Texas Instruments TI-15 User manual

1
TI-15 ExplorerTM Support Book
Chapter Name
Page
1. Introduction to the display
I. Display, scrolling up and
down, order of operations
and using brackets.
II. Clearing and correcting
2
2. Mode menus
I. Calculator
II. Problem solving
III. Fraction
3
3. Basic operations including
exponents (powers) and square root
6
4. Whole numbers and decimals
7
5. Fractions
9
6. Percent
12
7. Constant operations
13
8. Problem solving in Auto mode
14
9. Problem solving in Manual mode
16
10. Place value
17
11. Memory
19
12. Error messages
19
13. Display indicators
20
14. Copyright information
21
TI-15 Explorer ™ is a trademark of Texas Instruments

2
1. Introduction to the Display
a. Using your thumbs, press and hold down both and at the same time, then
release both keys at the same time. MEM CLEARED is displayed.
This RESETS the calculator to its default settings.
b. Press . The blinking triangle cursor is displayed. The calculator is ready to use.
c. Key in . 10 x 10 = 100 is displayed.
You can see both the problem and the answer at the same time.
d. Now key in  (10 x 9 = 90 is displayed), and  (10 x 8 = 80
is displayed). The “up arrow” indicator in the calculator window lets you know that
you can scroll up.
e. and move the cursor left and right, and move the cursor
up and down through previous entries.
A small arrow will appear at the left hand side of the screen when
this is possible.
f. is used to open an expression with brackets,
and must be used to close before selecting ,
otherwise Syn error is displayed.
Operations in brackets are always performed first.
You can review entries and look for patterns.
g. In terms of priority, the calculator will perform in the following order:
Brackets and 
Fractions 
Exponents and square roots and 
Negative 
Multiply and divide and 
Add and subtract and 
Convert to fraction or decimal 
Complete 
NB Since the calculator will always do what is in brackets first, the use of
brackets can change the required order and so change the answer or result.
h. Clearing and correcting
turns the calculator on and off, but will not clear settings or previous
entries.
clears only the last entry and any error statements. It does not affect mode
settings, memory or constants.

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will clear the last digit entered so that you do not need to re-enter an entire
number.
Pressing and simultaneously resets settings to defaults and clears
memory and constants.
2. Mode menus
See worksheets for further explanations and uses.
a. Calculator mode
[Press and , and to set.]
I. Press and choose style for division
II. Press , then and to select .
When +1 is underlined and selected, the Constant operation is displayed.
When ? is underlined the operation is not shown.
See worksheets

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b. Problem solving mode
Press to enter problem solving and 
with and and to set.
To exit problem solving press and the
small icon will disappear from the screen.
In MAN (manual mode) you can enter
your own problem –eg ? x ? = 36,
and the calculator shows that this has
9 solutions –it only counts positive whole
numbers, and 9 x 4 is different from 4 x 9.
Also in MAN mode,
the place value menu is available. See section 10 for further information.
Inequalities and equalities can be tested. Press once for LESS THAN,
and  for GREATER THAN. The calculator will indicate whether a
statement is correct (YES) or incorrect (NO).

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c. Fractions menu
Press and to choose then to set. See fractions section below.

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3. Basic operations, including exponent (powers) and square roots
a. These are the usual operations with , , , and , except
that the result of a division depends on which mode is set for
it.
This screen is accessed by pressing and using the side
arrows to choose whether the answer should be a decimal or
a fraction. Press to set.
If you attempt to divide by 0, an error message is displayed.
Negative numbers can be used by entering the symbol before the integer.
b. divides a whole number by a whole number and
displays the result as a quotient and remainder.
The divide symbol is slightly larger than the standard one
on the screen.
If this result is used in the next calculation, the remainder
is dropped.
c. lets you calculate a number to a given power.
It allows the use of negative exponents (see worksheets)
and lets numbers be entered in scientific notation.
eg entering  gives 8 ie (2 x 2 x2),
and entering   gives 0.125 which when
changed to a fraction becomes 1/8 after simplification.
d. calculates the square root of positive values
including fractions but the answer will be a decimal
which may or may not be able to change to a fraction.
NB brackets must be closed.
e. Numbers can be entered in scientific notation using the key.
eg 2.3 x 10^2 + 1.4 x 10^3 = 1630
2.3 x 10^8 + 1.4 x 10^10 = 1.423 x 10^10
When the number of zeros goes beyond the screen, the number will appear in
scientific notation.

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4. Whole numbers and decimals
a. The key sets the number of decimal places
together with the appropriate RED Place Value
key from the left hand side of the calculator.
The rounded result is displayed but the original
number is retained in the memory.
must be pressed each time the number is
to be rounded off.
removes the fixed decimal setting.
needs to be pressed before is effected.
It can be applied to and individual number or
before is pressed to complete a calculation.
eg Entering will do the
calculation but return an answer rounded to 1 dec place.
Pressing gives the full answer 167.832
While the symbol is visible numbers entered will
be displayed to the pre-set number of decimal places.
eg if  has been used, then until it is cleared, any further calculations will answer
to the nearest whole number, although the actual answer will still be stored.
b. When is used to change a fraction to a
decimal and back to a fraction, sometimes the
fraction needs to be simplified to get back to
the original.
eg 5/8 changes to 0.625 then back to 625/1000.
NB when a fraction can be simplified the symbols
d
n
D
N
will be displayed at the top of the screen
until no further simplification is possible.
This is changed back to 5/8 using the key.

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c. Three Results of Division
There are three different ways that a division can be displayed on the screen.
Decimal answer (i)
Quotient and remainder answer (ii)
Fraction answer (iii)
i. Decimal answer Key in 
5.429 
is displayed.
This shows the standard decimal answer to a division problem.
ii. Now key in This time
1429 r
is displayed.
This shows the quotient and remainder answer to a division problem.
iii.. Now set the calculator to give a fraction answer to a division problem.
Press . The selection . n/d is displayed.
This lets you select decimal or fraction answers to division problems.
Press the right arrow key to underline n/d. Press to confirm your selection.
The n/d indicator in the screen lets you know that the calculator will now give fraction
answers to division problems.
Press to exit the menu. Notice that n/d is still displayed.
Now key in .
10
5
429 
(a stacked fraction) is displayed.
This shows a fraction answer to a division problem. Notice also that the fraction result will not
be in simplest form necessarily. See later for how to simplify.
Press the up arrow key once to scroll up. Press again. The calculations you entered
previously are displayed. Press the Down arrow . Press the Down arrow again.
You can review the three different results of the division problem and explore with your
students why the same problem gets three different-looking answers.
Students will come to understand that all three answers are the same and make the
connection between decimals, quotients and remainders, and fractions.

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5. Fractions
a. displays a menu from which
the way a fraction is shown is set
- Un/d displays a mixed number and
- n/d displays a single fraction (improper fraction) result.
and whether any given fraction is unsimplified (Man) with
d
n
D
N
showing at the
top, or in simplest terms with Auto
This lets you select to display fraction results as mixed numbers or improper
fractions.
Press the left and right arrow keys and to move the underline. To select
mixed numbers, underline U n/d and press . To select improper fractions,
underline n/d and press .
Press the down arrow  . The selection MAN AUTO is displayed.
This lets you select to manually simplify fractions (using the key), or have the
calculator automatically simplify fractions.
Press and to move the underline.
Press to exit the Fraction Menu.
b. A mixed number is entered using the button after the whole number part,
after the numerator and after the denominator, followed by , or the next part
of a calculation.
c. changes a mixed number to an improper fraction and vice versa.
d. When the calculator is in Auto mode, and
d
n
D
N
is visible, pressing simplifies
the fraction to lowest terms in one step.
e. When the calculator is in Man mode, and
d
n
D
N
is visible,
pressing simplifies the fraction to lowest terms in steps where the factor or
divisor to be used can either be entered by the user or the calculator chooses the
factor.
Pressing shows the factor that was used, and pressing it again displays the
simplified fraction. This is repeated until the
d
n
D
N
is no longer on the screen.
The calculator uses the lowest prime number available as a factor first, then moves
to the next prime factor until the fraction is fully simplified.
f. For calculations, the denominator can be from 1 to 1000. For conversions to decimals,
the denominator can be from 1 to 100,000,000.

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g. Stacked fractions, Entering mixed numbers, numerators, and denominators
Key in .
8
3
9
8
5
4
3
8
is displayed.
You can enter either the numerator or denominator first. Fractions are stacked. You
can see the whole problem and the answer at the same time.
h. Converting mixed numbers to improper fractions
Press to convert the mixed number to an improper fraction.
8
75
is displayed. Press again to convert back to the mixed number.
8
3
9
is
displayed.
i. Converting fractions to decimals and vice versa
Press to convert the fraction to a decimal.
9.375 is displayed. Press again to convert back to the fraction.
This time
1000
375
9
is displayed.
The calculator uses the decimal value to create the fraction. The N/D n/d indicator at
the top of the screen lets you know that the fraction can be simplified further.
j. Simplify by a factor you choose.
Press .
40
15
9
is displayed. Press to see the factor used to simplify the fraction.
25 is displayed. The numerator and denominator were each divided by 25.
Press again to return to the fraction.
40
15
9
is displayed again.
The N/Dn/d indicator lets you know the fraction can still be simplified further.
k. Simplify by a factor the calculator chooses.
Press .
8
3
9
is displayed.
Press to see the factor used to simplify the fraction. 5 is displayed. Press
again to return to the fraction.
8
3
9
is displayed again.
The N/Dn/d indicator is no longer displayed. This means that the fraction cannot be
simplified any further.

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To summarise different fraction forms:
Dividing a fraction by a fraction gives fractional results regardless of the division
setting (decimal or fraction).
The mode settings provide 4 possible display options for computational
results displayed in fraction form.
For example, for 6 ÷ 4, the displays would look like this:
MANual simp/improper (n/d) : 6
4
AUTO simp/improper (n/d) : 3
2
MANual simp/mixed number (U n/d) : 𝟏2
4
AUTO simp/mixed number (U n/d) : 𝟏1
2
You can enter either the denominator or numerator first.

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6. Percent
a. enters % after a number. Pressing changes the % to a decimal
Pressing and will change the display from decimal to fraction and then to
percent.
b. Press  to see 0.25 change to 25%. Pressing changes the
percent back to 25
100. Note the
d
n
D
N
on the screen. This indicates that the fraction
can be simplified. Pressing again restores the 25%.
c. To find a percentage of a quantity eg 5% of 27.6, press these keys:
 The % key is pressed directly after the number.
7. Constant operations Op1 and Op2
a. These keys allow an operation to be stored and used repeatedly. The function can be
used with whole numbers, decimals and fractions, and with the operators , , ,
, , , , saved.
b. Op1 and Op2 can be used together if required.
eg If Op1 is +2 and Op2 is x 3, Op1 followed by Op2 will give a different result from
Op2 followed by op1. (Order of operations).
c. Remember the operation needs to be locked in by pressing eg Op1 before the
operation and also after it. When this is done a small Op 1 (or Op2) is visible at the
top of the screen.
d. Storing a constant and the constant operation
i. Press to open the operation. Press to enter “add 5” as the constant.
Press to store and close the operation and lock it in. + 5 is displayed.
The Op1 indicator at the top of the screen lets you know that the operation is stored.
ii. Press to “initialize” the constant with a starting value of 0. 0 = 0 is displayed.
You can choose any starting number.

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iii. Press to start the constant operation.
The “expression” 0 + 5 is displayed on the top line.
The 1 on the bottom line is the number of times the
operation has been performed.
The 5on the bottom line is the result.
iv. To continue the constant operation, press repeatedly. You can press the Up
and Down arrows to scroll up and down to review the series of constant operations but
they cannot be changed.
NB when the operation produces a fraction answer, eg when OP1 is
2
1

, the display takes
two lines to write fractions. This means that the number of the operation is on the left and the
answer fraction on the right. The actual expression being calculated is on the screen above,
accessed using the UP arrow.
e. Hiding the equation
i. Press . Press once.
The selection +1 ? is displayed.
This lets you select to show or hide the “expression”.
ii. Press to underline ? . Press to confirm your
selection. Press to exit the menu.
iii. Press . The constant continues, but the “expression” is no longer displayed on
the top line.
f. Clearing the constant
i. Press . Press Down twice.
The selection OP1 OP2 is displayed.This lets you select to clear OP1 or OP2.
ii. OP1 is underlined. Press to clear OP1.
The Op1 indicator is no longer displayed and the operation is cleared.
iii. Press to exit the menu.
g. Op2 is used in the same way. Both Op1 and Op2 can be stored and used in the
same problem. Eg if Op1 is “ Add 5” and Op2 is “ x 2” , then different answers will be
seen when Op1 and Op 2 are applied in a different order –useful for order of
operations work.

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8. Problem solving in Auto mode
a. Press the key to enter Problem Solving.
The Auto and indicators are displayed, indicating that you are
in the Automatic mode of Problem Solving.
A simple equation with one part missing is automatically
displayed. (Problems are random.) The default start is with
addition.
eg, 9 + ? = 12. Keying in 3 where the cursor is, then enter,
results in YES as shown.
Key in an incorrect answer and watch the = symbol in the display.
In this case, 6 + 12 = ?
Press  .
The calculator tells you the answer is wrong and gives you a hint (the
< or > symbol) to let you know how to adjust your answer to get the right answer.
Now key in the correct answer, in this case 18 . 6 + 12 = 18 and YES are displayed.
Then a new problem pops up for you to solve.
The calculator gives three tries before it gives the right answer and moves to the next
problem. After every 5 problems a scoreboard shows the number of correct and incorrect
answers.
d. Press The Problem Solving menu is displayed. First, your score is displayed.
YES and NO tell you how many correct answers you have given and
how many incorrect.
e. The first selection AUTO MAN is displayed.
AUTO is underlined because you are in AUTO mode.
f. Press Down . The selection 1 2 3 is displayed.
This selects the level of difficulty of the problems displayed;
level 1 is the simplest, level 2 intermediate, and level 3 the most difficult.
Press and to underline the level you want.
Press to confirm your selection.

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g. Press Down again. The selection is
displayed.
This selects the type of problems displayed; addition, subtraction,
multiplication, or division, or a ? in place of the operation symbol
so you have to choose the operation.
Press and to underline the operation you want.
Press to confirm your selection.
h. Press to exit the menu and return to Problem Solving.
Problems of the level and type chosen will appear.

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9. Problem solving in Manual mode
Manual problem solving
a. If you are not already in Problem Solving, press the key to enter Problem Solving.
The and Auto indicators are displayed, along with a randomly generated problem.
b. Press to enter the Problem Solving menu. First your score is displayed, and then
the first selection, AUTO MAN.Press to underline MAN. Press to confirm your
selection. Press to exit the menu and return to Problem Solving.
The indicator is displayed, but not the Auto indicator. You are still in Problem Solving, but
you are in Manual rather than Auto mode. No problem is automatically generated. You can
now enter your own problems.
Entering your own problems
a. Enter a problem such as .
There are 25 solutions to the problem.
Note that the calculator will only use positive integers and will
count 1 + 23 as different from 23 + 1.
The process is not algebraic either as the ? can represent different whole numbers.
b. Press . 2 + ? = 24 is displayed. 2 is one of the numbers that will fit..
c. Press  . 2 + 12 < 24 is displayed along with NO. 2 plus 12 is LESS than 24.
d. The original question appears again. Press . 2 + ? = 24 is displayed again.
e. Press . 2 + 22 = 24 is displayed along with YES.
2 plus 22 will equal 24.
f. Continue exploring all 25 combinations of integers that, when added together, equal 24.
Exploring inequalities while in MAN problem solving mode
Press once for LESS THAN, and  for GREATER THAN.
The calculator will indicate whether a statement is correct (YES) or incorrect (NO).
a. Key in 8 + 5 = 10 + 3 (YES is displayed)
b. Key in 16 –3 < 16 + 3 (YES is displayed)
c. Key in 25 = 12 + 13 (YES is displayed)
d. Key in 6 - 2 > 8 (NO is displayed, then the correct inequality 6 - 2 < 8 YES

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10. Place value
Overview
To use place value you must:
be in Problem Solving MANUAL mode.
enter the number before you press the key.
1. If you are not already in Problem Solving, press the key to enter Problem
Solving.
If Auto is displayed, follow all of these steps. [If Auto is not displayed, skip steps 2, 3,
and 4, and go to step 5.]
2. Press to enter the Problem Solving menu. First your score is displayed, and
then the first selection, AUTO MAN.
3. Press to underline MAN. Press to confirm your selection.
4. Press or to exit the menu and return to Problem Solving.
The indicator is displayed, but not the Auto indicator. You are still in Problem
Solving, but you are in Manual rather than Auto.
Press .
After your score, the selection AUTO MAN is displayed. You
must be in Manual mode!
Press Down .
The selection I I -- –I -- . is displayed.
This selects the different ways to explore Place Value.
[With the selection of I I -- . or –I -- . , the results displayed using the RED keys change.
The WHITE keys operate the same way for either selection.]
Press to exit the menu and return to Place Value.

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How many hundreds, tenths, ones (2 ways)
Enter a number such as 7896.453. Press .
and are displayed.
You are now in the Place Value part of Problem Solving Mode.
Press . _ 8 _ _. _ _ _, and then 8 -> 100 is displayed.
The 8 is in the hundreds place.
Press . _ _ _ _. 4 _ _, and then 4 -> 0.1 is displayed.
The 4 is in the tenths place.
Note that when a number has a repeated digit, the first of the digits analysed is the one to the
right most position in the number. Pressing the digit again moves to the next occurrence of the
digit to the left.
When the display option is l l -.
This mode tells “How many...” when used with the red keys.
The WHITE keys operate the same way for either selection!
Press the red key. 7 8 _ _. _ _ _ is displayed.
There are 78 hundreds in the number.
Press the red key. 7 8 9 6 4 . _ _ is displayed.
There are 78,964 tenths in the number.
When the display option is - l -.
This mode tells “What is the ... digit?” when used with the
red keys. The WHITE keys operate the same way for either
selection!
Press the red key. _ 8 _ _. _ _ _ is displayed.
8 is the digit in the hundreds place.
Press the red key. _ _ _ _ . 4 _ _ is displayed.
4 is the digit in the tenths place.
While the is visible on the screen the function remains active and need not be pressed
again until the number is cleared and a new number is entered.
Pressing returns the calculator to Manual Problem Solving mode.

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11. Memory
1. There are two memory keys and .
M is displayed on the screen if a value other than zero is in memory.
will recall whatever is in memory.
To clear the memory, press twice.
Integers, fractions and decimals can be stored.
2. Using memory
This will store the screen value to the memory.
It does not store until has been pressed.
Adds a value to what is stored.
Subtracts displayed value from memory.
Multiplies stored value by screen value.
Divides value in memory by screen value.
 This action will divide the stored value by the screen value.
Only the quotient result is stored and displayed when is pressed..
12. Error messages

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13. Display Indicators