and if anyone thought I was saying that or that I was being arrogant, then I'm sorry, that wasn't my intention. The whole reason BODMAS is taught is because this is such a common misconception. What I don't understand about this thread is why people continue to insist that the answer is 1 when countless people with clear and detailed knowledge on the subject have given thorough explanations. (I'm sure someone out there could tell me whether I've used "infer" and "imply" correctly above, and if they correct me then I'll bow to their knowledge and be happy to have learned something.)
There's nothing wrong with being mistaken every now and then, you know.
:-)
Great post! That's why I've never heard of BODMAS, people of my generation (who are smarter as the exam results showed) were straight on to Algebra.
You could chirps, you could do what I did, read the mathematical rules that apply, realise what you have thought all along was wrong, and accept with good grace that you don't know everything, and that it's never too late to learn...
And yet still your answer is wrong as it ignores mathematical rules as has been stated by many. Which is why when you put into a spreadsheet the calculation it gives the answer 41.
In mathematics, the only way to make the calculation answer 1 is to bracket the first two numbers together. The rules are that in the absence of any brackets, the answer is 41.
Because the act of using a calculator means that you bracket the first two numbers together. As has been stated by many, that is not how you solve the equation in the question according to mathematical rules.
Anyway it was fun while it lasted. Clearly the question is designed to create a debate and we've had one.
Not true for scientific calculators and only true for basic calculators because they are not sophisticated enough to make a stream of calculations. As a result, basic calculators have to rely on you to interpret the order of operations before inputting them.
If you type "40 + 40 x 0 + 1" into a basic calculator, it has to assume that there are brackets around the 40 + 40, otherwise you would have followed the rules and inputted the multiplication first.
A calculator can't think, it can only follow instructions. Unfortunately, your instructions were incorrect.
Comments
Can't someone just use a calculator !?
Anyone who thinks it's 1 should have paid more attention at school and learn not to argue with people who clearly know more on a subject than they do.
I feel cheated that my teachers failed me but I did attempt to do A level Maths and A level Super Maths or additional Maths but gave up after 3 months cos all the formula chuff was too much to take
I thought the answer was 1 but I am 41 and now know I was robbed of a proper education
40+40=80
80 X 0 = 0
0+1= 1
I really cannot make it any easier for you all.
I couldn't be arsed to do it for 80 X 0!
You could chirps, you could do what I did, read the mathematical rules that apply, realise what you have thought all along was wrong, and accept with good grace that you don't know everything, and that it's never too late to learn...
40+40=80
80 X 0 = 0
0+1= 1
It's still 1 and no Clever Dick chat will change that.
No one is changing anything, it's always been 41, we were just wrong Chirps.
It's no big deal.
But there are no brackets!
Try using a caluclator. You'll get 1!
Try putting it into a scientific calculator.
Or excel, like cafcpolo has done for you here
What more proof do you need?
Accept you made a mistake and move on
We've been robbed of a lifetime of maths views
Time to reluctantly accept that people who you'd think weren't better educated than yourself , have been !
Nope. We are right. If these youngsters want to move the goalposts that's up to them.
The more likely answer is you should have paid more attention at school.
Here's some homework for you:
http://mathforum.org/library/drmath/view/52582.html
Johnny "Hey Fred wanna do some mental arithmetic?"
Fred "Sure"
Johnny "Ok, here goes. Add 40+40"
Fred "Yep, 80"
Johnny " Now multiply by zero"
Fred "That gives me zero"
Johnny "Now add 1. What you got?"
Fred "1"
Johnny "Correct!"
Two different answers, how is this so complicated, I can't believe you really are this thick so have to assume your just on a windup.