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Day 1 (Lesson 2.1 Part I) Comparing and Ordering Rational Numbers
Lesson Focus: We begin our unit learning about rational numbers and learn to reduce
fractions, compare and order fractions, express fractions with a common denominator and
convert fractions into decimal form.
What are Rational Numbers? They are numbers that can be expressed in the form
where
a and b are integers and b 0. (They can be written as fractions or decimals.)
Examples:
1 3 7
, ,5 ,9,4,0,6.25,0.3
2 4 8
Reducing Fractions: To reduce fractions, find the greatest common factor for the
numerator and denominator.
1.
4

10
2. 
6

 15
3. 
 24

 30
Compare & Order Fractions: We can compare rational numbers by expressing them all
as fractions with a common denominator or by expressing them as decimals.
a) To compare fractions, express each pair of fractions with the common denominator.
To find a common denominator, determine the Lowest Comon Multiple (LCM) of the
given denominators.
Ex: Which is greater (larger),
or
?
Step 1: The LCM of 6 and 9 is ________.
Step 2: Re-write
and
as:
Step 3: Compare the numerators.
Practice: Replace with > or <.
1.
12
8
2
4
2.
 84
144
5
12
3.
6
11
5
8
3. List from least to greatest using a common denominator: 
1 4 5 1
,
,
,
3 9 6 2
b) To convert fractions to decimals, divide the numerator by the denominator. (A
fraction is a division operation.)
Example:
1.
means
= 0.75
3

5
2.
14

5
c) To convert decimals to fractions, determine the value of denominator by looking at the \
place value of the decimal and put over the division bar.
1. 0.3 =
2.  .438 
3. 0.024 =
Day 2 (Lesson 2.1 Part II) Comparing & Ordering Rational Numbers
Review:
A. Comparing Fractions
A fraction can represent parts of a whole.
The shaded part of the diagram shows
Compare
3
8
and
2
6
4
8
or
1
2
or 0.5.
. Use denominators that are the same.
9
24

8
24
Examples
1. Give the fraction and decimal value
for the shaded part of the diagram.
, therefore
3
8

2
6
2. What is the opposite of the rational
Number?
a)
a)
3
8
b)  0.2 3
B. Compare the Following Fractions. Which is greater? Replace with > or <.
1.
4
5

7
8
2.
3
4
7
10
C. Arrange from least to greatest (by finding the LCM)
1.
3
2 1
,  ,
8
7
3
2.
 11  3  16
7
,
,
,
8
2
10
4
New Lesson Focus: Today, we will learn to compare rational numbers using a number
line and identify rational numbers between two given rational numbers.
A. Match each fraction with a letter on the number line.
4
1
____
5
2
5
____
4
4
____
5
____
a) Which letter is closest to zero? ____
b) Which fraction is closest to zero? ____
c) Which fraction is smallest? ____
d) Is
5
4
or
4
5
closer to 0? Explain. _____________________________
___________________________________________________________
B. Match each letter on the number line to one of the following rational numbers.
7
4
–
1
3
____
–0.3 ____
____
–2.1 ____
2
1
5
____
 0.49 ____
C. Identify the rational number (in decimal and fractional form) between two given
rational numbers.
1.
3
4
and
4
5
2.  0.4 and  0.5
D. Find as many integers as you can between 
11
7
and ?
3
2
E. Compare and order the following rational numbers.
 2.2 ,
To solve:
a) Express your numbers in the same form (decimal or fractional)
5
,
8

9
,
10
 0.3 ,
9
10
Day 3 (Lesson 2.2) Rational Numbers in Decminal Form
Lesson Focus: Today, we will expand our understanding of decimal numbers. We
will learn to estimate and calculate decimals and apply operations with rational
numbers in decimal form.
Why estimate?
Estimation can help you work with decimal numbers. For example, you can use
estimation to place the decimal point in the correct position in the answer.
16.94 + 3.41 + 81.07
Estimate: 17 + 3 + 80 = 100
Calculation: 101.42
Place the decimal so
that the answer is
close to 100.
1. Without calculating the answer, place the decimal point in the correct position
to make a true statement.
a) 149.8 ÷ 0.98 = 15285714
b) 2.7 × 100.9 = 272430
c) 40.6 × 9.61 = 39016600
d) 317 ÷ 99
= 32020202
2. a) Is 349 × 0.9 greater than, less than, or equal to 349? ______________
b) How do you know? ________________________________________
3. a) You know that 48 ÷ 16 = 3. Without finding the exact answer, tell whether
the answer to 48 ÷ 15 is greater than, less than, or equal to 3. __________
b) Explain how you know.
______________________________________
Estimate, then calculate (to the neareast thousandth, if necessary).
1. Adding and Subtracting Rational Numbers in Decimal Form
Estimate
Calculate
a) 0.56 + (–3.14) =
__________________
____________
b) –6.92 + (–8.02) =
__________________
____________
c) 7.82 – 5.37 =
__________________
____________
d) –2.75 – (–4.13) =
__________________
____________
e) 0.594 – (–0.085) =
__________________
____________
2. Multiplying and Dividing Rational Numbers in Decimal Form
Estimate
Calculate
a) –5.1 × (–9.3)=
__________________
____________
b) –1.68 ÷ (–1.4)=
__________________
____________
c) 35.7 ÷ (–4.2)=
__________________
____________
d) (2.7)(–4.2)=
__________________
____________
e) –8.83 ÷ (–0.33)=
__________________
____________
3. Calculate: Order of Operations
a) –6.2 + (–0.72) ÷ (–1.3 + 0.4)
c) –6.2 × (–4.2) – 1.02 ÷ 0.51
b) –2.2 × (–3.2) + (–0.88) × 2.3
Applying Operations with Rational Numbers in Decimal Form
For Questions 4 and 5,
a) write an expression using rational numbers to represent the problem, then calculate
b) write a sentence to answer the problem
4. Camille’s chequing account balance is$135.25. She writes a cheque for the amount
of $159.15. What is the balance in her account now?
5. The hottest day in Canada on record was on July 5, 1937, in Midale and
Yellowgrass, Saskatchewan, when the temperature peaked at 45 °C. The coldest
day in Canada was in Snag, Yukon, at –63 °C. What is the difference in
temperature between the hottest day and coldest day in Canada?
Day 4 (Lesson 2.3 Part I) Multiplying & Dividing Rational #s.
Lesson Focus: Today, we will learn to multiply and divide rational numbers.
Recall:
Multiplying Integers:
Rules:
1. +  + = _____
2. –  + = _____
3. +  – = _____
4. –  – = _____
Dividing Integers:
Rules:
1) +  + =
2) –  + =
3) +  – =
4) –  – =
_____
_____
_____
_____
 1 
4)  

2
 1
5)    
 2 
Recall as well:
1)
1

2
2)
1

2
3)
 1 
 

2
Muliplying Fractions: Simplying the following expressions. Ensure your answer
is in lowest term.
When simplifying rationals, it is best to
1. Reduce the fractions first before multiplying
2. Find positive pairs of two negatives
 2  6
1. a)    
 3   7 
2.
3  2
 
4  3
or
64
42
3.    
 96  60 
 2  6
4
b)     =
 3   7 
7
16
20  15 
4.     

 30  48   10 
Dividing Fractions: Simplying the following expressions. Ensure your answer is
in lowest term.
When dividing fractions, we
1. Multiply the reciprocalof the divisor.
2. Ensure that our fractions are in the improper form.
6
2
1.     
2.
1
3
4.  1    2 
 6    2   14 
5. 



 12   3 
2 
–
3
4
 2

 5
3.
  
1
6

5 

 12 
 
  25    21    25 
4
Working backward: Complete each statement. Show your work.
1)
–1
3
8

____ =
2
1
4
2) ____

2
3
 –3
1
2
Word Problem:
1. Mark has 24 newspapers to deliver. In one apartment building, he delivers
them. In the next apartment building, he delivers
How many papers does he have left to deliver?
2
3
3
8
of the remaining amount.
of
2. John created a painting on a large piece of paper with a length of
width of 1
3
4
m. Write an expression in the form
a
b
c
2
5
8
m and a
that represents the area
of the painting in lowest terms.
NOTE: In solving problems with fractions, the word OF means to multiply.
Day 5 (Lesson 2.3 Part II) Adding & Subtracting Rational #s.
Lesson Focus: Today, we will learn to add and subtract fractions.
To add and subtract fractions, we need to
1. Find the Lowest Common Denominator (LCD)
2. Find positive pairs of two negatives
3. When subtracting, add the positives (or tick, tick)
Recall: to find the LCD, use the L method.
1
5
3
 Example: Find LCD of        
3  6  4
Recall as well: we can find positive pairs when there are two negatives
1)
1

2
2)
 1 
 

2
 1 
3)  

2
 1
4)    
 2 
Simplify:
1)
4.
2 1

3 4
3
10
 2

 5
– –
2)
–
3
4

 12
3  1
3)    
4  5 
1
2
 11
5.        
 15   6 
2
3
6.  2  1
9

10
Working backward: Complete each statement. Show your work.
1. 1
1
2
– ____ =
5
2.
6
2
5
 ____ = 
3
10
1. One January day in Prince George, British Columbia, the temperature read 10.6ْ C at 9:00 a.m. and 2.4 C at 4:00 p.m.
a) What was the change in temperature?
b) What was the average rate of change in temperature?
2. The Rodriquez family has a monthly income of $6000. They budget
1
4
for rent,
expenses?
1
5
for clothing, and
1
10
1
3
for food,
for savings. How much money is left for other
Day 6 (Lesson 2.3 Part III) Order of Operations with
Rationals
Lesson Focus: Today, we will learn to simplify rationals using order of operations.
Recall:
When solving equations, the
following order must be taken:
In addition, follow these simple keep
these orders in mind:
1) B____________________
2) E____________________
2. Start inside and work outward.
3) D____________________
3. Go Left to Right
M____________________
4) A____________________
S____________________
Do the following examples:
 1   10 
  
 6  4 
1)   
5
8
3  2
1 
3)          =
 7   5   4 
  17  27   3   1 
2) 


    
5
5
2



  2 

Day 7 (Lesson 2.4) Determining Square Roots of Rational #s
Lesson Focus: Today, we will learn to find square roots of rational numbers.
Key Ideas
 If the side length of a square models a number, the area of
the square models the square of the number.

If the area of a square models a number, the side length
of the square models the square root of the number.
 A perfect square can be expressed as the product of two equal rational factors.
ex.
3.61 = 1.9 x 1.9
1 1 1
 
4 2 2
 The square root of a perfect square can be determined exactly.
ex.
2.56  1.6
4 2

9 3
 The square root of a non-perfect square determined using a calculator is an
approximation.
ex.
1.65  1.284523258
Example 1
Determine whether each of the following numbers is a perfect square. Show your work.
a)
121
64
b) 1.2
c) 0.9
d) 0.09
Example 2
Evaluate (round to the nearest thousandth where necessary). Show your work
a) 2.25
b) 0.34
c) 256
d)
3.61
e)
1225
f) 0.0484
Example 3
A square garden has a side length of 5.2 m. Calculate the area of the garden.
Example 4
The area of Mara’s square pumpkin patch is 2.25 m2. She has a square tomato
garden with the same area. She wants to determine the dimensions of each
garden. Maras solution is shown below.
A = s2
2A = s2
2(2.25) = s2
4.5 = s2
4.5 = s
2.12 = s
What error did Mara make in her solution? Correct her solution and determine the
dimensions of each garden.
Example 5
A square lot has an area of 0.5 ha. What are the lot’s dimensions to the nearest
metre? Show your work. Hint: 1 ha = 10 000 m2
Rational Numbers Homework Assignments
Day 1:
Day 2:
Day 3:
Day 4:
Day 5:
Day 6:
Day 7:
Day 8:
Day 9:
Text page 51 # 4-6, 8-13, 19, 22, 25, 27 (2.1 Part I)
Text page 51 # 7, 14-16 (odd letters), 21a, 24, 29 (2.1 Part II)
Text page 60 # 4-9 (odd), 10-12, 14, 18, 19, 22, 27 (2.2)
Text page 68 # 7-10, 13, 16, 18 (2.3 Part I)
Text page 68 # 1, 5, 6, 12, 15, 19 (a, b) (2.3 Part II)
Text page 69 # 14, 17, 21, 23, 26 (2.3 Part III)
Text page 78 # 1, 2, 7-14(odd), 15, 18, 25 (2.4)
Review lesson
Unit Test