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50 Cards in this Set

  • Front
  • Back
What are real numbers?
Both rational and irrational numbers.

These are the numbers that you encounter each day and are classified into various sets and subsets.
Define Rational Numbers
Numbers that can be expressed as a fraction in the form a/b, where a and b are integers and b does not = 0. Rational numbers can be classified into subsets.

These are the numbers we actually use daily, and always have a known ending.
Define Integers
Whole numbers and their opposits. {...-3,-2,-1,0,1,2,3...} These are rational numbers. Negative, positive, include 0 (neither negative or positive) Add negatives in.
Zero is positive or negative?
Neither
Define Irrational numbers
Numbers that cannot be expressed as fractions such as sqrt 2, sqrt 3, sqrt 5, and pi. When expressed as decimals, they are non-terminating and non-repeating.

Numbers that we can't predict the end of.
What does PEMDAS stand for?
Parentheses (or other grouping symbols)-Exponents-Multipication & Division (left to right)-Addition & Subtraction (left to right)
Define Quotient
Result of division
Re Multiplication:

2 positive #'s = pos or neg?

2 negative #'s = pos or neg?

A negative and a positive #?
2 positive = positive

2 negative = positive

Neg and Pos = Neg
When you have more than 2 numbers, how do you determine if the product is positive or negative?
If it is an even amount of numbers it will be positive

If it is an odd amount of numbers it will be negative!
What is the reciprocal of any nonzero number?
1 over a
What is the product of any number and it's reciprocal?
a x (1 over a) = 1
How do you find the sum of a positive number and a negative number?
Find the difference of their absolute values and use the sign of the number with the larger absolute value.
What is the absolute value of a number?
It is the number of units a number is away from 0 on a number line.

Consider position on number line
How do you add integers?
If the signs are the same add and keep the sign. If the signs are different subtract and take the sign of the number with the larger absolute value.

Consider comparing the number of positives and negatives in a cloud.
How do you subtract integers?
Add the opposite of the number being subtracted and apply the sign of the greater number

switch signs
How do you multiply negative integers?
If there is an even number of negatives in the problem, the solution will be positive.

If there is an odd number of negatives in the problem, the solution will be negative.

evens vs odds
How do you divide negative integers?
If there is an even number of negatives in the problem, the solution will be positive.

If there is an odd number of negatives in the problem, the solution will be negative.

vens vs odds
How do you know if a number is divisible by 3?
If the sum of the individual digits of the number is divisible by 3.

312 is (3+1+2) = 6 which is divisible by 3 and 9,021 is (9+0+2+1) = 12 which is divisible by 3.
How do you know if a number is divisible by 4?
If the last two digits, taken as a two-digit number, are divisible by 4.

736 is because 36 is divisible by 4. 12,716 is because 16 is divisible by 4.
How do you know if a number is divisible by 8?
If the last three digits, taken as a three-digit number, are divisible by 8.

3,024 is because 024 is divisible by 8. 79,128 is because 128 is divisible by 8 (128/8 = 16).
How do you know if a number is divisible by 9?
If the sum of the individual digits of the number is divisible by 9.

9,135 is (9+1+3+5) = 18 which is divisible by 9 and 414,972 is (4+1+4+9+7+2) = 27 which is divisible by 9
How do you know if a number is divisible by 6?
If the sum is divisible by both 2 and 3.

336 is divisible by both 2 and by 3 (3+3+6) = 12
How do you know if a number is divisible by 12?
If it is divisible by both 3 and 4.
How do you know if a number is divisible by 7?
If you remove the last digit of the number, double it, and subtract it from the remaining digits and the result is divisible by 7.

357 becomes 35-(2*7) = 21 which is divisible by 7. 2,016 becomes 201-(2*6) = 189 which is divisible by 7.
What are the prime numbers?
2, 3, 5, 7, 11, 13, 17, 19, 23
What is the Least Common Multiple (LCM)?

How do you find it?
See page 381
What is the Greatest Common Factor (GCF)?

How do you find it?
It is the largest common factor of 2 or more numbers.


Product of all the primes that appear in each factorization, ising each prime the smallest number of times it appears in any of the factorizations.
Determine this by finding all the prime factors of both numbers, then taking the prime factors that are in both (match them up) and multiply them.
The product of the GCF and LCM of two numbers is equal to what?
The product of the two numbers.
Is 0 even or odd?
Why?
0 is a multiple of what integers?
Even

It is a multiple of 2

All integers. 0 = 0 * n
A) neg + pos = ?
B) neg - pos = ?
C) pos - neg = ?
D) neg - neg = ? larger value - turns pos and switches signs
A) which ever sign is larger abs sub + sign
B) neg add abs + neg
C) larger value - turns pos and switches signs
D) larger value - turns pos and switches signs
If one integer is even, and the other is odd, is the sum and difference even or odd?
Odd
When is the product of two integers even?
Always, unless both of them are odd.
Can you break down and/or combine the following?

2 Power of 5 * 2 Power of 3

s power of 5 over 2 power of 3

(2 power of 2) power of 3

2 power of 3 * seven power of 3
2 power of 8 2x2x2x2x2 * 2x2x2

2 power of 5-2 = 2 power of 2

2 power of 2*3 = 2 power of 6

(2*7)power of 3

Pg 382
a) b power of m b power of n= ?

b) the above expressed as a fraction?

c) (b power of m) power of n =?

d) b power of m by c power or m = ?

e) When DONT these rules apply?
a) b to the power of m+n

b) b power of m-n

c) b power of mn

d) (bc) power of m

e) When the bases are different
Page 382
A) If a is positive then a to the power of n is?

B) If a is negative and n is negative then a to the power of n is?

C) If a is negative and n is odd, then a to the power of n is?
A) pos

B) pos

C) neg
Define principal
Square root
Every ____ number has a square root
Positive
(sroot a) to the power of 2 equals?
sroot a * sroot a = a
For any positive numbers a and b:

sroot ab =?

sroot a over b = ?
sroot a * sroot b

sroot a over sroot b
What property does this equation represent?

a+b = b+a
commutative property of addition
What property does this equation represent?

a*b = b*a
Commutative Property of Multiplication
What property does this equation represent?

a+(b+c) = (a+b)+c
Associative Property of Addition

It states that changing the grouping (parenthesis or brackets) of addends in a sum does not change the resulting sum.
The Distributive Property
It states that multiplication distributes over addition and subtraction

a*(b+c) = a*b+a*c, where a,b, and c are real numbers
a*(b-c) = a*b-a*c, where a, b, and c are real numbers
What does this equation represent?
a*(b+c) = a*b+a*c The distributive property of multiplication over addition
What does this equation represent?
a*(b-c) = a*b-a*c The distributive property of multiplication over division
What three things preserves an inequality?

What two things reverse an inequality?
Page 388
a > b means that a - b is pos or neg?

a < b means that a - b is pos or neg?
a) pos

b) neg
1 is a divisor of?
Every integer.
Regarding the properties of 1:

1 is a divisor of what?
1 is the __, ___, integer
1 is even/odd?
1 is/ is not prime?
Divisor of every integer
Smallest and positive integer
It is odd
Is not prime
What is the only number that is equal to its opposite?
Zero