Chapter 1
Words to Know
 numerical expression
 average, mean
 variable
 polygon
 variable expression
 perimeter
 power
 exponent
 base
 decimal
 number line
Overview
1.1 Problem Solving &
Reasoning
1.2 Expressions & Variables
1.3 Order of Operations
1.4 Powers & Exponents
1.5 Comparing & Ordering
Decimals
1.6 Rounding Decimals
1.7 Adding & Subtracting
Decimals
1.8 Multiplying Decimals
1.9 Dividing Decimals
2.8 Connecting Decimals to
Fractions
1.1
Problem Solving Plan
1) Understand the problem – read the problem carefully.
Identify the question
2) Make a plan – decide on a problem solving strategy
3) Solve the problem – use the problem solving strategy to
answer the question.
4) Look back – Check that your answer is reasonable
Identifying Irrelevant Information
 Relevant information – information you need to know to
solve a problem
 Irrelevant information – information you do not need to
know to solve a problem
1.2
Evaluate the Expression
Find the value of the expression
Or
solve the problem
Four Mathematical Operations
Plus
Addition
3+4=7
Multiplication
Sum
Times
6 x 7 = 42
Terms
Subtraction
21 – 12 = 9
Minus
Difference
Factors
Product
Division
Divided By
Quotient
15 ÷ 5 = 3
Dividend
Divisor
A Letter in the Expression?
 Letters are used to represent variables
 Using variables and variable expressions to describe
relationships between quantities is the focus of algebra
Practice
Write a variable expression given by the phrase:
The sum of a and b is 71
n times m is 42
The product of x and y is 28
y minus z is 5
The quotient of d and r is 9
Practice
Evaluate the Expression:
k + 12
x – 36
9j
36 ÷ m
d/r
xyz
when k = 9
when x = 42
when j = 11
when m = 4
when d = 120 and r = 60
when x = 5, y = 6 and z = 9
1.3
Order of Operations
Please Excuse My Dear Aunt Sally
1. Parentheses or Brackets
2. Exponents or powers or roots
3. Multiply and divide (left to right)
4. Add and subtract (left to right)
Commutative Property
 In a sum, you can add terms in any order
a+b=b+a
 In a product, you can multiply factors in any order
 ab = ba
Associative Property
 The value of a sum does not depend on how the terms
are grouped.
 (a + b) + c = a + (b + c)
 The value of a product does not depend on how the
factors are grouped.
 (ab)c = a(bc)
Practice
Evaluate the Expression:
10 – 2 x 3
12 ÷ 3 x 2
6 – 3 + 10 x 5
14 ÷ (5 + 2) x 3
Where would the parentheses need to be to make this
statement true?
7–2+3=2
1.4
Using Exponents to Write Powers
The power am is a product of the form:
am = a x a x a x a x a…
The exponent (m) indicates the number of times the factor
(a)is repeated.
Practice
Evaluate the Expression:
x5
2x3
5x
136
87
510
when x = 2
when x = 2
when x = 3
Practice
Copy and Complete the Statement:
36 = 6?
81 = ?2
16 = 2?
64 = ?3
27 = 3?
1/1,000 = 1/10?
32 = ?5
1/10,000 = 1/?4
1.5
Place Value
Review: Place Values LEFT of the decimal point
Place Value
Place Values RIGHT of the decimal point
Place Value
Why they have those names?
How to Read Decimals
63.174
“sixty-three and one hundred
seventy-four thousandths”
“sixty-three point one seven four”
7.029
“seven and twenty-nine ten hundredths”
“seven point zero two nine”
Expanded Notation For Decimals
Remember…
These Place Values
Compare Decimals
Put in order: (smallest to largest)
.12
A
.8
B
.62
C
.7
D
.102
E
.0901
F
Practice
Write out the decimal:
One and three hundred five thousandths
One and thirty-five thousandths
One and thirty-five hundredths
One and three hundred five ten thousandths
Twelve thousandths
Practice
Complete the Statement with <,>, or =:
0.32
0.3109
0.98
1.9
1.075
1.57
3.60
3.600
0.18
0.108
1.6
Rounding Numbers
 If the digit to the right of the rounding digit is…
 4 or less – round down
 5 or greater – round up
What is the mean?
 It’s the average.
 To find the mean you add the numbers and divide the sum
by how many numbers are in the set
Define: Approximate
 Close to the actual, but not completely accurate or exact.
 The symbol for approximations is ≈
Practice
Find the mean:
1, 5, 2, 3, 4, 4, 2
20, 40, 40, 20, 30, 30
10, 12, 14, 11, 13
50, 25, 35, 40, 25, 45, 55, 35
80, 45, 60, 40, 5, 20, 50, 120
Practice
True or False
2.15 rounded to the nearest ones place is 2
13,099 rounded to the nearest thousand is 13,000
5.445 rounded to the nearest tenth is 5.5
411,990 rounded to the nearest hundred is 412,000
8.5165 rounded to the nearest hundredth is 8.517
1.7
Adding Decimals
3.21 + 4.5
5.649 + 39.27
3.21
+ 4.5
7.71
5.649
+ 39.27
44.919
Adding Decimals
528 + 7.49
528.00
+ 7.49
535.49
Subtracting Decimals
8.97 – 2.82
8.97
– 2.82
6.15
16.34 – 3.18
16.34
– 3.18
13.16
Subtracting Decimals
3.8 – 1.26
3.80
– 1.26
2.54
What’s a Polygon?
A 2-d shape
Triangle, Quadrilateral, Pentagon, Hexagon
The Perimeter of a Polygon
The sum of the lengths of its sides
E
D
A
B
H
C
P=A+B+C
F
G
P=D+E+F+G+H
Practice
Find the perimeter
1.6ft
1.1m
0.5m
0.5m
1.4ft
1.2ft
1.1m
1.5ft
Practice
Tell whether the vertical format is correct. If it is not
correct it then add.
4.35
+ 1.23
2.36
+ 0.4
9.1
+ 6.748
6.87
+ 7.24
13.6
0.95
+ 2.2
Practice
Tell whether the vertical format is correct. If it is not
correct it then subtract.
0.86
– 0.2
3
– 2.85
10.5
– 0.82
4.33
– 3.9
10
– 0.195
1.8
Multiplying Decimals
Count the decimal places
2.8 x 7
2.8 x 7
2.8
None
1
x 7
196
So… 196
19.6
Multiplying Decimals
3.1 x 5.9
3.1
x 5.9
1829
3.1 x 5.9
1
2
1829
18.29
Solving Distance Problems
To find the distance traveled, multiply the speed by the
time.
distance = (speed) x (time)
d = rt
Practice
Multiply then round to the hundredths place
4.1 x 2.5 =
6.643 x 1.495 =
5.6 x 2.115 =
5.1 x 0.02 =
2.01 x 8.01 =
0.985 x 2.5 =
6.113 x 31 =
2.25 x 5.61 =
8.57 x 9.44 =
7.72 x 0.08 =
Practice
On August 15-16, 1995, the Concorde, one of the world’s
first supersonic commercial planes, flew around the world.
It completed the trip in 31.46 hours and traveled at a
speed of 1114 miles per hour. How far did the Concorde
travel?
Practice
You want to purchase 2.5 yards of silk fabric. The price of
silk fabric is $17.95 per yard. What will be your total cost?
Practice
The perimeter of a soccer field is 356.62 meters. You run
12 laps around the field at a speed of 134.4 meters per
minute. How far do you run?
1.9
Dividing Decimals by Whole Numbers
47
2.35 ÷ 5
= 0.47
5
2.35
Dividing Decimals by Decimals
6.85 ÷ .5
=13.7
13.7
.5
6.85
5
68.5
Dividing Decimals by Decimals
Why does this work?
Lets look at this another way.
13.7
6.85
10
68.5
x
=
.5
10
5
.5
6.85
5
68.5
13.7
5
68.5
Practice
10.8 ÷ 4 =
1.32 ÷ 0.06 =
6.5 ÷ 2 =
10.4 ÷ 0.8 =
9.9 ÷ 3 =
0.36 ÷ 0.9 =
4.6 ÷ 4 =
3.14 ÷ 0.2 =