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Chapter 5 Note Packet (non calculator chapter!)
5.1 – Number Theory
Know this vocabulary! – Match them up!
A.
Prime Number
B.
C.
Composite Number
Unit
D.
Sieve of Eratosthenes
E.
Fundamental Theorem of Arithmetic
F.
Greatest Common Divisor
G.
H.
Least Common Multiple
Relatively Prime
I.
Divisible
J.
Twin Primes
The Sieve of Eratosthenes
Divisibility Rules
2–
3–
4–
5–
6–
7–
8–
9–
10 –
The smallest natural number that is divisible by every number
in a set of numbers
2. If a divides b with remainder zero
3. Two prime numbers that have a difference of two
Every composite number can be expressed as a unique product
4.
of prime numbers
5. Two natural numbers that have no common divisors
The largest natural number that every number in a set is
6.
divisible by
7. A number that is neither prime nor composite
8. A technique for determining prime numbers
Natural number greater than one that has more than two
9.
factors
10. Natural number, greater than one that has exactly two factors
1.
Determine whether 145,860 is divisible by the following numbers. State why or why not.
2–
3–
4–
5–
6–
7–
8–
9–
10 –
Find the prime factorization of 2100.
Find the Greatest Common Divisor of the following numbers
***Defining GCD:
54 AND 90 (USING THE KOREAN METHOD)
225 AND 525 (USING PRIME FACTORIZATIONS)
Find the Least Common Multiple of the following numbers
***Defining LCM:
144 AND 168 (USING THE KOREAN METHOD)
72 AND 432 (USING PRIME FACTORIZATIONS)
5.2 – THE INTEGERS
Know this vocabulary! – Define them!!
WHOLE NUMBERS
INTEGERS
INEQUALITY
MULTIPLICATION PROPERTY OF ZERO
Compare the following numbers with an inequality
a) -3
1
b) -3
-5
c) -6
-4
d) 0
-7
Perform the Indicated Operation
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
5.3 – Rational Numbers
Reducing Fractions
Switching between Mixed Numbers and Improper Fractions
Writing Fractions as Decimals
Adding & Subtracting Fractions
Multiplying & Dividing Fractions
Writing Decimals as Fractions

Non Repeating

Repeating
5.4 – IRRATIONAL NUMBERS
The parts of an irrational number
Practice Simplifying
Practice Adding & Subtracting
Practice Multiplying
Practice Dividing
Rationalizing Radicals
5.5 – Real Number System
Know this vocabulary! – YOU MUST KNOW THESE FOR CHAPTER 10 ALSO!!!!
CLOSURE
COMMUTATIVE
ASSOCIATIVE
IDENTITY
INVERSE
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