Introduction to Algebra using the TI-92 Ó 1997
by Nathan O. Niles
Associate Professor (Retired)
U. S. Naval Academy

1. Introduction

Take a good look at the TI-92 arrangement of the various keys. In describing various operations we make use of symbols.
 

The symbol Means
press "diamond" key (lower left in green)
, , ,  press "cursor pad" right, left, up, down (cursor pad blue at upper right) 
press "CLEAR" key (upper right)
press "ENTER" key (blue color, 3 of them) 
press "MODE" key (upper right)
8 press "F1" key followed by pressing the 8 key ( upper left, 8 lower right)
 
Home screen

Turn on the TI-92:  The ‘Home’ screen appears. (If it dosen’t:   should do it.) The contrast is adjusted by pressing and holding down  while pressing  (to lighten) or  (to darken). If the Home screen is not blank, clear it by:  8  ( displays the ‘Tools’menu.)

To turn off the TI-92:   (lower left) Many keys have two operations. The secondary operation is indicated in ‘yellow’ and is invoked by pressing  first.

We now show the arithmetic operations of addition, subtraction, multiplication, and division. The arithmetic operation keys are at the lower right.

Addition

(a) 5 + 2.      5  2 

Note that what is typed appears on the ‘entry line’ and the cursor moves to the right. When  is pressed note the display in the ‘history area’ is:  5 + 2 at the left and the answer 7 is at the right. Note the entry line is ‘highlighted’.

Subtraction

(b) To clear the entry line:  If an error is made in typing,  deletes the character to the left of the cursor. 17  14  Note the display. Where is the answer 3? What happened to the previous entry?

Multiplication

(c) 24  539  The answer is 12936. Note the entry line cleared when 3 was pressed. Also note the multiplication sign changed to *. This symbol, *, is used for multiplication by calculators and computers.

(d)  5  9  The display is an ERROR message. Press   (upper right) to cancel.

The error is at the flashing cursor. - 5 is a negative number. We used the ‘minus’ sign. It is different from the negative number key  (at bottom right). Now try   5  9  for an answer of - 45.

Division

(e) 162  81 The answer is 2. Note the division sign ¸ is changed to / in the entry line. This symbol, /, is used for division by calculators and computers.

(f) For  we type  2  3   8  At the left of the history area  is displayed and the answer at the right is displayed as 5/8. To obtain the decimal equivalent:   The answer is now displayed as .625.

When fractions, roots, exponents, and so forth are displayed in the form in which they are traditionally written, the format is called Pretty Print. Pretty Print is the default mode and we will use it. When Pretty Print is ‘OFF’ the results are displayed in a linear form on one line. To turn Pretty Print ON or OFF:   (7 times until Pretty Print is reached)  press 1 for OFF or 2 for ON followed by .

(g) 7  0  An error message (undefined). Division by zero is not allowed.

Example. Perform the following operations on a calculator. (a) 25 + 32. (b) 7 - 4. (c) 73 - 129. (d) 34 ´ 391. (e) 62 ¸ 31. (f) 35/8. (g) 3/11. (h) 37/0.

Solution: (a) 57. (b) 3. (c) -56. (d) 13,294. (e) 2. (f) 4.375. (g) 0.272727. (h) undef.

In parts (a) through (d) the answers are integers. In (e) through (g), for division, we obtained an integer, a terminating decimal, and a repeating decimal (the digits 27 repeat.) In (g) we obtained 6 digits. To show that the digits continue to repeat we may increase, on some calculators, the number of digits displayed. On the TI-92 this is accomplished by setting the MODE to FLOAT 12 (for 12 digits):

3  11     , press  repeatedly until FLOAT 12 is highlighted,

   

 Now the answer to 3/11 is .272727272727

To return to the default setting of FLOAT 6:

    , press  repeatedly until FLOAT 6 is highlighted,  

To check:   should display 6 digits.

Problem. Perform the following operations on a calculator and interpret the results. (a) 37 + 95. (b) 23 - 15. (c) 543 - 789. (d) 47 ´ 238. (e) 102 ¸ 3. (f) 21/8. (g) 5/11. (h) -357/0.

The order of evaluation of a quantity is important. We suggest the following:

Quantities inside grouping symbols evaluated before those outside.

Exponentiations carried out first from left to right.

Next multiplication and division from left to right.

Last additions and subtractions from left to right.

 Example. Evaluate .

When using a calculator with parentheses keys such as the TI-92 Graphing Calculator we would proceed as follows. First rewrite the expression using parentheses as the only symbol of grouping. Recall that for the radical symbol,, the ‘overbar’ is a grouping symbol. For calculators  is entered as Ö (23.45). Rewriting the given expression using parentheses exclusively we have

2((5 - Ö (3.7))/6 -3(4.1 -23) -(6.1 -2.7)2) Next we enter the expression as follows. Note that pressing  displays Ö and a left parentheses ( . 6.1 2.7   2  

The answer is 1.30549.

 Computers and some calculators use an exponential notation at times. Here an ordinary number is followed by the letter E (or e) and by an integer. The integer is the power of 10 that multiplies the number. If the integer is positive the + need not be written. If the integer is negative the - sign must be written.

Example. 2.5E3 = 2500 (2.5E3 could be written 2.5E+3)

-356.89E10 = - 3568900000000
0.678E- 5 = .00000678
- 45.9807E- 1 = - 4.59807 Problem. Write each of the following numbers in general form.
(a) 1E2. (b) 3.678E5 (c) -0.0987E-3. (d) 356.935E-7.

Problem. Write each of the following numbers in exponential form with one nonzero digit to the left of the decimal point.

 
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