Egyptian Numerals
Egyptian Numerals
Convert the Egyptian
numeral to Hindu-Arabic
form.
Convert the Egyptian
numeral to Hindu-Arabic
form.
2412
12,036
PAGE 161 IN YOUR TEXTBOOK
Egyptian Numerals
PAGE 161 IN YOUR TEXTBOOK
Chinese Numerals
Convert the Chinese
numeral to Hindu-Arabic
form.
Convert the Hindu-Arabic
numeral to Egyptian form.
306 090
306,090
3007
PAGE 161 IN YOUR TEXTBOOK
PAGE 164
1
Chinese Numerals
Expanded Form
Convert the Hindu-Arabic
numeral to Chinese.
Simplify the following expansion:
960
6209
PAGE 164
Expanded Form
Simplify the following expansion:
Expanded Form
Write the following number in expanded form:
3774
70,401,009
2
Abacus
Identify the number represented on the abacus:
Abacus
Sketch an abacus to show the following number:
3547
256
Number Base Conversion
Convert to decimal form (base 10):
Number Base Conversion
Convert to decimal form (base 10):
3
Number Base Conversion
Number Base Conversion
Convert decimal number to the given base:
Convert decimal number to the given base:
36401 to base 5
19 to base 2
Modular Systems
True or False?
12 ≡ 4 (mod 2)
Modular Systems
True or False?
36 ≡ 14 (mod 7)
True
False
4 and 12 have the same remainder when divided by 2.
36 has a remainder of 1 when divided by 7, but 14 has
a remainder of 0 when divided by 7.
Also, 2 evenly divides 12 – 4.
Also, 7 does not evenly divide 36 – 14.
4
Clock Arithmetic
Work each modular arithmetic problem.
35 − 22 (mod 5)
≡ 13(mod 5) ≡ 3(mod 5)
5 ⋅ 8(mod 3)
≡ 40(mod 3) ≡ 1(mod 3)
Groups
A mathematical system is called a group if,
under its operation, it satisfies the closure,
associative, identity, and inverse properties.
Properties of Mathematical Systems
Tell which of the following properties are satisfied.
☺
m
n
p
m
n
p
n
p
n
p
m
n
n
n
m
PROPERTIES
Closure:
Commutative:
Associative:
Identity:
Inverse:
______
______
______
______
______
Groups
Decide whether this system is a group. If not,
identify all properties that are NOT satisfied.
integers; multiplication
NOT A GROUP (does not satisfy inverse)
5