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NAME: _________________________________
DATE: __________________________
MILLER COMPREHENSIVE HIGHSCHOOL MATHEMATICS DEPARTMENT
MATHEMATICS 9
CHAPTER 2
RATIONAL NUMBERS
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 1
Day 1 (Lesson 2.1 Part I) Comparing and Ordering Rational Numbers
INTRODUCTION: Rational Numbers are numbers that can be expressed in the form
____ where a & b are integers and b 0. (They can be written as ________ or ________.)
Examples: 3.0,25.6,0,4,9,8
75,
4
3,
2
1
LESSON FOCUS: In this lesson, we will learn to reduce, compare and order rational
numbers, and express them in fractional form with a common denominator or decimal form.
Reducing Fractions: We begin by learning to reduce fractions. To reduce fractions, find
the ______________________________ for the numerator and denominator.
1. 10
4 2.
15
6 3.
30
24
Compare & Order Fractions: We can compare rational numbers by expressing them all
as ______________ with a common denominator or by expressing them as_____________.
A) To compare fractions, express each pair of fractions with the common denominator.
To find a common denominator, determine the ________________________________
(LCM) of the given denominators.
Ex: Which is greater → 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. 4
2
8
12 2.
12
5
144
84
3.
8
5
11
6
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 2
4. List from least to greatest using a common denominator: 2
1,
6
5,
9
4,
3
1
Note: Careful with negative numbers.
B) To convert fractions to decimals, divide the ______________ by the _____________.
Note: A fraction is essentially a _______________ operation.
Example: means = 0.75
1. 5
3 2.
5
14
C) To convert decimals to fractions, write the number as you would read it.
ex. 0.05 is read as 5 ____________. Therefore, put 5 over ________, and reduce to
lowest term.
1. 0.3 = 2. 48. 3. 0.024 =
Day 2 (Lesson 2.1 Part II) Comparing & Ordering Rational Numbers
REVIEW: We begin our lesson by reviewing what we learned yesterday.
A. Comparing Fractions
A fraction can represent __________ of a whole.
The shaded part of the diagram shows 4
8 or
1
2 or 0.5.
Ex. Compare 3
8and
2
6. Use denominators that are the same.
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 3
Examples
1. Give the fraction and decimal value 2. What is the opposite of the following l
for the shaded part of the diagram. rational numbers?
a) a) 8
3
b) 32.0
B. Compare the Following Fractions. Which is greater? Replace with > or <.
1. 8
7
5
4
2.
10
7
4
3
C. Arrange from least to greatest (by finding the LCM)
1. 2
1,
7
2,
8
3 2.
4
7,
10
16,
2
3,
8
11
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 below with a letter on the number line.
4
5 ____
1
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. _____________________________
___________________________________________________________
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 4
B. Match each letter on the number line to one of the rational numbers below.
7
4 ____ –0.3 ____
12
5 ____
1
–3
____ –2.1 ____ 0.49 ____
C. Identify the rational number (in decimal and fractional form) between two given
rational numbers.
To do this, we can express the rationals as fractions and determine
________________________.
1. 4
3 and
5
4 2. 4.0 and 5.0
D. Find as many integers as you can between 2
7 and
3
11?
E. Compare and order the following rational numbers. 2.2 , 8
5,
10
9 , 3.0 ,
10
9
To solve:
a) Express your numbers in the same form (decimal or fractional)
b) Place the numbers on a number line
c) Arrange the numbers in ascending order.
1 0 2 - 1 -2
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 5
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 _____________ in the answer.
16.94 + 3.41 + 81.07
Estimate:
Calculation:
1. Without calculating the answer, place the decimal point in the correct position
to make a true statement for each.
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. ______________________________________
Place the decimal so
that the answer is close to 100.
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 6
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) –2.75 – (–4.13) = __________________ ____________
2. Multiplying and Dividing Rational Numbers in Decimal Form
Estimate Calculate
a) –5.1 × (–9.3)= __________________ ____________
b) –1.68 ÷ (–1.4)= __________________ ____________
c) (2.7)(–4.2)= __________________ ____________
3. Calculate: Remember to apply order of operations
a) –6.2 + (–0.72) ÷ (–1.3 + 0.4) 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?
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 7
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: Dividing Integers:
Rules: Rules:
1. + + = _____ 1) + + = _____
2. – + = _____ 2) – + = _____
3. + – = _____ 3) + – = _____
4. – – = _____ 4) – – = _____
Recall as well:
Muliplying Fractions: Simply the following expressions. Ensure your answer is
in lowest term.
When simplifying rationals, it is best to
1. ___________ the fractions first before multiplying
2. Find _____________ pairs of two negatives
1.
7
6
3
2 2.
3
2
4
3
3.
10
15
48
20
30
16
1)
2
1 2)
2
1 3)
2
1 4)
2
1 5)
2
1
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 8
Dividing Fractions: Simply the following expressions. Ensure your answer is in
lowest term.
When dividing fractions, we
1. Multiply the _______________ of the divisor.
2. Ensure that our fractions are in the _____________ form before simplifying.
1.
3
2
12
6 2.
3 2–
4 5
3.
4
32
2
11 4.
25
14
21
2
25
6
Word Problem:
NOTE: In solving problems with fractions, the word ________ means to
multiply.
1. Mark has 24 newspapers to deliver. In one apartment building, he delivers 3
8 of
them. In the next apartment building, he delivers 2
3 of the remaining amount.
How many papers does he have left to deliver?
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 9
2. John created a painting on a large piece of paper with a length of 5
28
m and a
width of 3
14
m. Write an expression in the form bac
that represents the area
of the painting in lowest terms.
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 _______________ Common Denominator (LCD)
2. Find _____________ pairs of two negatives
3. When subtracting, add the positives (or _________, _________)
Note: When adding or subtracting:
1. you can only tick, tick two negatives that are _________ each other.
2. always move the negatives to the top.
3. always convert mixed fraction to the _____________ form first.
Simplify:
1) 4
1
3
2 2)
5
1
4
3
3.
6
11
15
12 4.
10
91
3
22
1)
2
1 2)
2
1 3)
2
1 4)
2
1
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 10
Word Problem:
1. One January day in Prince George, British Columbia, the temperature read -
10.6 ْ 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
3 for food,
1
4 for rent, 1
5 for clothing, and 1
10 for savings. How much money is left for other
expenses?
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:
1) B____________________
2) E____________________
3) D____________________
M____________________
4) A____________________
S____________________
In addition, follow these simple keep
these orders in mind:
2. Start inside and work outward.
3. Go Left to Right
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 11
Do the following examples:
1)
4
10
6
1
8
5 2)
2
1
2
3
5
27
5
17
3)
4
1
5
2
7
3= 4.
2
6
32
9
4
3
2
1
3
2
Working backward: Complete each statement. Show your work.
1) 3
–18
____ = 1
24
2) ____ 2 1
–33 2
3. 11 –
2 ____ =
5
6 4.
2
5____ =
3
10
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 12
Day 7 Part I - Perfect Squares and Square Roots
What is a square of a number? A number times ____________ (ex. the product x x )
Examples:
1. 1.11.1 2. 44
3. 8.8. 4. 3.13.1
What is a square root of number? The square root of a number x is the number that
when multiplied by itself gives the number x (ex. 55525 ).
Examples: Find the square root of:
1. 16 2. 64.0 3. 69.1
The radical sign, _______, is used to represent the _______________ square root of a number.
The positive square root is also called the principal square root.
Examples:
1. 9 2. 16 3. 25 4. 100
Note: 9 _________ and 9 _______________
16 _________ and 16 _______________
How do we find square roots of large numbers?
We use ____________________________
Examples:
1. 625 = 2. 225 =
3. 4225 = 4. 60 =
What about decimal roots?
If 64 = _______
Then 64. _______
What about 4 _______
And 4.0 _______
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 13
Try
1. 0081.0 3. 000001.0
2. 000169.0 4. 000324.0
Part II – Evaluating Square Roots
Simplify the following eexpressions:
1. 416 2. 01.016
3. 254 4. 94645
5. 645
10012
Evaluate the following if a = 5 and b = -4
1. ))((20 ba 2. 22 ba
3. aba 2321 2
Note: 2.02.0 does ______ = .4.
ex 1. 04.0 _______ 2. 0121.0 _______
Note also that each pair of numbers results in one decimal point.
ex1. 0004.0 _______ 2. 00000121.0 _______
Miller High School Mathematics (Mathlinks 9 Chapter 2) Page 14
Day 8 (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 ___________ of the number.
If the area of a square models a number, the side length
of the square models the ____________ of the number.
A perfect square can be expressed as the product of ________ equal rational factors.
ex. 61.3 4
1
The square root of a perfect square can be determined _____________.
ex. 56.2 9
4
The square root of a non-perfect square determined using a calculator is an
__________________.
ex. 65.1
Example 1
Determine whether each of the following numbers is a perfect square. Show your work.
a) 64
121 b) 1.2
c) 0.9 d) 0.09
Example 2
Evaluate (round to the nearest thousandth where necessary).
a) 25.2 b) 34.0 c) 256
d) 3.61 e) 1225 f) 0.0484
Page 15
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. Maras
solution is shown below.
A = s2
2A = s2
2(2.25) = s2
4.5 = s2
4.5 = s
2.12 = s
Example 5
Sean’s kitchen measures 4.3 m by 3.2 m. He wants to cover the floor with square tiles.
The side dimension of each square tile is 10.5 cm. How many tiles will he need to
cover the floor?
Example 6
Sarah wants to put a string across her paper with the dimensions of 30 cm by 45 cm.
What is the length of the string she needs. (Round to the nearest cm).
What error did Mara make in her solution? Correct her
solution and determine the dimensions of each garden.
___________________________________________________
Page 16
STUDENT PRACTICE SECTION
~Chapter 2 Day 1 Lesson 2.1~
Comparing and Ordering Rational Numbers
1. Reduce to the lowest terms.
a) 10
5
b)
30
12
c)
11
6 d)
14
4
e)
35
15
f)
28
42
2. Compare each pair of fractions. Replace the comma with > or <.
a) 3
2,
6
8 b)
5
12,
5
7 c)
11
9,
121
110 d)
4
11,
16
52
3. Reduce each set of fractions to lowest terms. Then list them from greatest to least.
a) 20
15,
12
33,
8
30,
16
28 b)
36
40,
63
91,
54
120,
18
34
4. In each set, express the fractions with a common denominator. Then list them from
least to greatest.
a) 3
4,
4
5,
5
6,
2
3 b)
4
7,
10
16,
2
3,
8
11
5. List these fractions from least to greatest.
9
18,
8
10,.
6
9,
16
12,
20
5,
28
7,
2
3,
10
5
6. List these fractions from greatest to least.
36
13,
18
7,
9
2,
4
1,
3
1,
8
3
7. Write in decimal form.
a) 5
3 b)
9
4 c)
21
7 d)
7
15 e)
16
5 f)
12
11
8. Express in fractional form.
a) 0.75 b) -0.625 c) -2.75 d) 16.4
9. Compare each pair of fractions. Replace the comma with > or <.
a) 4
25,4.6 b) 5.3,
7
27 c)
11
5,
8
3 d) 5.0,
100
57
10. Arrange these fractions from greatest to least.
15
13,
13
10,
11
9,
8
5,
7
6
~Chapter 2 Day 4 Lesson 2.3~
Multiplying and Dividing Fractions
1. a) 5
8
2
1 b)
7
6
3
2 c)
3
2
4
1 d)
21
1
8
3
Page 17
e)
45
2
2
15 f)
5
36
12
5 g)
5
6
3
7 h)
4
9
3
8
2. a) 2
1
8
1 b)
9
4
10
7 c)
4
3
8
5 d)
15
8
5
1
e)
3
4
2
8 f)
4
5
3
10
g)
2
5
4
5 h)
7
5
3
2
i)
12
7
6
11
3. a)
9
21
7
18 b)
7
9
28
3
c)
35
18
5
36
d)
13
64
39
4 e)
16
6
48
9 f)
11
2
55
15
g)
49
12
7
72 h)
4
15
3
75 i)
22
7
4
33
4. a)
14
3
32
21
9
4 b)
28
45
20
8
27
10
c)
25
14
21
2
25
6
d)
5
18
9
10
39
12
e)
16
9
5
4
32
15 f)
25
14
15
8
28
12
g) 3
8
3
10
2
5
h)
5
6
5
8
4
15
i) 3
4
6
14
9
35
3
20
~Chapter 2 Day 5 Lesson 2.3~
Adding and Subtracting Fractions
1. a) 3
2
4
3 b)
5
2
7
5 c)
6
5
8
3 d)
8
3
12
5
e) 6
5
9
2
f)
3
2
5
4 g)
5
2
4
3 h)
4
5
8
3
2. a) 1.37.1 b) 9.58.2 c) 1.26.3
d) 9.87.1 e) 3.96.7 f) 8.114.6
g) 8.97.8 h) 9.236.15 i) 7.413.36
3. a)
4
1
3
2 b)
2
3
6
5
c)
4
3
8
3
d)
6
1
8
5
e) 10
3
3
2
f)
8
5
4
3 g)
3
7
4
9 h)
3
13
6
20
4. a) 4
21
3
7 b)
3
8
8
47 c)
5
49
2
13 d)
4
35
5
17
e) 5
12
3
14 f)
5
9
7
9 g)
6
11
5
13 h)
7
47
3
43
Page 18
5. a) -2.387 + 4.923 b) 33.78 – (-64.35) c) 204.9 – 256.1
d) -0.405 – 18.924 e) -12.37 + 8.88 f) -45.8 – (-327.6)
g) 4.29 + 563.08 h) 84.91 – 37.08 i) -0.046 + (-0.104)
6. a)
3
7
10
7 b)
6
13
4
15
c)
7
3
8
13
d)
4
13
2
25 e)
3
4
4
11 f)
3
22
9
20
g)
18
11
6
11 h)
7
3
5
14 i)
3
16
11
3
~Chapter 2 Day 6 Lesson 2.3~
Order of Operations with Fractions
1. a)
6
5
4
1
3
2 b)
4
3
8
3
2
3
c)
3
2
6
1
8
5
d)
8
5
4
3
10
3
e) 6
29
3
17
4
9 f)
2
1
10
7
5
3
g)
6
5
3
4
2
7 h)
6
7
3
2
9
5
i)
3
4
4
7
3
2
2
13
2. a)
14
3
32
21
9
4 b)
28
45
20
8
27
10
c)
25
14
21
2
25
6 d)
5
18
9
10
39
12
e)
16
9
5
4
32
15 f)
25
14
15
8
28
12
g) 3
8
3
10
2
5
h)
5
6
5
8
4
15
i) 3
4
6
14
9
35
3
20
j)
7
2
2
3
77
6
3
22
3. a) 6.174.07.3 b) 11.809.238.0
c) 46.3807.1868.54 d) 0.609.273.25
4. a) 4.107.236.14 b) 9.12.2958.12
c) 5.126.140.145 d) 9.02.2952.966
e) 31.095.001767.0 f) 5.003.108.0
5. a)
4
7
8
3
5
4 b)
3
7
2
7
7
3
c)
7
16
4
3
7
6
Page 19
d)
11
6
5
27
5
18
e) 5
9
6
7
9
5
f)
3
4
8
3
9
4
6. a) 6
5
4
3
3
2
6
5
b)
3
5
6
5
3
2
5
3
c)
2
5
3
1
5
1
4
3
d) 4
1
8
3
4
3
16
3
e)
2
1
4
3
3
2
5
3 f)
3
5
8
314
12
7
~Chapter 2 Day 7 Lesson 2.4~
Part I – Perfect Squares and Square Roots
Evaluate : indicate the imperfect roots with “IR”
1. a) 64 b) 64.0 c) 225 d) 0225.0 e) 100
f) 00001.0 g) 441 h) 625 i) 069.0 j) 000144.0
k) 139 l) 44 m) 2025 n) 0121.0 o) 206
p) 00000009.0 q) 000081.0 r) 576 s) 009.0
t) 289 u) 00000289.0 v) 31 w) 729 x) 2304
2. a) 964 b) 09.064.0 c) 16169
d) 0004.00001.0 e) 9
225
f) 0004.00016.0
g) 4392 h) 45
254
i) 144516910
Part II – Evaluating Square Roots
1. Evaluate.
a) 49 b) 04.0 c) 1600 d) 169 e) 3600
f) 44.1 g) 225 h) 1210 i) 625 j) 42
2. Simplify.
a) 3664 b) 916 c) 43162
d) 252363 e) 361005 f) 97531
g) 497812 h) 2252894 i) 812
3.) Evaluate each expression for a = 5 and b = -3.
a) a20 b) 29a c)
a
125
Page 20
d) ba 132 e) b12 f) 133 ba
g) ba 32 h) 587 ba i) ba 3114
j) 2423 22 ba k) 22 25.0 baba l) 2322 22 ba
4.) Evaluate each expression for x = 3, y = -4, and z = -7.
a) x12 b) yz 62 c) 224 yx
d) zx 6 e) yx 155 f) 147 yx
g) zyx 222 h) xyz 52 2 i) 0236 xy
j) )242( zyx k) 22 2 zxx l) 22 23 zyx
~Chapter 2 Day 9 Review~
Fractions (Days 1, 4, 5, 6)
1. a) 8
7
3
2 b)
12
9
8
5 c)
39
30
15
13 d)
36
25
15
12
5
6
2. a)
14
9
7
3 b)
4
9
8
7 c)
12
9
12
5
5
3
3. a) 7
4
5
3 b)
8
3
12
5 c)
24
7
24
13 d)
9
4
3
2
4. a) 6
1
9
7 b)
10
3
6
5 c)
20
12
20
17 d)
4
1
8
7
5. a)
4
1
6
5
3
2 b)
3
2
5
2
4
5
6. a) 4
5
3
11
2
5 b) 2
4
3
4
3
7. a)
3
1
6
5
2
1
4
3 b)
4
3
5
3
6
5
2
1
3
2
8
3
Page 21
Chapter 2 Answer Key
Chapter 2 Day 1 Lesson 2.1 (Equivalent Fractions)
1. a) 2
1 b)
5
2 c)
11
6 d)
7
2 e)
7
3 f)
2
3
2. a) b) c) d)
3. a) 4
3,
4
7,
4
11,
4
15 b)
9
20,
9
13,
9
10,
9
17
4. a) 2
3,
3
4,
4
5,
5
6 b)
8
11,
2
3,
10
16,
4
7
5. 6
9,
28
7,
20
5,
10
5,
16
12,
8
10,
2
3,
9
18
6. 18
7
9
2,
4
1,
3
1,
8
3,
36
13
7. a) 0.6 b) 4.0 c) 3.0 d) 142857.2 e)0.3125 f) 691.0
8. a) 4
3 b)
8
5 c)
4
11 d)
5
82
9. a) 4
254.6 b) 5.3
7
23 c)
11
5
8
3 d) 5.0
100
57
10. 8
5,
13
10,
11
9,
7
6,
15
13
Chapter 2 Day 4 Lesson 2.3 (Multiplying and Dividing Fractions)
1. a) 5
4 b)
7
4 c)
6
1 d)
56
1 e)
3
1
f) 3 g) 5
14 h) 6
2. a) 4
1 b)
40
63 c)
6
5 d)
8
3 e) 3
f) 3
8 g)
2
1 h)
15
14 i)
7
22
3. a) 6 b) 12
1 c)
175
648 d)
48
1 e)
128
9
f) 121
6 g) 42 h)
3
20 i)
8
21
4. a) 16
1 b)
21
5 c)
2
9 d)
13
1 e)
3
2
f) 20
9 g) 2 h) 5 i) 3
Chapter 2 Day 5 Lesson 2.3 (Adding and Subtracting Fractions)
1. a) 12
17 b)
35
11 c) -
24
11 d) -
24
19 e)
18
11
f) -15
22 g) -
20
7 h)
8
13
2. a) 8.4 b) 1.3 c) 5.1 d) 2.7 e) 9.16
Page 22
f) 5.4 g) 1.1 h) 8.3 i) 4.5
3. a) 12
11 b)
3
7 c)
8
9 d)
24
11 e)
30
11
f) 8
11 g)
12
1 h) 1
4. a) 12
91 b)
24
77 c)
10
33 d)
20
107 e)
15
34
f) 35
18 g)
30
23 h)
21
442
5. a) 2.536 b) 98.13 c) 2.51 d) 329.19 e) 49.3
f) 8.281 g) 567.37 h) 47.83 i) 15.0
6. a) 30
49 b)
12
71 c)
56
67 d)
4
63 e)
12
49
f) 9
86 g)
9
11 h)
35
113 i)
33
167
Chapter 2 Day 6 Lesson 2.3 (Order of Operations with Fractions)
1. a) 12
1 b)
8
9 c)
24
5 d)
40
17 e)
12
37
f) 5
9 g)
3
4 h)
18
19 i)
4
11
2. a) 16
1 b)
21
5 c)
2
9 d)
13
1 e)
3
2
f) 20
9 g) 2 h) 5 i) 3 j) 3
3. a) 5.13 b) 4.6 c) 85.1 d) 62.6
4. a) 3598.608 b) 3.1 c) 169.36 d) 79.29 e) 06.0 f) 0412.0
5. a) 10
11 b)
98
129 c)
7
18 d)
33
4 e)
10
31 f)
123
32
6. a) 20
3 b)
10
9 c)
12
35 d)
32
27 e)
5
2 f)
3
2
Chapter 2 Day 7
Part I Perfect Squares and Square Roots
1.a) 8 b) 0.8 c) 15 d) 0.15 e) 10 f) IR g) 21 h) 25 i) IR j) 0.012 k) IR l) IR
m) 45 n) 0.11 o) IR p) 0.0003 q) 0.009 r) 24 s) IR t) 17 u) 0.0017 v) IR
w) 27 x) 48
2a) 11 b) 1.1 c) 9 d) 0.02 e) 5 f) 0.02 g) 12 h) 2 i) 70
Part II EvaluatingSquare Roots
1. a) 7 b) -0.2 c) 40 d) 13 e) -60 f) 1.2 g) -15 h) 610 i) 25 j) -4
2. a) 10 b) 7 c) 2 d) 28 e) 40 f) 5 g) -31 h) 32 i) 6
3. a) 10 b) 15 c) 5 d) 7 e) 6 f) -5 g) 4 h) 8 i) -32 j) -12 k) 4 l) 10
4. a) -6 b) 5 c) 20 d) 5 e) 35 f) -6 g) 10 h) -9 i) 42 j) 6 k) 8 l) -11
Page 23
Chapter 2 Day 9 Fractions Review (Days 1, 4, 5, 6)
1. a) 12
7 b)
32
15 c)
3
2 d)
3
2
2. a) 3
2 b)
8
7 c)
25
48
3. a) 35
41 b)
24
19 c)
6
5 d)
9
10
4. a) 18
17 b)
15
8 c)
4
1 d)
8
5
5. a) 20
11 b)
6
7
6. a) 12
1 b) 0
7. a) 72
47 b)
60
13
Chapter 2 Assignments:
DAY SECTION ASSINMENT
1 2.1 (Part I) Booklet Day 1 Pg. 16 #1-10 (all)
2 2.1 (Part II) Text Pg. 51 – 54 #4,5,7(all), 8,9,13 – 17 (o.l.), 21, 22 (o.l), 25, 26 – 30 (o.l) omit 27
3 2.2 Text Pg. 60 – 62 #4 – 9 (o.l.), 10, 13, 16, 17. 19, 22, 24 (o.l), 29 (o.l.)
4 2.3 (Part I) Booklet Day 4 Pg. 16-17 #1 – 4 (o.l.); Text Pg. 68 – 70 #7 & 8(all.), 9,10, 13, 16, 18,
5 2.3 (Part II) Booklet Day 5 Pg. 17-18 #1 – 6 (o.l.), Text Pg. 68 – 70 #5 & 6 (all), 12,14,
6 2.3 (Part III) Booklet Day 6 Pg. 18-19 #1 – 4 (o.l), 5 & 6 (all), Text Pg. 70 #15, 19, 21 (all), 26
7 2.4 (Part I) Booklet Day 7 Pg. 19-20 Part I #1-2 (o.l), Part II #1-4 (o.l)
8 2.4 (Part II) Text Pg. 78 – 81 # 1, 2, 7 – 14 (o.l), 15, 16, 18, 20, 22 – 30, 36
9 Review/ Quiz Booklet Day 9 Pg. 20#1- 7 (all), Text Pg. 84 & 85 # 1 – 20 (all)
Answer Key:
1. A 2. D 3. C 4. B 5. D 6. B 7. C 8. 4.8 9. Left
10. Example: Any integer can be written as a quotient of two integers by making
the integer the dividend and the number 1 the divisor
11. , 0.94 , 12.
13. a) b) -1.37 c) d) e) f)
14. 9.89 s 15. 0. Exmaple: [1.2 + (-1.2)] ÷ 2 = 0
16. Yes. Example: Both 3136 and 100 are perfect squares.
17. a) 37.21 b) 0.37 c) 2.65 18. a) 62.5 cm² b) 43.8 cm
19. $19.11 Assume that all shares are the same price
20. a) 1. Example: The sum must be 1 because no other elements make up a quarter’s
content. b) 1 c) 15.6 times as great d)2.816 g greater
10 Test Date: ________________________________