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Implied Multiplication and TI Calculators

Date: 05/02/2008 at 09:24:12
From: Rob
Subject: Multiplying parenthetical phrases and order of operations

I have found that depending on how I type an expression into my TI-85,
it comes out with two different answers.  If I type 36/6(25-11*2), the
answer comes out to be 2.  However, if I type 36/6*(25-11*2), the
answer comes out to be 18.  The difference is whether I put the
multiplication symbol between the 6 and the parenthesis or not.  

I've been under the impression this should make no difference; with or
without the symbol, a number up snug against the parenthesis still
implies a multiplication symbol.  Help?

Date: 05/02/2008 at 13:20:22
From: Doctor Peterson
Subject: Re: Multiplying parenthetical phrases and order of operations

Hi, Rob.

Your two expressions in the calculator are

  36 / 6 ( 25 - 11 * 2 )


  36 / 6 * ( 25 - 11 * 2 )

The problem is that some calculators that allow multiplications to 
be implied as in the former case treat that as a higher precedence 
operation (as some algebra texts say), while others treat all 
multiplications alike (as most texts do, in my experience).  You can 
read a little about that here:

  Order of Operations 

That has a bad link to TI's site; a current version can be found by 
going to their Knowledge Base and searching for "implied 
multiplication". Here is a quote:

  Solution 11773: Implied Multiplication Versus Explicit
  Multiplication on TI Graphing Calculators. 

  Does implied multiplication and explicit multiplication have the
  same precedence on TI graphing calculators?

  Implied multiplication has a higher priority than explicit
  multiplication to allow users to enter expressions, in the same
  manner as they would be written. For example, the TI-80, TI-81,
  TI-82, and TI-85 evaluate 1/2X as 1/(2*X), while other products
  may evaluate the same expression as 1/2*X from left to right.
  Without this feature, it would be necessary to group 2X in
  parentheses, something that is typically not done when writing
  the expression on paper. 

  This order of precedence was changed for the TI-83 family, TI-84
  Plus family, TI-89 family, TI-92 Plus, Voyage™ 200 and the
  TI-Nspire™ Handheld in TI-84 Plus Mode. Implied and explicit
  multiplication are given the same priority. 

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum 
Associated Topics:
High School Basic Algebra
High School Calculators, Computers
Middle School Algebra

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