How would you do this maths equation?

Yet another query about my son's school work and how things have changed over the years.
(Don't worry gang, he only has two and a quarter years to go and then I'll leave you all alone! )

Today he is learning about equations with multiple parts to it.
( / is the division key - drives me nuts there isn't a real one!)

For example ... 1+2x3-4/2=?

What answer would you come up with?

Since nothing is in parentheses, I'd do this

2X3 = 6
4/2 = 2

so 1+6 = 7
7-2 = 5

5 is the answer.

Multiplication and division, then addition and subtraction. Unless this has changed since I was in school.

Yep, I'm with agony here. 5 is the answer

Why would you not add the 1 and 2 first, then multiply 3 x 3, subtract the 2 and arrive at 7 as the answer? In other words, is there a rule that says the multiplication must be the first part of the equation performed? I really don't know and am simply curious.

Yep. It's taught differently in different places, but here in Scotland I learned the rule as BODMAS or BEDMAS, standing for Brackets, Exponentials, Division, Multiplication, Addition, Subtraction. The rule is called order of operations.

I'm closer to Jabb on this one .. I would always do the brackets first if there were any and then work left to right. My answer would be 2.5 LOL.

BODMAS is what is in the work now and is as Reeshy said. It's the first I've seen of it.
I've only been looking at it this morning and have had a couple of problems

This one ...

(23-4+9)x(half - quarter) of 24 = ?

I got the answer 60 but the correct answer is 168 .. quite a difference!!!

SO we do brackets first .. and here is where I think I went wrong ... the BODMAS rule doesn't apply?
Using the BODMAS rule in that first bracket you would get 10 (so 10 x 6 = 60)
but if you do it left to right you get 28. (28 x 6 = 168)

SO why doesn't the BODMAS rule apply in the brackets?

So confused!

The problem is expressed badly.

It should be

(23-4+9) x ((1/2-1/4)x 24) or even 24 x (1/2-1/4) x (23-4+9)

28 x (1/4 x 24) = 28 x 6 = 168.

But it's still that first bracket that I stuffed up ... I used the BODMAS rule within that bracket and got 10 but to get the right answer you DON'T use the rule .. you just work left to right.

I wrote it different to the paper and put the words to half and a quarter to get away from putting the / sign which I had used before to mean divide.
In the book it is

(23-4+9)x(1/2 - 1/4) of 24 =

TO my way of thinking if he got the problem

23-4+9=
the answer would be 10 using BODMAS

but as it's within that bracket the answer is 28.

I've never heard of BODMAS or BEDMAS before. I was taught "PEMDAS", meaning Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Same idea, just different word to remember it I guess.

But it DOES mean to divide. A quarter is simply one divided by four, ie, 1/4.

One more vote for 5. Do the multiplying and dividing first:

1 + 2x3 - 4/2
= 1 + 6 - 2
= 5

The bad thing about BODMAS/BEDMAS/PEMDAS is that it is easy to think that multiplication or division comes first, and that addition comes before subtraction.

I think that is what the teacher means, Lesley. He probably hasn't reached the BODMAS (eg using brackets etc)stage yet. Yes I reckon it's 5.
(ps Lesley How D--- I- F--- T- B- R---- AGAIN ?)

Technically we learned P then E then M/D interchangeable then A/S interchangeable. I dunno, but math always just clicked for me so order of operations wasn't that difficult to keep straight. Math was by far my best subject...which kind of explains my desire to go to grad school for engineering. I missed all the math (and science) that I didn't get while I was an undergrad studying architecture.

I don't understand how you got 10 from 23-4+9?

How does 23-4+9 not equal 28?

I read it as 23-4= 19, 19+9=28, or if you like 23+9=32, 32-4=28, or even -4+9=5, 23+5=28.

Can you please explain how you got 10?

And with PEMDAS/BODMAS, as a general rule everything in the parentheses is done first. So you would compute both 23-4+9 and 1/2-1/4, before multiplying the two results together. Then once you're in the parentheses, you do all of the exponents first, then multiplication/division, then addition/subtraction. Then you'd do the second or third (or however many parenthetical phrases there are) before you do the operations between the parenthetical phrases. Make sense?

So for example:

(2^2 * 4 - 2) * (2 - 2^3) = ?

Starting with the first ( ), you do E first, so 2^2 = 4. Then M/D, 4 * 4 = 16. Then A/S, 16 - 2 = 14.
Then with the second ( )...starting with E, 2^3 = 8. Then 2 - 8 = -6.
Then you do the ( ) * ( ), so 14 * -6 = -84.
So the overall order used in this case is P1, E1, M1, S1, P2, E2, S2, M(overall), where 1 and 2 refer to the 1st and second set of ( ).

In the special case where you'd have a term that is ( )^x, you would do everything inside the parentheses first as seen above, since P comes before E, and then you would apply the ^x to your final result from inside the ( ).

*thinking time*

Because if you were supposed to do the addition first according to BODMAS?
So 4+9= 13
23-13=10

This morning I would have gotten 28 straight away and now this has *&^%$$# me right up.

But the 4 isn't actually a 4 in this case, it's a -4.

Think of the equation like this.

23 + -4 + 9. It's actually all addition. You're just adding both positive and negative numbers together.

Or like 1/2 - 1/4. This is actually just multiplication and addition, though I know it doesn't seem that way.

This could be written as 1 * 2^(-1) + (-1) * 4^(-1). No division or subtraction symbols.

I think what's confusing you in this case is the level of operation and the order of operation, though the terms are generally interchangeable.

Think of the levels as P, E, MD, and AS.

Think of the order as Left to Right. Within every LEVEL you then perform the ORDER.

So in the AS LEVEL, you have 23 - 4 + 9. You then look to the L to R ORDER. This means you do 23 - 4 first, because it's on the "left". then you do 19 + 9, because that's on the "right".

Still confused? I might be able to explain it another way if this doesn't clear it up So sorry you're frustrated.

Edit: Multiplication and Division are, in order of operation, Equals. Addition and Subtraction are also Equals. This means the BODMAS, or PEMDAS, could just as easily be written BOMDSA, or PEDMSA. The letters MD and AS appear in the order they do in BODMAS and PEMDAS, because they're easier to pronounce and therefore easier to remember.

Since M and D are equal, this means that one does not hold precedence over the other, 2/3*4/5 is the same as 2*4/3/5.

Since A and S are equal, this means that one does not hold precedence over the other, 1+2-3+4 is the same as 1+2+4-3.

Multiplying and dividing are one kind of thing, and are done first, before you touch any adding and subtracting. When deciding which of these to do first, you go left to right - multiplying does not come before dividing, unless it happens to be to dividing's left.

Adding and subtraction are another kind of thing, and are done after the multiplying and dividing. Again, once you are at the adding/subtracting phase of the question, you go left to right. Adding does not come before subtracting, unless it just works out that way.

Does that help, or does it confuse it further?

This is what I'm trying to get at, agony. It seems easy to me, but that's because I already understand how it works, and I use it all the time. Trying to teach someone else on the other hand just makes it feel so much more complicated.

Copago, I'm not sure I know how to explain it any other way. The best way I'd say to understand how to do it is just to work complicated multi-function problems over and over and over again, and sit down with someone who understands it and can work through the problems with you until it becomes second nature.

No no, I have it now. Thanks for the explanations Kaddarsgirl and Agony

I did have it at your first explanation, K, but had no idea how to explain that to a ten year old. I didn't want to start him off being confused by it all and not being able to recover from it!

Glad I could help I didn't mean to overload you with replies by the way. I just got so into it! Good luck with your ten year old I wouldn't want him to start off being so confused by it all either...that's how we get people who don't like math

Exactly! He's pretty good at maths and does it enjoy it so I wanted to make sure I had it right before trying it out on him.

I'd love to be able to show you the page that was sent out for him to do (I've scribbled all over it) - it shows FOUR ways of working out (left to right, working backwards, doing what you want and BODMAS)... I don't understand why we would show them how to do something, get them to do it and THEN tell them that is the wrong way to do it? It confused me and I'm a seemingly intelligent adult LOL

That would confuse, and frustrate, the crap out of me too! That certainly, to me, doesn't seem like a very logical way to teach children math. They've got so much to learn anyway, it doesn't make sense to teach them something that's wrong and then tell them to forget it. Very strange indeed.

Your son is very lucky to have a parent like you who cares so much about him, as you clearly do

When all the liquid paper dries I'll scan it and post it to show.

and thank you!

Well it's half past midnight here, so I think I'll be heading to bed, but I will definitely take a look at the paper tomorrow if you do post it on here sometime tonight. You've gotten me so very curious about it now. Goodnight

G'night and thanks again!

For your viewing pleasure tomorrow ..

http://i870.photobucket.com/albums/ab261/copagostation/BODMAS001.jpg


(oops, meant to post link to actual pic!)

Copago
I was explaining to my (nearly) 10 year old the same thing a few weeks ago. Possibly your son and mine are in the same year at school and learning the same thing? My son is in year 4. He hasn't learnt it in class yet but some of his homework comes home with this sort of thing on it. It frustrates me that he gets homework that hasn't even learnt yet. I send him back to school with his homework covered in notes and with attachments so the teacher can correct me if I am teaching him the wrong way. So far so good...

yep, mine is in Year 4 also (and it's the first time this kind of equation has been introduced) ... and don't get me started on the actual work! lol Mine does school of the air so all the work gets sent out and I have to deliver it to him and similar to you they expect him to be able to do a 'test' each week on stuff that hasn't been covered yet.

Possibly they are testing where the parents' skills lie and not the child's

23-1(4+9){or, 23-(4+9}=23-4-9=23-13=10
23-4+9=19+9=28
Artificially inserting a set of brackets or parentheses where they aren't specifically expressed leads to the wrong (+/-) being assigned to the individual units. Copago, you seem to insert brackets on your own to separate out the steps as you perform them. This can lead to errors. In the first example above the negative sign is applied across the board into the parentheses, changing a plus 4 to a negative 4 and a plus nine into a negative 9. when it is only the 4 unit that is negative. Once all brackets, exponents and multiply/divides have been done and you are left with only +/-, work left to right, addding and subtracting (whichever is called for in order) as you go.

Thanks everyone for explaining the rule. I imagine I learned it once upon a time, but it's so far back in the distant mists of elementary school that I have no memory of it.

Looking back on these posts I've just realized something...how young the kids are that are learning this. My first exposure to PEMDAS was in 7th grade algebra (1st year of middle school). 10 years old seems awfully young to me to be learning such things. I was in the highest level of math that my school district offered for my grade (advanced programs since 4th grade/9yo) and I was young for my class. I didn't even get it until I was 12. Some people didn't even get Algebra until 9th grade/freshman year of high school. Maybe they just start teaching things at a later age in the US than they do in Australia...

I remember learning it in primary school (somewhere between year 5 and 7 - which is about 10-12 years old). I learnt it as BIMDAS though. Nothing has changed (except what people are calling it) it's just difficult to explain concepts to your kids if you aren't entirely sure of it yourself.

I feel sorry for those parents who struggled in school and now have to try to explain some of these things to their own kids.

"it's just difficult to explain concepts to your kids if you aren't entirely sure of it yourself. "

Oh God, isn't that the truth?!?

As I said to the teacher .. going soley on that page I posted up there it doesn't say anything about Multiplication and Division together or additon and Subtraction.. just that it should be done in a specific order which is what confused me. I took it too literally.
And I just flat out said I'm not gettting him to work something out a "wrong way".

I am willing to bet that this doesn't come up for a while again in his work .. which does annoy me somewhat. If pressed the teacher would say we are just "exposing" them to it for teaching at a later stage. it seems to be a common answer.

It's funny this has come up as a topic for discussion right now, as my oldest grandchild, a 10 year old boy in 5th grade, was struggling with his math homework today. He brought it to his mom, my oldest daughter, who majored in theatre at University and thinks math is Satan! She took one look at it, said, "That's algebra! Go talk to your stepdad. I don't do algebra!"

÷

Hold down Alt key and type 0247

Knew it would be there somewhere .. Thanks Sue.

lol Jabb It's not that I think Maths is Satan but, after this, it's certainly hanging out with him.

Alt and 0247 on my computer gives me a string of a bunch of symbols: º™¢¶. To get the ÷ symbol I have to type Alt and the / key. I have a Mac.

That last sentence says it all.

They should just have a key for it .. and one for the most common fractions too come to that.

I have another question for anyone still coming in ..
What would 3.25 hours mean to you?
3 hours and 15 minutes or three hours and 25 minutes?

It would definitely be great if there was a key that had the ÷ key on it.

I read it as 3.25 hours to be 3 hours 15 minutes. 3.25 as in 3 and 1/4 hrs. Usually when I want to write 3 hrs and 25 minutes (like for keeping time at work) I will write 3h25, which is just as fast as 3.25 to write, but not as confusing to me when I go back to look later. I use .25, .5, and .75 to me 15mins, 30mins, and 45mins, but if I have a weird time, I'll write h05, or h40, or h35, just so I don't confuse myself!

I would think that 3.25 means three and a quarter hours (3hr 15 mins). 3:25 would be twenty-five past three.

Another for three and a quarter.

Three and a quarter hours.

yep

When I was in school, I was shuffled through grade to grade without understanding math. I didn’t, nor do I now, have the patience before it. Whenever I see an equation, I get a headache (although I do seem to remember in my last year or so of high school that somebody finally thought to give me extra support in that subject—and I went from getting Ds to Bs.

When I took math in college, I had to take prerequisites—and failed the first time I took it (this was bef ore I realized that a D constituted a failing grade). I had to repay to take the course, switched to another instructor (who had a reputation around campus as being “great,”) and got an A or a B (I don’t remember which offhand).

My problem has always been compounded by the way math equations (and graphs) are portrayed in Braille (depending on the type of graph, it needed an interpreter—and as for the equations… and one math book was at least 28 Braille volumes!) Anyone surprised I routinely fell behind?

There’s something fundamentally wrong with a school system that teaches students this way

The boundaries to my back property line are 11.33 feet (expressed as 11.33' on the plat) from the back of the structure. There is a utility easement in the last five of that footage. My neighbor also has a five foot easement on his side of the line. He did some building in that five foot meaning any utility work would be essentially forced to take place on my property and not fairly on his too. I filed a complaint (it is legally called encroachment). The Committee responsible for enforcing those rules sent out a woman who read the plat as saying my property went 11 feet thirty three inches in back of my house. How can someone who needs to make decisions about property lines not know that if 11 feet 33 inches was what was real it would have been expressed in whole feet and fractions of a foot and not whole feet and multiples of feet? Eleven point three three feet turned into 11 feet 33 inches to this arbiter and so she measured 13 feet 9 inches back from my house to find where the property divide was. "Well you filed a valid complaint because this work has been done on your property," she said!
When I told her that 11.33' meant 11 and a third feet or 11'4" and she went to remeasure, she then tried to tell me my property line only went back 6.33 feet because the utilities companies owned the land the easement was on. I then had to explain that I paid taxes on the 11.33' and that the easement meant I owned the land but ceeded certain activities on my land could be performed by the utilities. She just shut up and left. I went to the office to ask why they sent such an unknowledgable person on such a job. I heard crying and arguing coming from an office down the hallway as I stood at the front desk. It was her as I saw from the front desk when she left the office where the disturbance was. She then accused me of sneaking around and eavesdropping as she reported her findings. She recommended not to find in my favor. Seems when people are shown they are wrong, they'll go that extra mile to make your life miserable.
I can fully appreciate the problem that 3.25 hours can present to people who know and need correct interpretation of time statements by someone who does not understand fractional notation.

You could probably guess this but the answer was 3 hours and 25 minutes.
*sigh*
the question was something along the lines of adding 3.25 hours to six thirty. i think the kids were supposed to guess that "six thirty" meant that it was a digital clock and that 3.25 on a digital clock is 3 hours and twenty five minutes. I still think it's 'wrong' even after the answer was explained.

Then it ought to have had a colon, not a fullstop.

Agreed, 3:25 means Twenty-five minutes past Three O'Clock but I've never seen that notation to mean three hours and twenty-five minutes. The notation 3.25 means three and a quarter hours. The only way I know to express Three hours and twenty-five minutes in just numbers and punctuation is 3 5/12 hrs. There is no decimally exact way to express it.
Note there is a similar method used in baseball when recording the number of outs a pitcher records. Since an inning has three outs and you want to say that he (sorry ladies) pitched 2 and two-thirds (2.666...) the current convention is to state it as 2.2 innings, Two point three innings would be the same as three point zero innings, So, the types of notion you'd see in a statistics list for baseball pitchers would all end in point zero, one or two. It makes sense in the context if you know the convention. In the time problem, the convention of twenty-five minutes being expressed as point two five flies in the face of the convention widely accepted that point two five equals a quarter hour and nothing else.

3.416 (the 6 needs a bar over it) would be decimally correct.

I cannot fathom going through math that is systematically incorrect.

I am a diehard for the use of a colon in times. Here is Australia, it has become standard practice to use a full stop (no shift key needed) in printed documents, but I retype every document I get my hands on to change it to a colon. As a maths teacher, I want that decimal point to have a consistent meaning. Of course, the universal practice of showing the cricket progress scores in terms of how many overs have been bowled using a full stop (when the number that follows is out of a maximum of 6) totally undermines my position in the adolescent mind.

A maths teacher! Please pass by here often, Looney - I'm sure I'll be needing more help along the way!