Rational Numbers

1
Rational Numbers and Opposites
Technology 1.1
Figure 1.1
For Figure 1.1,
Enter the fraction, , as a quotient, and
choose to have your answer displayed as a
fraction by selecting ? FRAC, option 1, under
the MATH menu. The negative symbol is .
(-)
(-)
ENTER
2
1
MATH
?
3
Enter the mixed number, 2 as a sum of a whole
number, 2, and the fraction, Choose to have
the answer displayed as a fraction.
2

3
?
4
MATH
1
ENTER
1 of 2
2
Technology 1.1
Rational Numbers and Opposites
Figure 1.1
Enter the negative mixed number as the opposite
of a sum of the whole number, 3, and the
fraction, Use as an opposite sign.
Choose to have the answer displayed as a
fraction.
(-)
(-)
(
3

1
?
4
)
MATH
1
ENTER
Note that the mixed-number answers are displayed
as improper fractions. Directions for changing
an improper fraction to a mixed number are given
in Section 1.2, Calculator Exercises.
2 of 2
3
Technology 1.2
Absolute Value
Figure 1.2
For Figure 1.2,
To enter an absolute-value expression on your
calculator, use the abs function found under the
MATH NUM menu option 1. Close the set of
parentheses that are opened for you to enclose
each of the numbers, 3.5 and , in each set
of parentheses.
MATH
1
)
5
.
3
ENTER
?
MATH
?
1
1
(-)
?
2
)
MATH
1
ENTER
4
Technology 1.4
Adding Rational Numbers
c.
d.
Figure 1.4
For Figure 1.4,
Enter the fractions, and in
parentheses for proper grouping and ease in
reading. Choose to have the answer displayed as a
fraction. This option, FRAC, is located
under the MATH menu option 1.
?
)
3
(-)

)
2
?
1
(
(
2
?
1
MATH
ENTER
1 of 2
5
Technology 1.4
Adding Rational Numbers
c.
d.
Figure 1.4
Mixed numbers are written as the sum of the whole
number and the fraction. Negative mixed numbers
have the negative sign outside the parentheses.
Choose to have the answer displayed as a fraction
by using option 1 under MATH menu.
(-)
(
1

2
?
3
)

(
2

3
?
5
)
MATH
1
ENTER
2 of 2
6
Technology 1.5
Subtracting Rational Numbers
a.
d.
Figure 1.5
For Figure 1.5,
Negative integers and decimals may be entered
without parentheses. Note the difference in the
negative, , and the minus, .
(-)
-
8
3
6
9
.
(-)
-
.
ENTER
1 of 2
7
Technology 1.5
Subtracting Rational Numbers
a.
d.
Figure 1.5
Enter the fraction, , in parentheses for
proper grouping and ease in reading.
Negative numbers have the negative signs outside
the parentheses. Choose to have the answer
displayed as a fraction. This option, ? FRAC, is
located under the MATH menu option 1.
1

1
(
-
1
(-)
)
4
?
(
?
)
2
ENTER
MATH
1
2 of 2
8
Technology 1.7
Multiplying Rational Numbers
a.
d.
Figure 1.7
For Figure 1.7,
There is no need to place decimal numbers in
parentheses. You may use the multiplication sign
instead.
(-)
(-)
4
6
9
8
4
.
.
ENTER
?
Place the negative mixed number as a sum in
parentheses with the negative outside the
grouping. Choose to have your answer displayed as
a fraction. This option, ? FRAC, is located under
the MATH menu option 1.
?
?
(
)
(
(-)
5
3
2
3
2
1

?

)
MATH
1
ENTER
9
Technology 1.8
Dividing Rational Numbers
d.
c.
d.
Figure 1.8b
Figure 1.8a
For Figure 1.8a and 1.8b,
There is no need to enter the whole number 0 in
the decimal -0.34.
?
(-)
.
ENTER
0
4
3
Since it is not possible to divide by 0, an error
is displayed on the screen when you enter the
expression.
?
(-)
.
ENTER
9
8
0
ENTER
Press to quit the error screen
and return to the default home screen.
10
Technology 1.9
Integer Exponents
a.
Figure 1.9a
To enter an exponent, use the key. For
Figure 1.9a, There is a special key, , that
may be used to square a number. To square a
number, enter the base followed by .

x2
x2
)
(
1
3
2
?
ENTER
MATH
x2
or
)
(
2
3
2
?
ENTER
MATH

1
1 of 3
11
Technology 1.9
Integer Exponents
b.
Figure 1.9b
For Figure 1.9b, There is a special function
under the MATH menu option 3 that may be used to
cube a number.
3
5
1
ENTER
MATH
.
or
3
5
1
ENTER

.
2 of 3
12
Technology 1.9
Integer Exponents
d.
For Figure 1.9c,
Figure 1.9c
Enter the mixed number 9 , as the sum of 9 and
enclosed in parentheses. Use the for
inserting the exponent.

)
(
1
5
3
1
9

ENTER
MATH

?
Since the result is not a fraction, enter the
fraction answer that we are checking,
and compare the decimal values.
ENTER
?
3
4
2
8
6
3
0
1
2
7
1
3 of 3
13
Technology 1.10
Square Roots
c.
d.
e.
Figure 1.10a
For Figure 1.10a and Figure 1.10b,
To enter a square root, enter .
Close the parentheses that are opened for you in
order to enclose the number in a set of
parentheses.
2nd
2nd
1
9
4
?
)
MATH
ENTER
5
2
)
ENTER
2nd
(-)
1 of 2
14
Technology 1.10
Square Roots
e.
Figure 1.10b
Since the square root of a negative number is not
defined as a real number, if your calculator is
in Real mode (the default mode), an error will
be displayed when you enter the expression.
5
2
)
ENTER
2nd
(-)
Press to quit the error screen and
return to the default home screen.
ENTER
2 of 2
15
Technology 1.11
Cube Roots
a.
b.
c.
Figure 1.11
For Figure 1.11,
The cube root is located under the MATH menu
option 4. Remember to close the set of
parentheses that is opened for you.
7
MATH
(-)
2
4
)
ENTER
0
MATH
3
4
)
ENTER
1
MATH
7
2
1
4
)
?
ENTER
MATH
16
Technology 1.13
Order of Operations
c.
d.
e.
Figure 1.13
For Figure 1.13, It is necessary to enter both
the numerator and the denominator in a set of
parentheses to ensure proper grouping.
(
(
)
3
3
2
6
1
-
?

x2
)
2

ENTER
1 of 2
17
Technology 1.13
Order of Operations
c.
d.
e.
Figure 1.13
Use a set of parentheses instead of brackets and
braces.
)
)
(
(
(
7
4
3
2
2
-
-

)
(
5
3
8

ENTER
(-)
)
Enclose the radicand in a set of parentheses.
1
5
1
2


2nd
ENTER
(-)
)
6
2 of 2