Introduction to the TI-84/83 Graphing Calculator Part 1: Basic Arithmetic Operations & Features 1. Turning the calculator ON & OFF, adjusting the contrast, and clearing the memory The
ON
key is located in the lower-left corner of the calculator. When you turn the
calculator on, you will see the whatever was last displayed when the calculator was last on. Press the
CLEAR
(under the arrow keys, right side) to clear the screen. This screen is
called your home screen, and this is where you will do most of your calculations. To adjust your contrast (how light or dark the screen is), press the yellow (upper-left corner) and then the up arrow
to lighten the screen.
If you’d like some text to look at while you change the contrast, you can press 2nd
key
to darken the screen (just hold down the
arrow to get darker) or the down arrow
which is next to the yellow
2nd
MODE
key. You’ll see a lot of text which will help you decide
if the screen is too light or too dark. To leave the MODE screen or any other screen, press QUIT by using the
2nd
key and then the
MODE
key.
To clear out the calculator’s memory (kinda like starting with a fresh sheet of paper), press the 2nd
key and then the
+
you should be seeing:
key (notice the MEM in yellow above the key?). Here’s what Unless you have programs to save, or other data you want to hang onto, choose Option 5: Reset. You’ll be given two choices: “All Memory” or “Defaults”. We’ll reset back to the defaults (factory settings) so the whole group can stay together
more easily. Option 2: All Memory means just that – all programs, data, lists, graphs, etc. Choose this option with care! After resetting to defaults, your screen may have disappeared. The calculator reset the contrast, also, so you may have to go through changing the contrast again. Then clear your screen so you have a blank home screen with just the cursor flashing at you. Kathy Berry Monroe County ISD, Michigan
TI-84/83 Intro Part 1 Page 1 of 8
2. Basic Arithmetic Operations As complicated as this calculator looks, it still does basic math just fine. The four basic operations are the blue keys on the right hand side of the calculator. You use them just like you would on a basic or scientific calculator. One difference you’ll notice is which symbol is displayed when you hit
¯or ¥.
Instead, you’ll see an asterisk ( * ) and a backslash ( / ) .
Another difference when using the graphing calculator is that the
ENTER
key is used
like an equal sign. ENTER tells the calculator to do whatever you have typed in.
3. Take a few moments, and try these… a. 582 + 163 _______
b. 5978 + 4169 _______
c. 421,758 + 29,694
d. 884 – 238 _______
e. 4832 – 1756 _______
f. 252,525 – 181,818 _______
g. 457 x 5
h. 216 x 29
_______
j. 28,905 ÷ 5
_______
k. 597,531 ÷ 11 _______
l. 15 450
_______
m. 26 12443.08
_______
n. 63.8 + 14.9
_______
o. 1.385 + 0.715 _______
p. 2.5 • 4.3
_______
q. 1.6034 • 10
_______
r. 7.29 ÷ 27
s. 5 ÷ 0.2
_______
_______
_______
_______
4. My screen is cluttered…. Oops! I erased a problem I needed! By now your screen is probably pretty cluttered. Notice each problem has just scrolled up the screen. To clear off your screen, you can press any time. CLEAR What if you hit clear, but you really didn’t mean to? Maybe you forgot to write down that last number, or you need the answer to a problem from a minute ago. The TI-83 remembers a lot of your past calculations! To get back your last problem, just press and then the 2nd ENTER key. Notice in yellow it says “ENTRY”? Entry means your last entered problem and solution. You can press 2nd and ENTRY over and over to scroll back through the last 30 problems or so. Use this feature to help you with these problems: (HINT: You’ll want to use the INSert and DELete keys as well. INSert is found with the DELete key. Just press 2nd and then DELete to change to insert mode. Use your cursor keys (arrow keys) to position your cursor where you want to insert or delete. a. 15,297 • 29 __________
b. 15,397 • 29 __________
c. 156,397 • 29 __________
d. 56,397 • 294 __________
e. 56,397 – 294 __________
f. 56,397 – 29401 __________
Kathy Berry Monroe County ISD, Michigan
TI-84/83 Intro Part 1 Page 2 of 8
5. Dealing with fractions. The TI-83 does not have a “fraction key”. However, you can trick the calculator into doing fractions, up to a point (as in decimal point). Let’s say you want to add ½ and ¼ . Those fraction bars are really division signs in disguise! So you can just type in ½ + ¼ and the calculator will solve the problem but give a decimal result. What is it? _________. Because of the way the calculator works (it follows the rules of math, a.k.a. the order of operations) get in the habit of putting your fractions in parentheses ( ). The parentheses keys are above the 8 and 9 keys. So, if I was doing 1/3 + 5/6 I would type in (1/3) + (5/6). You need to be careful when working with mixed numbers (like 3 ½ ) because of the way the calculator interprets what you type. For the number 3 ½, think about how you read it: ________________________________. See that little and in there? What does “and” mean in math? __________________. So if you want to type in 3 ½ , you’ll really need to type what keys? __________________________. And again, your best bet is to put them in ( ). Try these problems now: a.
1 1 + = 4 8
b.
1 3 + = 2 8
c.
d.
2 1 − = 3 9
e.
5 3 ÷ = 8 16
f. 2
5 1 +3 = 8 2
g.
7 2 • = 10 5
h. 3
j. 8
3 3 ÷2 = 5 10
7 1 •2 = 8 2
2 1 + = 5 4
There is a way to get a fractional answer, if the answer turns out to be a “nice” fraction. After you type in your problem and before you hit enter, go to the menu and choose Option 1: Frac. Then, press enter. This tells the calculator to turn the result into a fraction if it can. It will calculate with mixed numbers also, but give you an improper (top-heavy) fraction instead of a mixed number. Try the same problems in a – j above again, but this time, write your results as fractions. a.
1 1 + = 4 8
b.
1 3 + = 2 8
c.
d.
2 1 − = 3 9
e.
5 3 ÷ = 8 16
f.
5 1 2 +3 = 8 2
g.
7 2 • = 10 5
h.
7 1 3 •2 = 8 2
j.
3 3 8 ÷2 = 5 10
Kathy Berry Monroe County ISD, Michigan
2 1 + = 5 4
TI-84/83 Intro Part 1 Page 3 of 8
One quickie shortcut for you… The calculator will automatically use your last answer (ANS) in your next calculation if you start your typing with an operation (+, -, x, ÷). You can recall this last answer anytime you want by using (notice ANS in yellow above the negative key?). 2nd ( - )
6. Fractions, decimals, and percents. You can use your calculator to turn any fraction into a decimal and some decimals into fractions. Fractions to decimals: Method #1 Since a fraction is just a division problem anyway, just divide numerator by denominator (top # by bottom #). You may need to round your result to a convenient number of decimal places. Fractions to decimals: Method #2 Use the “change to a decimal” feature in the menu, Option 2. Type in your fraction, being sure to use parentheses on any mixed numbers. Then hit ENTER.
, 2, and
Decimals to fractions: In general, if your decimal number has 3 or fewer decimal places, the calculator will turn it into a fraction (possibly an improper one) for you. Type in your decimal number. Go to the MATH menu and select Option 1. Press enter. Voila, instant fraction. Of course, if it is improper you usually should simplify it to a mixed number. Percents: There is no percent key on this calculator. That’s OK – you now know how to work with fractions and decimals. Percents can easily be written as fractions or decimals. Percent means “out of 100”, and “out of” usually means to divide. So, if you have a percent and wish it was a decimal, just divide by 100! For example, 25% is 25 ÷ 100, which is 0.25. If you have a more complicated percent like 6 ¼ %, change the ¼ part to a decimal first (1 ÷ 4), add on the 6 (6.25), then divide by 100 (0.0625). Once your percent is a decimal (with 3 or fewer places), you can go to your math menu to turn it into a fraction if you need to. For example, 25% = 0.25. Hit MATH, Option1, ENTER, and you get ¼. Of course, easy percents like 25% can be done in you head faster than on the calculator. To turn a fraction to a percent, turn it into a decimal. You then need to do the opposite of dividing by 100…..multiplying instead. Then press ENTER. For example, if you have the fraction ½, take 1 ÷ 2, which is 0.5. Then multiply by 100, and you get 50. Tack on your percent sign (%), and you’re all set (50%). Again, you may need to so some rounding of your decimal to a reasonable number of places.
Kathy Berry Monroe County ISD, Michigan
TI-84/83 Intro Part 1 Page 4 of 8
Complete the chart below: FRACTION
DECIMAL
PERCENT
FRACTION
1 4
DECIMAL
PERCENT
2 3 0.60
1.25 85%
0.5% 0.0625
3 20 0.90
2
1 2
7. Exponents, and Square and Cube Roots You may remember an exponent is a shortcut for showing repeated multiplication. For example, 53 means to us the number 5 as a factor 3 times (5 • 5 • 5). So 53 = 125. How can you do this on your calculator? Right above the division key is black key with a little upside-down V called a caret
›.
You can think of this as the “raised to the ____ power” key.
For example, if you need to do 84, which is read “eight to the fourth power”, just type in 8
›
4.
This works with decimals, too. You could do 0.252.8 if you needed to. BE CAREFUL if you work with negative numbers. If you intend to take a negative number to a power, your best bet is to put the number in parentheses before hitting the carat key. Also, BE SURE you use the NEGATIVE button
Ì rather than a minus or
subtraction sign in front of any negative numbers. To your calculator, they are VERY DIFFERENT SIGNS. For example, to do (–4)8, read as “negative four to the eighth power”, I would type in (
Ì 4 ) › 8.
This will give a different result than if your problem says -48 which is
actually –1 • 4•4•4•4•4•4•4•4. You can even take numbers to negative powers, but that’s another lesson. A SHORTCUT for squaring numbers is to use the
Kathy Berry Monroe County ISD, Michigan
¡
key, which is on the left side of the
TI-84/83 Intro Part 1 Page 5 of 8
calculator above the EXAMPLE: 212
« key.
Just type your number and then hit
Type 21, then hit
¡and then ENTER.
¡ and then ENTER.
Square and Cube roots. Doing roots is asking the opposite question of doing exponents. For example problem 52 asks the question, “What number do I get if I multiply two 5’s together?” Finding the square root asks, “What number would I multiply by itself to get 25?” You may have noticed above the
¡ a funny little symbol (called a radical sign) in yellow.
Used plain like you see it √ means to find the square root of a number (what number times itself gives you the starting number under the √ sign?). For example, here’s one you can do in your head: find the square root of 36…. right? Because 6 • 6 = 36. On your calculator, just press
y¡
36 . It’s 6,
to display the
radical sign, and then type in 36, and press ENTER. Cube roots work in a similar way. Just as raising a number to the third power is called cubing it (43 = 4 cubed = 4 • 4 • 4 = 64) you can go backwards and ask the question, “What number times itself three times gives me 64?” To cube a number just use the caret key, or you can go into the MATH menu and choose Option 3: cube. Example: 123 Type 12, press , press option 3, press ENTER. You get 1728, the same number you would have gotten doing 12
› 3 and then ENTER.
To find a cube root of a number, like 1728, first we need to tell the calculator we’re going to do a cube root. Press ,, choose option 4, and then type your number to cube root. Close out your parentheses with a right hand ). Then press ENTER.
Kathy Berry Monroe County ISD, Michigan
TI-84/83 Intro Part 1 Page 6 of 8
Now try these problems: a. 53 =
b. 82 =
c.
d. 103 =
e.
676 =
f.
g. 143 =
h.
3375 =
j.
3
121 = 3
27 = 16525 =
Try these. Look for at pattern. q.
( 36 )2 =
r.
92 =
s. ( 144 ) =
t.
1 .5 2 =
u.
42 =
v.
2
( 4)2 =
What happens when you square a square root, or vice versa?
8. Please Excuse My Dear Aunt Sally. After all, your calculator does! Remember how we said your calculator follows the rules of math? When we do problems that have more than one operation in them, we ALL have to agree on what order to do those operations in. Otherwise, we’ll all get different answers. Your calculator follows the same rules as we do: FIRST: Take care of anything in PARENTHESES. If you have parentheses inside parentheses (or brackets or braces), start from the innermost pair and work your way out. Also, radical signs act like parentheses –they’re part of a family we call “grouping symbols”. If you have operations going on under a radical sign, take care of them before trying to find the root you need. P for ( ) = Please. 2ND: Take care of any exponents (and roots). E for exponents = Excuse. At this point, all you should have left is just basic math. 3RD: Do all Multiplication and Division from left to right, whatever shows up first. M from Multiplication = My, D from Division = Dear. 4th: We save the easiest stuff to last. Do all Addition and Subtraction from left to right. A from Addition = Aunt, S from Subtraction = Sally.
Kathy Berry Monroe County ISD, Michigan
TI-84/83 Intro Part 1 Page 7 of 8
If you are working with fractions that have operations to be done in the numerator and/or the denominator, that’s ok! Fractions bars sometimes act like grouping symbols. Pick a part (of the fraction (top or bottom) to work on first, get that down to a number, and then work on the other half. Reduce your final answer if necessary. To help YOU remember the order of operations, you might remember the phrase Please excuse my dear Aunt Sally. Just recall multiply and divide go left to right (not whichever you like best first). Same for addition and subtraction.
Now the real test.
Use everything you’ve learned about the graphing calculator to help you simplify these expressions.
a. ( 5 + 3 ) ÷ 2 + 2
b. 53 – 8 • 5 + 6
c. ( 3 + 6 ) ÷ 32
d. 125 ÷ [ 5( 2 + 3 ) ]
e.
12 − 2 5•3
g.
62 − 42 – 2(3 − 2)
j.
f.
3
8
(6 + 2) 2 +3•9 16
h. 6 –
⎡2 + 7 ⎤ ⎢⎣ 3 − (2 • 3 − 5)⎥⎦
− 1 + 12 − 4(1)(−20) 2(1)
Kathy Berry Monroe County ISD, Michigan
TI-84/83 Intro Part 1 Page 8 of 8
