Re: [Math4u] Sequence of Operations

And here is the next point...

 

6. We may total the minuends and subtrahends before subtraction.

(a)         10 – 5 + 8 – 4  =  (10 + 8) – (5 + 4)

=            18 – 9           

=            9

 

(b)         9 – 5 + 3 – 4 – 6 + 7 + 9 – 8  =  (9 + 3 + 7 + 9) – (5 + 4 + 6 + 8)

=   28 – 23  

=   5

----- Original Message ----
From: Vinaire <vinaire@yahoo.com>
To: Math4u@yahoogroups.com
Sent: Tuesday, December 11, 2007 9:55:50 PM
Subject: Re: [Math4u] Sequence of Operations

Here is the next point from my Milestone:


5. We may replace all the subtrahends by their total without changing the final outcome.

(a)         12 – 5 – 3   =   12 – (5 + 3)   =   12 – 8    =   4

We may check the above by carrying out the operations from left to right.

12 – 5 – 3   =   7 – 3     =      4

(b)        17 – 5 – 7 – 2   =   17 – (5 + 7 + 2)   =   17 – 14  =   3

We may check the above by carrying out the operations from left to right.

17 – 5 – 7 – 2   =   12 – 7 – 2   =      5 – 2    =    3

Vinaire

----- Original Message ----
From: Vinaire <vinaire@yahoo. com>
To: Math4u@yahoogroups. com
Sent: Tuesday, December 11, 2007 2:21:29 PM
Subject: Re: [Math4u] Sequence of Operations

Rick,

 

Thanks. That is a good point. I shall add "When there is consequitive subtraction, use the left to right rule."

 

Here is the next point from my "milestone."

 

1. The numbers may be moved around within the expression, but only if their operational signs are moved with them.

(a)   When we add 0 to the whole expression, the outcome remains the same; but we note that the "no sign" in front of the first number is actually a "plus" sign.

10 – 5 + 8 – 4            =            0 + 10 – 5 + 8 – 4

(b)   The numbers in an expression may be moved around as long as they carry their + and – signs with them.

0 + 10 – 5 + 8 – 4            =            0 – 5 + 8 – 4 + 10            =            0 – 4 – 5 + 10 + 8

Regards,

Vinaire

 

 

----- Original Message ----
From: Rick <rcastrap@yahoo. com>
To: Math4u@yahoogroups. com
Sent: Tuesday, December 11, 2007 12:09:31 PM
Subject: Re: [Math4u] Sequence of Operations

Vinaire,

The problem isn't necessarily that your "rule" is incorrect. It is that
it is too complicated. What does the beginning algebra student do if
there is more than one consecutive subtraction? I think strict left
association is easier to teach and easier to remember.

-- Rick

--- Vinaire <vinaire@yahoo. com> wrote:

> When addition and subtraction are present together they may be
> carried out from left to right.
> 10 – 5 + 8 – 4 = 5 + 8 – 4 =
> 13 – 4 = 9
> 3 + 9 – 4 + 7 = 12 – 4 + 7 =
> 8 + 7 = 15
> When addition and subtraction are present together they may also be
> carried out safely with subtraction first.
> 10 – 5 + 8 – 4 = 5 + 4 =
> 9
> 3 + 9 – 4 + 7 = 3 + 5 + 7 =
> 15
> Mistakes are likely if addition is carried before subtraction.
> 10 + 8 – 6 + 3 = 18 – 9 =
> 9 (incorrect)
> 10 + 8 – 6 + 3 = 10 + 2 + 3 =
> 15 (correct)
>
>
> Can anybody come up with an exception to the above?
>
> Vinaire
>
>
>
>
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