>One of my former students who is now starting to teach asked me the >following question for which I don't have a good answer; > >On the TI-82: 10/5*2 equals 4 > >but 10/5(2) equals 1. > >The order of operations rules that I've been using for twenty years would >agree with the answer equal to one. Multiplication and division are >"equal" in power and you work from left to right. The parentheses in this >case don't change the order of operations. > >Have I missed something? Thought I'd throw this out to the list serve >for any thoughts. > >Thanks , >Jerry Brodkey >Menlo-Atherton High School >Atherton, Ca
The TI-85 computes the same "erroneous" value of 1 for 10/5(2), but the 83 and 86 both return a "correct" value of 4. I use the quotes because the manual for the 85 (and probably the 82 - I don't have its manual handy) states that implied multiplication is done before explicit multiplication so the result is correct in that context. The 83 and 86 both do implied multiplication at the same level of precedence as explicit multiplication abd division.
I suspect the reasoning for the older models (82, 85) was guided by looking at an expression with variables. For example, store 2 to variable x and then evaluate 10/5x. Although I've been teaching math for almost 30 years and know my order of ops backwards and formwards, when I look at 10/5x what I see in my minds eye is 10 "over" 5x. I have to force myself to visualise it as 10 "over" 5 times x. My proclivities notwithstanding, I am pleased that TI apparently decided that rules like order of ops should be dealt with a bit more consistently.
Charles J. Schwing St. Francis High School Sacramento, CA