Download Chapter 1 Review Notes

Chapter 1 Review Notes
1.1 Placing fractions, decimals and whole numbers on a number line.
Interpreting and writing statements of inequalities using ( <, > )
Tips:
 Number lines always have the lowest number to the left on a
horizontal line
1
1.5 2
2½ 3
 On a Vertical Number line the lowest number always starts
on the bottom.
4
3
2
1
.
 Always use a on the number line to indicate what should be
Represented.
Lower# < Higher #
or
Higher # > Lower #
1.2 Express a whole number as a product of its prime factors ( prime
factorization)
Two methods:
Factor Trees
Ladder
2 X 2 x 7 = 42
2 x 2 x 2 x 3 x 7 = 168
1.3 Finding common factors and greatest common factor (GCF) of two
whole numbers.
Finding common multiples and least common multiple (LCM) of two
whole numbers.
 Common Factors : list the factors of the whole numbers and find
the common numbers
16: 1, 2, 4, 8, 16
24: 1,
2,
3,
4,
6,
8,
12, 24
 Finding GCF use one of three methods:
Listing factors and finding the largest
16: 1, 2, 4, 8, 16
24: 1, 2, 3, 4, 6,
8,
12, 24
GCF = 8
Using the prime factorization
16 =2 x 2 x 2 x 2
24 =2 x 2 x 2 x 3
2x2x2=8
GCF = 8
Using the Ladder:
2
16
24
2
6
12
2
4
6
2
3
2x2x2=8
GCF = 8
 Finding Common Multiples:
List the multiples of each number until you find the ones
they have in common
5: 5, 10, 15, 20, 30, 35, 40, 45
15: 15, 30, 45
Hint once you find the 1st common multiple you can count by that number to find
additional common multiples
 Finding LCM:
List:
5: 5, 10, 15, 20, 30, 35, 40, 45
15: 15, 30, 45
Prime Factorization:
16= 2 x 2 x 2 x 2
24 =2 x 2 x 2 x 3
2 x 2 x 2 x 2 x 3 = 48
Ladder:
2
2
2
16
8
4
2
24
12
6
3
LCM = 48
2 x 2 x 2 x 2 x 3 = 48
LCM = 48
LCM = 30
1.4 Finding the square of a number
Finding a square root of a perfect square
82 Exponent means 8 x 8 = 64
Base
32 --- 3 x 3 = 9
 Square Root
100
2 x 2 x 5 x 5 = 100
10 10
make two matching sets ( for the 2 exponent)
2 5 2 5
(2x5)
(2 x 5 )
10
10
The square root of 100 = 10
1.5 Finding the cube of a number
Finding the cube root of a number
Order of Operations
 23 means 2 x 2 x 2 = 8
 Cube Root
8
4
2
8
2
2
2
4
2 2
2x2x2x2x2x2
Make 3 matching sets (3 exponent)
( 2x2) ( 2x2) (2x2)
4
4
4
 Order of Operations
Step 1 – Evaluate Exponents
Step 2 – Evaluate inside Parentheses
Step 3 – Multiply and divide from left to right
Step 4 – Add and Subtract from left to right
4 + 6 x 3 – (23- 2)
4 + 6 x 3 – (8 – 2)
4+6x3–6
4 + 18 – 6
22 – 6
16