Rules

Question 1

Rules of operation

Answer 1

PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction)

Question 2

Communicative Laws of Addition and Multiplication

Answer 2

switching any two numbers will not change the sum or product

Question 3

Associative Laws of Addition and Multiplication

Answer 3

regrouping a set of numbers does not affect results (e.g. (a+b) + c = a + (b+c)

Question 4

Distributive Laws of Multiplication

Answer 4

can distribute a factor over numbers that are added/subtracted (e.g. 4(3+7) = 4(3) + 4(7)

also works for numerator of a fraction (e.g. (a+b)/c = (a/c) + (b/c)

Question 5

Multiple

Answer 5

the product of a specified number and an integer (e.g. -9, 21, and 300 are multiples of 3)

Question 6

Factor

Answer 6

the number multiplied by another number to get a desired number (e.g. 3 and 4 are factors of 12)

Question 7

How to determine if 3 is a factor of a given number

Answer 7

if the sum of the digits add to a multiple of 3

Question 8

How to determine if 4 is a factor of a given number

Answer 8

if the last 2 digits are a multiple of 4

Question 9

How to determine if 6 is a factor of a given number

Answer 9

if it is divisible by both 2 and 3

Question 10

How to determine if 9 is a factor of a given number

Answer 10

if the digits add up to a multiple of 9

Question 11

odd + odd =

Answer 11

even

Question 12

even + even =

Answer 12

even

Question 13

odd + even =

Answer 13

odd

Question 14

odd * odd =

Answer 14

odd

Question 15

even * even =

Answer 15

even

Question 16

odd * even =

Answer 16

even

Question 17

How does one find the greatest common factor between two numbers?

Answer 17

1. break both integers into their prime factorizations
2. multiply all the prime factors they have in common
   e.g. 36 and 48
   36 = (2)(2)(3)(3)
   48 = (2)(2)(2)(2)(3)
   GCF = (2)(2)(3) = 12

Question 18

Least common multiple

Answer 18

smallest number that is a multiple of each integer

Question 19

How does one find the least common multiple of two numbers?

Answer 19

1. find prime factorization of each
2. extract each prime number the maximum times it appears in any one of the factorizations
3. multiply those numbers
   e.g. LCM of 6 and 8
   6 = (2)(3)
   8 = (2)(2)(2)
   LCM = (2)(2)(2)(3) = 24

Question 20

What does one do when multiplying two identical bases with different exponents?

Answer 20

add the exponents together

e.g. (2^3)(2^5) = 2^8

Question 21

What does one do when dividing two identical bases with different exponents?

Answer 21

subtract the exponents from each other

Question 22

What does one do when raising a power to another power?

Answer 22

multiply exponents

Question 23

What does one do when multiplying two different bases with the same exponents?

Answer 23

multiply the bases together; the exponent remains the same

Question 24

What does a negative exponent symbolize?

Answer 24

a reciprocal of the positive

e.g. 2^-2 = 1/4

Question 25

What does an exponent of 0 symbolize?

Answer 25

all numbers raised to the 0 = 1

Question 26

What does one do when subtracting/adding like radicals?

Answer 26

subtract/add them like usual

Question 27

What does one do when multiplying/dividing radicals?

Answer 27

multiply/divide the radical and number outside the radical separately
e.g. 6sqrt(5) * 4sqrt(3) = 24*sqrt(15)

Question 28

When comparing fractions, what is an easy way to tell which is larger?

Answer 28

1. multiply the numerator of the first fraction by the denominator of the second, and vise versa
2. write number next to numerator
3. largest number next to numerator indicates that fraction is largest
   e.g. which is larger: 5/6 or 7/9?
   59 = 45
   67 = 42
   5/6 is larger