Chapter 6: Mathematics

Question 1

What is number theory?

Answer 1

number theory is the study of the natural numbers 1,2,3

Question 2

What is prime factorization?

Answer 2

breaking down a large number into the prime numbers that times together to make that number

Question 3

What is a prime number?

Answer 3

a number that can only be divided equally by itself and 1, ie 11. 1x11 is the only way to get 11 by times

Question 4

what is a factor?

Answer 4

a factor is any number that can divide into another number evenly (without leaving a remainder) i.e. 12 = 3x4 3 & 4 are factors, but they are not prime factors because 4 is not prime

Question 5

what is a prime factor?

Answer 5

when all the numbers that can divide into another number are prime numbers, 12 = 3x2x2 all prime numbers

Question 6

what is the primer factorization of 8?

Answer 6

2x2x2

Question 7

what is the prime factorization of 30

Answer 7

2x3x5

Question 8

what is the prime factorization of 15

Answer 8

3x5

Question 9

What does LCM stand for

Answer 9

Least common mulitple (some places say lowest common multiple)

Question 10

What would be multiples of 3 & 5?

Answer 10

15, 30, 45, 60 etc

Question 11

what would be the Least Common Multiple of 3 & 5?

Answer 11

15

Question 12

Using Least Common Multiple helps you to find what fractions item easier?

Answer 12

LCM helps you to quickly find the common denominator to add or subtract fractions

Question 13

How can you quickly find the LCM of two numbers?

Answer 13

do the prime factorization of each number, see how many times each prime number appears and record the most times, then times them all together

Question 14

What is the prime factorization way of finding the LCM of 6 and 28?

Answer 14

6=2x3
28=2x2x7
so 2x2x3x7 = 84
so the LCM of 6 & 28 is 84

Question 15

What is the prime factorization of 18?

Answer 15

2x3x3

Question 16

What is the prime factorization of 75?

Answer 16

2x5x5

Question 17

What is the prime factorization of 18 & 75?

Answer 17

2x3x3=18
2x5x5=75
3x3 x2x5x5=450

Question 18

What is Guass Summation?

Answer 18

Pairing up numbers so they equal the same amount when you are adding a sequence, thus saving you time

Question 19

What would be the sum of 1-30 if you add each number consecutively? Do the pairs trick from page 90

Answer 19

1-10 = 1+10=11 for each of the 5 pairs 55
11-20 = 11+20=31 for each of the 5 pairs 155
21-30 = 21+30=51 for each of the 5 pairs 255
55+155+255=465
Did you notice the pattern in the way the numbers added up in each section?

Question 20

What is modular arithmetic?

Answer 20

clock math

Question 21

what is clock math?

Answer 21

we have a special way of counting our hours, so that when we get past noon or midnight we go back to 1

Question 22

If you are leaving home at 10 am and travel for 6 hours, what time will you get to your destination?

Answer 22

4pm
BUT did you just add 10+6? shouldn’t we say 16? In the 24 hour clock we would say 16, so in modular arithmetic or clock math 4=16 (just think 24 hour clock time to figure it out)

Question 23

What is Congruent Modulo

Answer 23

Congruent (same) modulo is when numbers have the same difference between them always. i.e. 12,24,36 are congruent modulo 12

Question 24

How would we show that 2 and 14 are the same on a clock?

Answer 24

2=14(mod 12)

Question 25

what is the mathematical symbol for congruency?

Answer 25

=

Question 26

Why is 3=39(mod12) ? why isn’t it mod 36?

Answer 26

36 is divisible by 12, which is why they put mod12

Question 27

If there was a 7 hour clock instead of 12. You would say two numbers are modulo 7 if their difference was divisible by 7

Answer 27

2=9(mod7) is correct

Question 28

In a 7 hour clock world, how would you show 5 and 14?

Answer 28

5=14(mod7)

Question 29

Is 3=9(mod7) correct?

Answer 29

no 9-3=6 so not divisible by 7

Question 30

Is 1=7(mod7) correct?

Answer 30

no 7-1=6 so not divisible by 7

Question 31

is 2=16(mod7) correct?

Answer 31

yes 16-2=14 which is divisible by 7

Question 32

What is modulo arithmetic?

Answer 32

using the mod, such as the 12 hour clock, to show the equivalent place not the clock in 24 or 12 hour time. i.e. 2(mod12) is the same as 14

Question 33

What’s a quick way to figure out a mod answer?

Answer 33

use division
9+5=14, mod 12
so divide 14 by 12 = 1 remainder 2
answer is
2(mod12)
weirdly the number of times it divides is not important in modulo arithmetic

Question 34

Use mod 7 and figure out 3+18

Answer 34

3+18=21
21 divided by 7 = 3 no remainder
ANSWER: 0(mod7)

Question 35

use mod 7 to figure out 2+4

Answer 35

2+4=6
6 divided by 7 = 0 with a remainder of 6
ANSWER: 6(mod7)

Question 36

use mod 7 to figure out 19+10

Answer 36

19=10=29
29 divided by 7 = 4 remainder 1
1(mod7)

Question 37

could you do math in modulo 890009?

Answer 37

yes the number doesn’t matter, it is just showing the consistent number that is between each set, i.e.: 1, 890010 is mod 890009