Algebra II Unit 1

Identity

the result is itself; 4+0=4, 4*1=4

Closure Property

A set is ___ (under an operation) if the operation always produces an element of the same set. If an element outside the set is produced, then the operation is not ___.

Z; Ex: ... -3, -2, -1, 0, 1, 2, 3...

Integers

True

Integers are closed under multiplication.

I; Ex: 3.14..., e

Irrational Numbers

False; sq. root of 10- sq. root of 10=0

Irrational numbers are closed under subtraction.

N; Ex: 1, 2, 3...

Natural Numbers

True

Natural numbers are closed under division.

True

Negative numbers are closed under addition.

Rational Number

Numbers in which the deciaml form either terminates or repeats.

Irrational Numbers

Numbers which the decimal form never terminates and does not repeat.

False; 5+3=8

Odd numbers are closed under addition.

False; 13-7=6

Prime numbers are closed under subtraction.

Q; Ex: 1/2, 2 2/3, 10/6, 0, 1, -1

Rational Numbers

R; Ex: all numbers learned so far

Real Numbers

Integers, Whole Numbers, Natural Numbers

Subsets of Rational Numbers

W; Ex: 0, 1, 2, 3...

Whole Numbers

False; 7/6

Whole numbers are closed under division.

Distributive

a(b+c)=ab+ac

Associative

changing ( ); 2+(4+6)=(2+4)+6

Commutative Property

changing order; 2+4=4+2, xy=yx

Inverse

the result is zero for addition and one for multiplication; 4+(-4)=0, 4*1/4=1