Chapter 1 Vocabulary

Question 1

Natural numbers

Answer 1

numbers used for counting

Question 2

Whole numbers

Answer 2

natural numbers and 0

Question 3

Integers

Answer 3

natural numbers, their opposites, and 0

Question 4

Rational numbers

Answer 4

fractions and decimals

Question 5

Irrational numbers

Answer 5

square roots and decimals that don’t terminate or repeat

Question 6

Properties of Real Numbers:

Answer 6

Closure, Commutative, Associative, Identity, Inverse, Distributive

Question 7

Closure

Answer 7

a+b, ab

Question 8

Commutative

Answer 8

a+b=b+a, ab=ba

Question 9

Associative

Answer 9

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

Question 10

Identity

Answer 10

a+0=a, 0+a=a, a x 1=a, 1 x a=a

Question 11

Inverse

Answer 11

a+(-a)=0, a x 1/a = 1, a does not equal 0

Question 12

Distributive

Answer 12

a(b+c) = ab+ac

Question 13

Properties for Simplifying Algebraic Expressions

Answer 13

Definition of Subtraction, Definition of Division, Distributive Property for Subtraction, Multiplication by 0, Multiplication by -1, Opposite of a Sum, Opposite of a Difference, Opposite of a Product, Opposite of an Opposite

Question 14

Definition of Subtraction

Answer 14

a-b=a+ (-b)

Question 15

Definition of Division

Answer 15

a/b=a/b=a x 1/b, b does not equal zero

Question 16

Distributive Property for Subtraction

Answer 16

a(b-c)=ab-ac

Question 17

Multiplication by 0

Answer 17

0 x a =0

Question 18

Multiplication by -1

Answer 18

-1 x a = -a

Question 19

Properties of Equality

Answer 19

Reflexive Property, Symmetric Property, Transitive Property, Addition Property, Subtraction property, Multiplication Property, Division Property, Substitution Property

Question 20

Reflexive Property

Answer 20

a=a

Question 21

Symmetric Property

Answer 21

If a=b, then b=a

Question 22

Transitive

Answer 22

If a=b, and b=c, then a=c

Question 23

Addition

Answer 23

If a=b, then a+c=b+c

Question 24

Subtraction

Answer 24

If a=b, then a-c=b-c

Question 25

Multiplication

Answer 25

If a=b, then ac=bc

Question 26

Division

Answer 26

If a=b and c doesn’t equal 0, then a/c=b/c

Question 27

Substitution

Answer 27

If a=b, the b may be substituted for a in any expression to obtain an equivalent expression