Simple maths question...

Discussion in 'Off-Topic Chat' started by TheMusicMan, Dec 24, 2007.

  1. TheMusicMan

    TheMusicMan tMP Founder Staff Member

    OK, simple enough, but warranted an excellent debate in the Burns household this evening after being advised by my Sister in Law that apparently an adult got this wrong on "Are you smarter than a 10 year old" this week. She did get it wrong, 100% wrong... but I consider the answer given by the show was also 100% wrong. let's see what you think...

    Please let me know what the answer to this question is:

    5 + 3 x 0

  2. Robhibberd29

    Robhibberd29 Active Member

  3. TheMusicMan

    TheMusicMan tMP Founder Staff Member


    What about

    3 x 0 + 5

    ... which is mathematically, in fact, the very same question.
  4. Robhibberd29

    Robhibberd29 Active Member

    No it's not, in changing the order I believe you change the outcome. Try it on a calculator and you will see.
  5. Aardvark

    Aardvark Member

    Searching my mind back to Maths O and A levels ( a long time ago......) I would agree with Ron.

    As there are no brackets round any of the arguments you just take them in order, so 5 +3 is 8 then x 0 is zero.

    If it were 5 + (3 x 0), then then answer would be 5. As would 3 x 0 + 5.

    I think.............:rolleyes:
  6. DublinBass

    DublinBass Supporting Member

    the answer is 5 in america...

    I don't know what you do in the UK, but order of operations in the US treats it as 5 + (3x0)=5+0=5
  7. Robhibberd29

    Robhibberd29 Active Member

    Do your calculators work differently in the US then Pat?!!!! ;)
  8. geo

    geo New Member

    The question is ambiguous unless brackets are included.
  9. Robhibberd29

    Robhibberd29 Active Member

    That's fair point however in this case they're not so I would have to go along with literally keying into a calculator the question as it reads, which gives the answer zero. Otherwise you're saying that all calculators don't work correctly!
  10. Kiz7

    Kiz7 Member

    Okay, official 10 year old answer from my daughter (earlier this evening obviously) is 5 plus 3 equals 8. 8 times zero equals zero or nothing.

    She then went on to say "its a bit like saying you get 10% pay rise if you get paid nothing (zero). You got a pay rise but you still get nothing (zero) in your pocket cos 10% of nothing is still nothing!!!!)

    When do they become SOOOO savvy???
    Last edited: Dec 24, 2007
  11. mikelyons

    mikelyons Supporting Member

    The rule of BODMAS (or BIDMAS) should apply:

    Brackets, Order (index), Division, Multiplication, Addition, Subtraction.

    You do the multiplication first, then the sum,so the answer is 5 - as Pat said.
  12. mikelyons

    mikelyons Supporting Member

    All calculators don't work correctly, neither do all computers. Most simple calculators will do the problem from left to right. That is wrong. There is a rule for precedence (see above) which an expensive calculator should follow. When you are looking for one to buy for your child check whether it follows BODMAS(BIDMAS).

    This is one reason why our children are so awful at maths. They don't learn the basic rules and rely on calculators to do the hard work - result our children are innumerate.

    This is one reason why our children are so awful at English. They don't learn the basic rules and rely on word processors to do the hard work - result our children are illiterate.

    Need I go on?
  13. mikelyons

    mikelyons Supporting Member

    Sorry, Rob, it IS the same as both addition and multiplication are associative(?) Pythagoras where are you when I need you? I can't remember the correct term!

    Basically if you swap two numbers in an addition or a multiplication round the reult is the same:-

    2+5 = 7 and 5 + 2 = 7


    2 x 5 = 10 and 5 x 2 = 10
  14. TheMusicMan

    TheMusicMan tMP Founder Staff Member

    The correct answer is 5, as Mike points out.

    One always calculates multipliers and dividers before addition and subtraction - oh, and there's no rule per country!!!

    Here's the unusual thing... most calculators used by students in schools will give 5 as the answer - maybe the cheap £1.00 calculator you purchased from poundland or that came free with a box of corn flakes will not calculate this correctly, but any scientific calculator would - because they have been correctly coded to to as Mike also points out - BODMAS.

    For PC (XP) lovers: Try this using 'Calculator' on your PC... you will get 0

    For Mac (OSX 1.5) lovers: Try this usinc 'Calculator' on your Mac... guess what you get... :)
  15. johnmartin

    johnmartin Active Member

    The question is not ambiguous. Strict operator precedence will take effect in the abscence of brackets. The multiplication has a higher precedence than the addition so therefore all multiplier operands should be evaluated first. In the example above then 5 + 3 x 0 is equivalent to (5 + (3 x 0)) = (5 + 0) = 5

    Cheap calculators do not work out operator precedence all that well. They tend to work out a sum from left to right and use internal memory stores for holding temporary results . The human brain can process information much more efficiently and correctly. In my opinion the use of calculators should be baned in schools.
    Last edited: Dec 24, 2007
  16. Morghoven

    Morghoven Member

    I have to admit this one took me longer than it should! What was I doing in my maths lessons?!

    It's like any other piece of equipment - you just have to be taught how to use it properly.

    In my mock GSCE maths my calculator went completely kaput - not helpful. I did what I could be hand, but there was no way I was going to get answers to the trig problems and suchlike. But why did I know the calculator was broken? Because the first trig I attempted, it gave me a totally ridiculous answer, and then gave me different answers every time...including a negative number for the length of side of a triangle! However, I was able to show all the working, just not a final answer. I was doing the maths, the calculator was just providing the numbers.
  17. DocFox

    DocFox Retired

    First, mathematics has to work the same around the world or we would have no way to communicate engineering, math, and science problems and their results.

    For Real Numbers
    Powers first (raise everything to a power first!)
    Then brackets next!
    No brackets, or if brackets are already calculated, then do the multiplication and division from left to right.
    Then do addition and subtraction from left to right.

    This is UNIVERSAL!

    Calculators that allow input for formulas will do it the same around the world. They do not make (outside maybe different keys for language) different calculators for different parts of the world.

    Hence the original problem: 5 + 3 x 0

    No powers
    No brackets
    Multiply and divide from left to right. So ignore the 5 +3 for now
    3 x 0 =0
    Now add the 0 to the 5 and it equals 5

    DO NOT DO THIS ON A CALCULATOR. That is common trap. I used to put these on Algebra tests all the time to see if simple problems students would use a calculator or their heads to remember the order or computations.

    You can do it on a calculator that will let you enter equations. Don't believe it, go to any spreadsheet cell and enter =5+3*0 and hit enter. Since a spreadsheet sees things as an equation, the answer will be 5!

    Do it on a calculator, 5+3 will equal 8. Stop. Then it takes 8 and multiplies it by 0 equaling, of course, zero. That is because a common calculator will STOP and not process and equation unless it is an equation capable calculator (popular today). It will instead do the calculation in two steps - in the order you enter them which is the INCORRECT order.

    Of course, if you know your order, you can make any calculator make it work right. 5 + 3 x 0, a person using the correct ORDER would multiply first, 3 x 0 and get zero, and then would add the 5. So it is not the calculators fault, it is operator error. Learn your orders! They are always on math and algebra exams. Trust me. Not only that, but a person who knows numbers well cannot be fooled easily by such problems. If your boss REALLY did try to give you a raise with a strange formula, you had better know how to calculate it

    What is really fun to do on a test is this:

    5 + 3 x 0 =?
    (5 + 3) x 0 =?

    You would be surprised how many come up with the same answer. The second really is zero.

    The [FONT=Arial, Helvetica, sans-serif]Commutative[/FONT] Property for addition and multiplication states (does not work for subtraction)
    [FONT=Arial, Helvetica, sans-serif]For all a,b,c elements (of real numbers, but that is technical),
    a + b + c = b + a + c
    a * b * c = c * a * b

    In other words, you can change the order of the numbers when multiplying or adding, and your answer remains the same.

    Savvy -- Yes. But wrong. She will learn -- at age 10 this is not an easy question. I have had university students FAIL tests on this. If your boss wants to give you a 10% raise the only way her logic would work is if you were unemployed and making nothing (zero). Then 10% of zero, is well, nothing.

    In retail business, they often list prices at retail. Your discount is 50%. But then the company sends you a flyer saying this month, the discount is 50% + 20%. Some retail merchants figure it is a 70% discount. Nope! Lets say the item cost £100. 50% gets it to £50. Then another 20% or .20 times £50 or another £10 off making is cost £40, not £30 like some would think. Best to know basic math!

    Dr. Jim Fox
    Long Time University Algebra Teacher
  18. Robhibberd29

    Robhibberd29 Active Member

    Looks like the question wasn't quite as simple as first suspected then, either that or it's too long since I did maths at school....I'm suspecting the latter!
    Ah well, it's not that often I get to feel a right prat so thanks for that! :p
  19. TheMusicMan

    TheMusicMan tMP Founder Staff Member

    Great set of responses here - and it looks as though the show actually gave the incorrect answer, which I knew all along!

    There is no doubt that the correct answer is 5. My wife is still arguing with me about this though, saying that if you do this on a PC the answer is 0. PC's eh!!!
  20. dyl

    dyl Active Member

    Another case of PC gone mad?

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