Download Unit 3: Rational Numbers Rational Numbers

November 15, 2011
Unit 3: Rational Numbers
How many numbers are there in between -35 and -40?
Rational Numbers
How many numbers can you write between 11 and 12?
11
12
In pairs or by yourself, create a number line from 11 to 12. Write
expressions or numbers in the following __ ways and place them on your
number line:
- A decimal
- A repeating number
- A sum
- A fraction
- A product
- A difference
- A mixed fraction
- A quotient
November 15, 2011
Rational Numbers
Can you do the same thing with negative numbers?
-12
-11
- A decimal
- A fraction
- A mixed fraction
- A repeating number
- A product
- A quotient
- A sum
- A difference
3.1 What is a Rational Number?
Rational Number:
- Any number that terminates (stops) or has a repeating pattern
- Any number that can be written in the form:
1
ex. 7, 12.2215, -5.8, 0.2, 9
What are some examples of non-rational numbers?
The label on a package of frozen cranberries says
that it must be stored at a temperature between
-18˚C and -22˚C. What are some possible
temperatures that they could be stored at?
m
n
where n≠0
November 15, 2011
3.1 What is a Rational Number?
-18˚C
-22˚C
Determine each quotient (evaluate):
12
2
12
-2
-12
2
Based on your answers above,
What do you know about
-3
2
3
-2
-
3
2
?
Place the following rational decimal
numbers on the number line below:
5
0
-5
-12
-2.09
1.2
7
-3.99
24
5
November 15, 2011
Place 3 more numbers on the
following number lines:
-0.25
-0.26
-
1
1
2
2
Order the following numbers on the number from least to greatest:
2
-2
5
1.13
-3
10
3
7
-3.4
-4
-
2.7
6
Practice P. 101-103 #5, 6a, 8ac, 12cfh, 13, 16ace, 18ac, 20, 25b
November 15, 2011
3.2 Adding Rational Numbers
Find the answer to the following:
3+7=
-3 + 7 =
-3 + (-7) =
3 + (-7) =
3.2 Adding Rational Numbers
Find the answer to the following:
3
8
+
7
8
=
3
8
+
7
8
=
3
8
+(
7
)
8
=
3
8
+(
7
)
8
=
November 15, 2011
3.2 Adding Rational Numbers
Find the answer to the following:
7
+
2
1
8 =
3
8
7
2
+
1
8 =
3
8
7
) =
(
+
2
1
8
3
8
7
3
1 8 + ( 28) =
3.2 Adding Rational Numbers
Strategies for adding rational numbers:
- Use a number line:
move to the right when adding positive numbers
Ex. -4 + 5
move to the left when adding negative numbers
Ex. -3 + (-2)
November 15, 2011
3.2 Adding Rational Numbers
Use common denominators or equivalent fractions
when adding positive and negative fractions or:
1
4
+
7
8
=
use compatible number lines:
3.2 Adding Rational Numbers
1
4
+ ( 87 ) =
2
5
+(
4
10 )
=
November 15, 2011
3.2 Adding Rational Numbers
Red = Negative
Black = Positive
What is the largest sum that can be made with two random cards?
What is the smallest sum that can be made with two random cards?
3.2 Adding Rational Numbers
Homework: p.111
November 15, 2011
3.3 Subtracting Rational Numbers
Using any two numbers between -10 and 10
What is the largest number you can make with an addition?
What is the smallest number you can make with an addition?
What is the largest number you can make with a subtraction?
What is the smallest number you can make with a subtraction?
3.3 Subtracting Rational Numbers
Red = Negative
Black = Positive
What is the largest difference possible between two random cards?
What is the smallest difference possible?
November 15, 2011
3.3 Subtracting Rational Numbers
Find the answer to the following:
3-7=
-3 - 7 =
-3 - (-7) =
3 - (-7) =
3.2 Subtracting Rational Numbers
Find the answer to the following:
3
8
-
7
8
=
3
8
-
7
8
=
3
8
-(
7
)
8
=
3
8
-(
7
)
8
=
November 15, 2011
3.3 Subtracting Rational Numbers
Find the answer to the following:
7
2
1
8 =
3
8
7
2
1
8 =
3
8
7
) =
(
2
1
8
3
8
7
3
1 8 - ( 28) =
3.3 Subtracting Rational Numbers
Strategies for subtracting rational numbers:
- Use a number line:
move to the left when subtracting positive numbers
Ex. -1 - 3
move to the right when subtracting negative numbers
Ex. -3 - (-2)
November 15, 2011
3.3 Subtracting Rational Numbers
1
4
- ( 87 ) =
2
5
-(
4
10 )
=
3.3 Subtracting Rational Numbers
Homework: 3cd, 5cd, 7def, 8, 9def,
10, 11, 13cd, 14cd, 15ace
November 15, 2011
3.4 Multiplying Rational Numbers
If a x b = c
Solve the following:
a x -b =
-a x b =
-a x -b =
3.4 Multiplying Rational Numbers
Review:
Ex:
(+) Number x (+) Number = (+) Answer
7x8=
(-) Number x (-) Number = (+) Answer
-7 x -8 =
(+) Number x (-) Number = (-) Answer
7 x -8 =
(-) Number x (+) Number = (-) Answer
-7 x 8 =
November 15, 2011
3.4 Multiplying Rational Numbers
Multiplying Fractions:
1. Multiply the numerators together
2. Multiply the denominators together
* Tip = if there is a "negative", move it to the numerator
()
3
6
X
5
7
11 1
12 3
For mixed fractions, convert them to improper fractions first, then multiply
2
35
X
6
9
1
7
9
1
85
3.4 Multiplying Rational Numbers
Fractions should always be written in simplest terms:
Common factors can be found at the end or at the beginning:
11
X
7
21
44
( )( )
8
3
7
4
November 15, 2011
3.4 Multiplying Rational Numbers
Homework: p.127
#3cd, 4cd, 6-10, 11cd, 12cd, 13-15
3.5 Dividing Rational Numbers
If a ÷ b = c
Solve the following:
a ÷ -b =
-a ÷ b =
-a ÷ -b =
November 15, 2011
3.5 Dividing Rational Numbers
Ex:
Review:
(+) Number ÷ (+) Number = (+) Answer
20 ÷ 5 =
(-) Number ÷ (-) Number = (+) Answer
-20 ÷ -5 =
(+) Number ÷ (-) Number = (-) Answer
20 ÷ -5 =
(-) Number ÷ (+) Number = (-) Answer
-20 ÷ 5 =
3.5 Dividing Rational Numbers
Dividing Fractions:
1. Find the reciprocal of the second fraction
2. Multiply
* Tip = remember whole numbers can be turned into fractions by putting them over 1
3
6
÷
5
7
11
1
÷
12
3
For mixed fractions, convert them to improper fractions first
8÷
3
5
November 15, 2011
3.5 Multiplying Rational Numbers
Homework: p.134
#3cdef, 4ef, 6, 8, 9def, 10, 11, 12cdef, 13, 14, 15, 17cd, 18cd, 19
3.6 Order of Operations with Rational Numbers
Evaluate:
(-8) - 2(24 ÷ (-8))2
Try it with your calculator
Try it without your calculator
Did you get the same answer?
November 15, 2011
3.6 Order of Operations with Rational Numbers
Evaluate:
( )( ) ( ) ÷ [ ( )]
1
2
-
1
2
- -
2
3
1
3
+ -
3.6 Order of Operations with Rational Numbers
Remember our order of operations:
B
E
D
M
A
S
3
12
November 15, 2011
3.6 Order of Operations with Rational Numbers
Using your calculator:
Key in the expression -2.8 - 1.4 x 4.5 in your calculator
Does your calculator follow order of operations from left
to right?
What is the answer?
-9.1 or -18.9
3.6 Order of Operations with Rational Numbers
Practice:
a)
(-3.2) - 0.9 ÷ [0.7 - (-1.2)]2
b)
(- ) ÷[ + (- )] x ( )
2
3
1
4
1
2
1
3
November 15, 2011
3.6 Order of Operations with Rational Numbers
Treat 'fraction bars' the same as brackets
Ex.
-0.3 x
1
4
+ (- 21 )
4
3.6 Order of Operations with Rational Numbers
In Wood Buffalo national park, the highest temperature for the month of
January was -21.8oC and the lowest temperature was - 31.7oC. What was the
mean temperature for that month? Show the order of operations that you will
use.
November 15, 2011
3.6 Order of Operations with Rational Numbers
Homework:
p. 140
#3cd, 4cd, 7cd, 8, 9, 10, 11, 12cd, 13 - 17
Challenge: p. 143 #19-21