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Principles of Mathematics 9
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iii
NEL
Table of Contents
Chapter 1: Rational Numbers 3 3.2 Exploring Linear Relations 150
3.3 Investigating Properties of Linear Relations 152
Getting Started 4
Mid-Chapter Review 160
1.1 Addition and Subtraction of Mixed Numbers 8
Curious Math 19 3.4 Equivalent Linear Relations 164
Curious Math 172
1.2 Multiplication and Division of Mixed
Numbers 20 3.5 Linear and Nonlinear Relations 173
1.3 Integer Operations with Powers 31 Chapter Review 182
Mid-Chapter Review 37 Chapter Self-Test 185
1.4 Rational Numbers 41 Chapter Task 186
1.5 Rational Number Operations 48
1.6 Powers of Rational Numbers 57 Chapters 1–3Cumulative Review 187
Chapter Review 65
Chapter 4: Linear Equations 191
Chapter Self-Test 68
Chapter Task 69 Getting Started 192
4.1 Interpreting the Solution of a Linear
Equation 196
Chapter 2: Powers and Polynomials 71
4.2 Solving Linear Equations Using Inverse
Getting Started 72 Operations 205
2.1 Representing Powers Up to Degree 3 76 4.3 Equation-Solving Strategies 213
2.2 Multiplying and Dividing Powers 83 Mid-Chapter Review 224
2.3 Power of a Power 92 Curious Math 229
Curious Math 99 4.4 Solving for a Variable in a Linear Relation 230
Mid-Chapter Review 100 4.5 Solving a Linear System Graphically 239
2.4 Adding and Subtracting Polynomials 102 Chapter Review 248
2.5 Multiplying a Polynomial by a Monomial 113 Chapter Self-Test 252
2.6 Simplifying Polynomial Expressions 119 Chapter Task 253
Chapter Review 128
Chapter Self-Test 133 Chapter 5: Analytic Geometry 255
Chapter Task 135
Getting Started 256
5.1 Exploring the Equation of a Line 260
Chapter 3: Linear Relations 137
5.2 Different Forms of the Equation of a Line 264
Getting Started 138 5.3 Slope of a Line 272
3.1 Relations 142 Mid-Chapter Review 281
iv Table of Contents NEL
5.4 Using Points to Determine the Equation 7.5 Reasoning About Properties of Polygons 410
of a Line 285
Chapter Review 416
5.5 Parallel and Perpendicular Lines 295
Chapter Self-Test 420
Curious Math 306
Chapter Task 421
Chapter Review 307
Chapter Self-Test 311
Chapter 8: Measurement 423
Chapter Task 313
Getting Started 424
Chapter 6: Investigating 8.1 Determining Optimum Area and
Perimeter 428
Relationships 315
8.2 Problems Involving Composite Shapes 434
Getting Started 316 8.3 The Pythagorean Theorem 442
6.1 Interpreting Data 322 8.4 Surface Area of Right Pyramids and Cones 448
6.2 Lines of Best Fit 330 Mid-Chapter Review 458
Curious Math 340
8.5 Volumes of Pyramids and Cones 461
Mid-Chapter Review 341 8.6 Volume and Surface Area of a Sphere 466
6.3 Curves of Best Fit 344 Curious Math 473
6.4 Reasoning About Data 354 8.7 Exploring Optimum Volume and
6.5 Describing Situations From Graphs 363 Surface Area 474
Chapter Review 373 8.8 Optimum Volume and Surface Area 476
Chapter Self-Test 376 Chapter Review 482
Chapter Task 378 Chapter Self-Test 486
Chapter Task 487
Chapters 4–6Cumulative Review 379
Chapters 7–8 Cumulative Review 488
Chapter 7: Properties of 2-D Figures 383
Appendix A:
Getting Started 384 REVIEWOFESSENTIALSKILLSANDKNOWLEDGE 491
7.1 Exploring Interior Angles of Polygons 388
Appendix B:
7.2 Angle Properties of Polygons 391 REVIEWOFTECHNICALSKILLS 516
Mid-Chapter Review 397
Glossary 542
7.3 Exploring Quadrilateral Diagonal
Answers 549
Properties 399
7.4 Reasoning About Triangle and Index 616
Quadrilateral Properties 402 Credits 620
Curious Math 409
NEL Table of Contents v
2
NEL
Chapter
1
Rational
Numbers
GOALS
You will be able to
•
Relate rational numbers to decimals,
fractions, and integers
•
Evaluate expressions involving rational
numbers
? What might the negative values
in the photo represent?
3
NEL
1
Getting Started
WORDS YOU NEED to Know
1. Match each term with the example that most closely represents it.
a) opposite integers d) lowest common denominator g) power
b) numerator e) mixed number h) base of a power
c) denominator f) improper fraction i) exponent
34 2 10
# " !
i) iv) 5 and 5 vii)
9 3 15
1 3
!
5 15
2
ii) 1 v) 73 viii)73
3
5 5
iii) 73 vi) ix)
7 7
SKILLS AND CONCEPTS You Need
Aid
Study
• For more help and practice, Addition of Fractions
see Appendix A-6 and A-7.
You can add two fractions using fraction strips, number lines, or by using a
common denominator.
EXAMPLE
1 2 Solution: fraction strips
#
3 5
Solution: common denominator
$ $
1 5 2 3
! #
$ $
3 5 5 3
5 6 Solution: number line
! #
1 ! 5 2 ! 6
15 15 3 15 5 15
11
!
15 11
0 15 1
2. Determine each sum.
1 1 3 3
# #
a) c)
2 3 10 5
3 1 2 2
# #
b) d)
4 8 5 3
4
Chapter 1 NEL
Getting Started
Subtraction of Fractions
You can subtract two fractions using fraction strips, number lines, or by
using a common denominator.
EXAMPLE
2 1 Solution: fraction strips
"
3 5 2 !10
3 15
Solution: common denominator 1 ! 3
5 15
$ $
! 2 5 " 1 3 10 3 ! 7
15 15 15
$ $
3 5 5 3
10 3 Solution: number line
! "
3 10
15 15
15 15
7
!
15
0 7 1
15
3. Determine each difference.
1 1 3 1 3 3 6 1
" " " "
a) b) c) d)
2 3 4 8 5 10 7 2
Multiplication of Fractions
You can use an area model to help you visualize the product of two fractions.
EXAMPLE
5 2 Solution: area model
$
8 3 5
8
Solution: multiplying 2
3
$
5 2
!
$
8 3
10
!
24
5
!
12
4. Determine each product.
1 1 2 3
$ $
a) c)
2 4 5 10
2 3 1 4
$ $
b) d)
3 4 6 5
5
NEL Rational Numbers
