**ORDER OF OPERATIONS**

As with any calculator, it is important that the correct

order of ope rations is used to ensure the correct

answer is found. The appropriate use of parentheses

is critical when typing a problem into the calculator.

Use of parentheses to ensure proper order of

operations

**Step 1 **Type (53+15) ÷ (17 −13)

**Step 2** Press “ENTER”

Consider the same problem entered without the

parenthesis.

Notice the answer here is 695/17 because only the 15 is being

divided by the 17. This is not the correct answer to the

problem presented.

The TI-89 will fol low the basic rules of operations if

parenthesis are not applied. Consider the problem:

5 + 2× 4 − 2 .

Following the order of operations, the multiplication is

completed first, simplifying the problem to 5 + 8 − 2 .

Then we add and subtract from left to right giving us

the answer 11.

Now do the same problem on the TI-89.

Notice, the answer is given correctly.

**Problem Set.**

**SCIENTIFIC NOTATION**

There are many different ways that the TI-89 can

display your answers. The choices vary from scientific

notation to a number with a fixed number of decimal

places or to a number that lets the decimal float. The

TI-89 will show a number with 100 digits or

approximate the same number showing 8 characters

depending on how you set the mode of your calculator.

The following example explores this further using

scientific notation.

**Example: Rewrite 5,000,000 in scientific notation:**

**Step 1:** Press the
button

**Step 2: **Scroll down to Exponential Format. Press

the
button

**Step 3:** Press the
button. Press the ¸ button

**Step 4:** Press the
button

**Step 5:** Scroll down to Exact/Approx. Press the

button

**Step 6:** Press the 3 button. Press the
button

**Step 7:** Enter 5000000 in the entry bar of the

calculator. Press the
button

The Answer is 5. E 6 or 5×10^{6}

**Problem Set**

Rewrite each in scientific notation.

1) 7,100,000

2) .12345

3) (432)(367)

4) 23/12345678

**FACTORING, GCD, & LCM**

Every integer can be rewritten as an unique product of

prime numbers, the process of rewriting numbers as

this product is called factoring.

Factor the integer : 568. To do this enter:

(This accesses the Algebra Menu , and the

factoring command)

The display should read:

This can be used to find the greatest common divisor

(gcd) of two numbers. For example, to find the gcd of

120 and 345, use the factor operation on each of these

integers, so that the screen will display:

Now take the lower of the two exponents on each

prime occurring. The following table summarizes the

process :

The gcd is thus , or
15. For the least

common multiple (lcm), just take the higher of the two

exponents. Thus the lcm of 120 and 345 is

or 2760.

**Problem Set:**

1. Factor the integer 12345.

2. Factor the integer 33880.

3. Find the gcd of 12345 and 4200.

4. Find the gcd of 2240 and 65065.

5. Find the lcm of 300 and 120.

6. Find the lcm of 500 and 2783.

The TI-89 is a powerful mathematical tool. The extent

to which the calculator does the calculation is

completely up to the user. It can do steps of the

process or all of the process. This is true for finding

the Greatest Common Divisor (GCD) or the Least

Common Multiple (LCM) of a set of integers.

The calculator can do part of the process, as

demonstrated previously in this lesson, or the

calculator can compute the GCD or LCM directly. Let’s

find the GCD and LCM of 120 and 345.

First turn the calculator on and access the
Menu

by pressing . The Screen should look like
this .

Choose the Number Option and then Scroll down to

the gcd( command.

After selecting the gcd( command, type

Notice that the calculator output is 15, and this is

consistent with our answer using the factoring method

above.

Let’s repeat this basic process to find the lcm.

First turn the calculator on and access the
Menu

by pressing . The Screen should look like
this.

Choose the Number Option and then Scroll down to

the lcm( command.

After selecting the lcm( command, type

Notice that the calculator output is 2760, and is again

consistent with our answer using the factoring method

above.

Now repeat Problems #3-6 from the pervious problem

set in this lesson using this direct method of finding the

gcd and lcm on your calculator.

Are your answers consistent with what you calculated

above?

**EVALUATING EXPRESSIONS**

One of the strength of the TI-89 Calculator is that there

are often multiple ways to get solutions to a particular

problem. The following lesson looks at four different

ways to evaluate expressions: first using the “with” key,

second using a table, third using function notation and

fourth using the graph screen.

**Evaluating expressions using the WITH Key **

If you have a function solved for y, and you want to

know what y equals for a specific x-value, the WITH

key is for you! The WITH key is the key just
below

the .

For example, suppose y = 4x − 7 . What is y when x

= 3?

Press Your screen

should look like this.

As you can see, the calculator substitutes the value of

3 for x and evaluates the expression. The result, 5, is

displayed at the right.

Now suppose we want to know what y equals when x =

8. Instead of typing the expression over again, we can

edit the highlighted expression on the entry line. Press

to remove the highlight, then
to delete the 3.

Press 8 and then

The with key can be used to evaluate expressions that

have more than one variable . Suppose your want to

find the value of a + 3b when a = 2 and b = 6 .

First evaluate the expression when a = 2 by typing the

following:

Now evaluate the new expression 3b + 2 when b = 6 ,

by doing the following steps.

Use the up arrow key to highlight the expression

3b + 2 and push enter. This will copy the

expression to the entry line of your calculator.

Now, using you’re the WITH key, you can type the final

condition of b = 6 . Use the following key strokes:

Therefore, our answer is 20.

**Problem Set:**

1. Use the WITH key to evaluate y=19x+41 for x= 7.

2. Use the WITH key to evaluate y=19x+41 for x=11