Transcript Chapter 5 Review

Math 170 – Chapter 5
Misc
Math
Prime
Composite
GCF
LCM
10
10
10
10
10
20
20
20
20
20
30
30
30
30
30
40
40
40
40
40
50
50
50
50
FINAL
Primes
10 Point Question
What is the smallest prime
number?
2
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20 Point Question
Is 209 prime?
No. 209=11*19
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30 Point Question
Find the prime factorization
of 2008.
2*2*2*251
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40 Point Question
What is the fundamental
theorem of arithmetic?
Any number can be written uniquely as
the product of primes
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50 Point Question
Find the prime factorization of
140.
2*2*5*7
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Composite
10 Point Question
What is the smallest composite
number?
Four.
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20 Point Question
Is the 36 digit number consisting only of
4’s divisible by 3?
Here is the number:
444,444,444,444,444,444,444,444,444,444,444,444
Yes. The sum of the digits will be 144,
and 144 is divisible by 3.
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30 Point Question
How can you tell if a number is divisible by 6?
It is divisible by both 2 and 3
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40 Point Question
Suppose that 24|b. What else must divide
b?
1, 2, 3, 4, 6, 8, and 12
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50 Point Question
Show that if a|b and a|c, then a|(b+c).
Since a|b, b can be made out of rods of length a. Since
a|c, c can also be made out of rods of length a. By putting
these two together, you get b+c, which can also me made
of rods of length a. Thus a divides (b+c)
a
a
a
b
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a
a
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a
a
c
a
GCF
10 Point Question
List all the factors of 42
1, 2, 3, 6, 7, 14, 21, 42
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20 Point Question
Use prime factorization to
find the GCF of 12 and 30.
12 = 2*2*3
30 = 2*3*5
Primes in common: 2& 3. GCF =
2*3=6
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30 Point Question
Use the subtraction method to
find the GCF of 75 and 120.
GCF(75,120) = GCF(75,45)=
GCF(30,45) = GCF(15,30) =
GCF(15,15) = 15.
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40 Point Question
Joe the Baker baked up 84 spice cookies and 90
sugar cookies. Joe is planning on selling the cookies
in trays. Each tray should contain only one type of
cookie, and each tray, regardless of the type should
contain the same number of cookies. Joe wants to
use the least number of trays. How many cookies
should he put on each tray?
6 cookies per tray
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50 Point Question
Find the GCF of these three numbers:
2*2*2*3*3*5*7*11
2*2*3*3*3*7*11*17*19
2*2*2*2*3*5*7*11*19*23
2*2*3*7*11
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LCM
10 Point Question
List the first 6 multiples
of 7.
7, 14, 21, 28, 35, 42
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20 Point Question
Carol is laying down rods that are 8 units
long. Mike is laying down rods that are 6
units long. If they both started at the same
place, when will the ends of their rods line
up again?
When they each have reached a length
of 24 units.
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30 Point Question
Find the LCM of 48 and 40 using the prime
factorization of each number.
240
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40 Point Question
Juan will only by a CD if it has exactly 14
songs on it. Marty will buy a CD only if it
has exactly 12 songs on it. If they have the
same number of songs in their collection,
what is the fewest number of CD’s each
owns?
Juan owns 6, Marty owns 7. They both
have 84 songs in their collection.
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50 Point Question
Find the LCM of the following numbers
2*2*2*3*3*5*7*11
2*2*3*3*3*7*11*17*19
2*2*2*2*3*5*7*11*19*23
2*2*2*2*3*3*3*5*7*11*17*19*23
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Misc. Math
10 Point Question
Which property of addition
does the following
demonstrate?
(a + b) + c = a +(b + c)
The Associative Property of Addition.
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20 Point Question
Explain how to do the following
problem using mental math.
21X36 + 21X64
Use the distributative property to make it
21X(36+64) Add the compatible numbers,
then multiply to get 2100.
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30 Point Question
Use the range method to get
estimates for 236+153.
Low: 300, high 500.
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40 Point Question
Explain how to use the compensation
method to find 248+296.
I would take 4 from the 248 and add it to the
296 so the sum becomes 244 + 300 = 544.
I guess you could also take 2 from the 296 and
add it to the 248 so the problem becomes 250
+ 294, but my way results in an easier sum.
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Final Question
Most numbers have an even number of factors.
For example, there are 6 numbers that evenly
divide into 12 (1, 2, 3, 4, 6, & 12), 4 numbers that
divide evenly into 15 (1, 3, 5, & 15) and only 2
numbers that divide into 19.
What is special about numbers with an odd
number of factors?
They are perfect squares. For example, 36
has 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, 36
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