Download Unit 3: Rational Numbers

Unit 3: Rational Numbers
3.1 What is a Rational Number?
A. Investigate p. 94
B. Connect
A rational number is any number that can be written as fraction.
m
i.e.
where n  0 and m, n are integers
n
Examples of Rational Numbers:
2
7
, 0.4,  5,  , 1.3, 2 34
3
3
Non-repeating, non-terminating decimals like  and
as fractions and are examples of irrational numbers.
2 cannot be written
Examples:
1. Sketch a number line and label three rational numbers between each pair
of given numbers.
a) 2.45 and -1.75
b) 
1
1
and 
2
4
2. Using a number line, order these fractions from least to greatest:
8 4 3 7 6 5
, ,1 , , ,
3 5 5 8 5 9
3. Sketch a number line and mark the following rational numbers on it:
2.15,
14
4
,  1.3, ,  2 53
3
7
Assignment: Pages 100-103, #1, 2, 3, 5, 7, 8, 9, 10, 11, 12 (a d f g), 13, 14(a
d f g), 15, 19
AFQ# 20, Reflect in journal
Challenge Questions # 22, 26, 27
3.2 Adding Rational Numbers
A. Investigate p. 106
B. Connect
Using a number line is one strategy to add/subtract fractions:
(“see it” video on DVD)
1.
2.
3.
4.
Find a common denominator; n.
Draw a number line divided into nths.
Label the number line.
Start at the first number and move the appropriate direction and
spaces for the second number.
a)
2 5
 
3 6
1
3
b)  3  2
5
6
Here is another strategy for adding/subtracting fractions:
1. Change mixed fractions to improper fractions, if necessary.
2. Find a common denominator.
3. Add/subtract the numerators and keep the denominators the same.
4. Reduce, if possible
a)
3  1
  
8  4
1
3
b)  3  2
3
4
You can also use a number line to add decimals:
a) 4.5 + 5.7
b) (- 4.5) + (-5.7)
c) 4.5 + (- 5.7)
d) - 4.5 + 5.7
Another way:
When adding two numbers that have the same sign, add the numbers and
keep the sign.
When adding two numbers that have different signs, subtract the numbers
and take the sign of the bigger number.
Do #15 from the assignment with the class using the literacy strategy “It
says, I say, And so”:
IT SAYS
I SAY
AND SO
On Tuesday, December
23rd, the lowest
temperature in Winnipeg
was -13.4 . By noon
the next day, the
temperature had
increased by 5.7 .
What was the
temperature at noon?
On Wednesday,
December 24th, the
lowest temperature was
3.7
less than the
lowest the previous day.
What was the lowest
temperature on
Wednesday?
(Section 3.2, p. 112, #15)
Assignment: Pages 111-113, #1- 11(within each question do every second
letter), 13, 14, 17
AFQ# 12, Reflect in journal
Challenge Questions: #20, 21
3.3 Subtracting Rational Numbers
A. Investigate p. 114
COMPANY
(price at the end of the day) – (price at the start of the day)
Bombardier
4.670 – 4.710 = -0.04
Canadian National
Railway
Canadian Tire
Corporation
Potash Corporation of
Saskatchewan
50.630 – 51.330 = -0.7
64.840 – 65.970 = -1.13
144.580 – 144.15 =
0.43
B. Connect
When subtracting numbers, you can use a number line OR change to
“adding the opposite” and then follow the rules for addition.
Using a number line: “see it” video on DVD.
1  1
1   
2  4
More Examples – Subtracting Fractions:
1.
4  1
  
5  4
2.
1
3
2 4
4
16
We can use a number line to visualize subtracting decimals:
a) 5.7 – 4.5
b) 4.5 – 5.7
c) - 4.5 – 5.7
e) 5.7 – (- 4.5)
Solving a problem by adding/subtracting rational numbers:
You have $145.67 in your bank account. You owe your brother $18.00. You
help you mom with the house cleaning and she gives you $7.50. How much
do you have now?
Assignment: Pages 118 - 120 #1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13
AFQ #10, Reflect in journal
Mid-Unit Review: page 121 # 1- 10 all
Game: p. 122 (need several decks of cards)
3.4 Multiplying Rational Numbers
A. Investigate p. 123
B. Connect
Rules for Multiplying:
When two rational numbers have the same sign, their product is positive.
(+)(+) = (+)
(-)(-) = (+)
When two rational numbers have opposite signs, their product is negative.
(+)(-) = (-)
(-)(+) = (-)
Examples – Multiplying Decimals (try estimating first)
1. (- 0.6)(- 1.8)
2. (- 1.34)(5.6)
3. The price of a share in the Royal Bank changed by -$1.54. A person owns
24 shares. By how much did the shares change in value that day?
Steps for multiplying fractions:
1. Predict the sign of the product
2. Change mixed numbers to improper fractions, if necessary.
3. Reduce the fractions, if possible.
4. Multiply the numerators.
5. Multiply the denominators.
6. Reduce the final answer, if possible.
Examples – Multiplying Fractions
1.
 8  14 
   
 7  20 
2.
 1  16 
 2   
 8  3 
Assignment: Pages 127-129 #1, 2, 5, 6, 7, 9, 10, 11, 12, 14
AFQ #13 and Reflect in journal
3.5 Dividing Rational Numbers
A. Investigate p. 130
B. Connect
Same sign rules for multiplying also apply for division.
One strategy for dividing fractions:
1. Change mixed numbers to improper fractions, if necessary.
2. Change division to multiply by the reciprocal.
3. Multiply the fractions using steps from 3.4
Another strategy:
1. Change mixed numbers to improper fractions, if necessary.
2. Find a common denominator
3. Divide the numerators and denominators; write the answer as a fraction
Examples – Dividing Fractions
 3   10 
1.      
 5  4 
2. 7
1  2
  1 
7  3
Examples – Dividing Decimals
1. 0.21  (0.7)
3.
2.  50   (0.25)
(3.08)  (0.4) (try estimating first)
Solving problems with rational numbers:
On a winter day the temperature drops 14.6°C in 4 hours. What is the mean
(average) change in temperature per hour?
Assignment: Page 134-136 #1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 14, 15
AFQ # 10, Reflect
3.6 Order of Operations with Rational Numbers
A. Investigate p. 137
B. Connect
The order of operations for rational numbers is the same as for integers:
BEDMAS!
Examples:
1.
4 1  3 1
   
5 3  10 2 
2.
4.7  2.4  1.5
3.2 1.2
Assignment: Pages 140-142, # 1 - 5, 7, 8, 9, 11, 12
AFQ #15, Reflect in journal
Study Guide: page 143
Unit Review: pages 144-145, # 1 – 20, 23