algebra vocabulary - chapter 2

Question 1

Which property is represented by the following?
For all real numbers a and b:

a+b is a unique real number
ab is a unique real number

The sum and product of any two real numbers are also real numbers. Moreover, they are unique which means that there is one and only one possible answer then you add or multiply two real numbers.

Answer 1

Closure Properties

Question 2

Which property is represented by the following?
For all real numbers a and b:

a+b=b+a and ab=ba

The order in which you add or multiply two numbers does not affect the result.

Answer 2

Commutative Properties

Question 3

Which property is represented by the following?
For all real numbers a,b, and c:

(a+b)+c=a+(b+c)
(ab)c=a(bc)

When you add or multiply any three real numbers, the grouping (or association) of the numbers does not affect the result.

Answer 3

Associative Properties

Question 4

in the sum of a+b, what are a and b called?

Answer 4

terms

Question 5

in the product “ab”, what are a and b called?

Answer 5

factors

Question 6

which property says a=a?

Answer 6

reflexive property

Question 7

which property says if a=b, then b=a?

Answer 7

symmetric property

Question 8

which property says if a=b and b=c, then a=c

Answer 8

transitive property

Question 9

which property says, there is unique real number 0 such that for every real number “a”, a+0=a and 0+a=a

Answer 9

identity property of addition

Question 10

which property says that for every real number a, there is a unique real number -a such that a+(-a)=0 and (-a)+a=0

Answer 10

addition property of opposites

Question 11

a number and it’s opposite which add up to zero are called what?

Answer 11

additive inverses

Question 12

which property is illustrated by the following:
for all real numbers a and b:

-(a+b)=(-a)+(-b)

The opposite of a sum of real numbers is equal to the sum of the opposites of the numbers

Answer 12

Property of the Opposite of a Sum

Question 13

Which property is illustrated by the following?
For all real numbers a and b, the “difference” a-b is defined by

a-b=a+(-b)

To subtract b, add the opposite of b.

Answer 13

Definition of Subtraction

Question 14

For all real numbers a,b, and c:

a(b+c) = ab + ac AND (b+c)a=ba+ca
a(b-c)= ab - ac AND (b-c)a= ba - ca

Answer 14

Distributive Properties

Question 15

The properties of real numbers and equality guarantee that for all values of the variable x, 9x+5x and 14x represent the same number. Therefore, the two expressions are…

Answer 15

equivalent

Question 16

Replacing an expression containing variables by an equivalent expression with as few terms as possible is called what?

for example…9x+5x is replaced by 14x

Answer 16

simplifying the expression

Question 17

what is the identity ELEMENT for multiplication?

Answer 17

1

Question 18

Which property is illustrated by the following?
There is a unique real number 1 such that for every real number “a”,

a x 1= a and 1 x a=a

Answer 18

Identity Property of Multiplication

Question 19

The following illustrates which property?
When one (or at least one) of the factors of a product is zero, the product itself is zero.

For every real number a:

a x 0 = 0 and 0 x a = 0

Answer 19

Multiplicative Property of Zero

Question 20

Which property is illustrated by the following?

for every real number a:

a(-1) = -a AND (-1)a = -a

Multiplying any real number by -1 produces the opposite of the number

Answer 20

Multiplicative Property of -1

Question 21

For all real numbers a and b:

(-a)(b) = -ab
a(-b) = -ab
(-a)(-b) = ab

Answer 21

Multiplicative Property of Opposites

Question 22

Rules for Multiplication:

1a. If two numbers have the same sign, their product is _________.
1b. If two numbers have the opposite signs, their product is ________.
2a. The product of an even number of negative numbers is __________.
2b. The product of an odd number of negative numbers is __________.

Answer 22

1a. positive
1b. negative

2a. positive
2b. negative

Question 23

What kind of integers do you have when you count by ones from any number in the set of integers?

For example, -2, -1,0,1,2

Answer 23

consecutive integers

Question 24

what is it called when numbers are listed in order from least to greatest?

Answer 24

natural order

Question 25

an integer that is the product of 2 and any integer is an _____ integer.

Answer 25

even

Question 26

If an integer is not even what is it?

Answer 26

odd

Question 27

if you count by 2’s beginning with any even integer what do you obtain?

Answer 27

consecutive even integers

Question 28

if you count by 2s beginning with any odd integer what do you obtain?

Answer 28

consecutive odd integers

Question 29

Two numbers whose product is 1 are called what?

Answer 29

reciprocals of each other OR multiplicative inverses

Question 30

Which property is illustrated by the following?

For every nonzero real number a, there is a unique real number 1/a such that

a x 1/a = 1 AND 1/a x a = 1

Answer 30

Property of Reciprocals

a and 1/a are reciprocals

Question 31

Which property is illustrated by the following?
For every nonzero number a,

1/-a = -1/a

Read, “The reciprocal of -a is -1/a.”

Answer 31

Property of the Reciprocal of the Opposite of a Number

Question 32

Which property is illustrated by the following?
For all nonzero numbers a and b,

1/ab = 1/a x 1/b.

The reciprocal of the product of two nonzero numbers is the product of their reciprocals.

Answer 32

Property of the Reciprocal of a Product

Question 33

Which property is illustrated by the following?

For every real number a and every nonzero real number b, the “quotient” a/b is defined by:

a/b - a x 1/b

To divide by a nonzero number, multiply by its reciprocal

Answer 33

Definition of Division

Question 34

Rules for Division:

1. If two numbers have the same sign, their quotient is ________.
2. If two numbers have opposite signs, their quotient is _________.

Answer 34

1. positive

2. negative