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Positive numbers

Negative numbers

Intergers

Absolute value

The numbers to the right of zero on the number line

The numbers to the left of zero on the number line

the numbers ... -3 ,-2 ,-1 , 0, 1,2,3'...

The distance between 0 and a number on the number line

Positive numbers

The numbers to the right of zero on the number line

Negative numbers

The numbers to the left of zero on the number line

Reflexive Property

Symmetric Property

Transitive Property

Substitution Property

Any quantity is equal to itself

If one quantity equals a second quantity, then the second qua…

If one quantity equals a second quantity and the second quant…

A quantity may be substituted for its equal in any expression.

Reflexive Property

Any quantity is equal to itself

Symmetric Property

If one quantity equals a second quantity, then the second qua…

Integers

Absolute value

Opposite

Experssion

The numbers- -3,-2,-1,0,1,2,3

The distance between 0 and a number on the number line

Numbers with the same absolute value on opposite sides of zer…

A number or group of numbers written with operation signs

Integers

The numbers- -3,-2,-1,0,1,2,3

Absolute value

The distance between 0 and a number on the number line

positive numbers

negative numbers

integers

absolute value

the numbers to the right of the zero

the numbers to the left of the zero

the numbers... -3, -2, -1, 0, 1, 2, 3

the distance between 0 and a number on the number line

positive numbers

the numbers to the right of the zero

negative numbers

the numbers to the left of the zero

terminating decimal

repeating decimal

rational number

irrational number

A decimal number that ends or terminates

A decimal that repeats a digit or group of digits forever

a number that can be expressed as a ratio (fraction) of two i…

a number that cannot be expressed as a ratio of two integers…

terminating decimal

A decimal number that ends or terminates

repeating decimal

A decimal that repeats a digit or group of digits forever

integers

whole numbers

opposites or additive inverses

absolute value

the set of whole numbers and their opposites: ...., -3, -2. -…

the set of natural, or counting, numbers and zero: 0, 1, 2, 3…

numbers that are the same distance from 0, but on opposite si…

a number's distance from 0 on a number line

integers

the set of whole numbers and their opposites: ...., -3, -2. -…

whole numbers

the set of natural, or counting, numbers and zero: 0, 1, 2, 3…

Positive numbers

Negative numbers

integers

Absolute value

the numbers to the right of zero on the number line

the numbers to the left of zero on the number line

the numbers ... -3, -2, -1, 0, 1, 2, 3....

The distance between 0 and a number on the number line

Positive numbers

the numbers to the right of zero on the number line

Negative numbers

the numbers to the left of zero on the number line

What is a natural number?

What is an integer?

What is a rational number?

What is a real number?

any positive whole number

any whole number, positive or negative, including 0.

a number that can be represented as a fraction

all rational and irrational numbers

What is a natural number?

any positive whole number

What is an integer?

any whole number, positive or negative, including 0.

Additive Identity

Additive Inverse

Multiplicative Identity

Multiplicative Property of 0

For any number a, a + 0 = a.

For any number a, a + (-a) = 0.

For any number a, a • 1 = a.

For any number a, a • 0 = 0.

Additive Identity

For any number a, a + 0 = a.

Additive Inverse

For any number a, a + (-a) = 0.

Integers

Negative (Integer) Numbers

Positive (Integer) Numbers

Whole Numbers

A set of whole numbers and their opposites.

an integer less than zero

any integer greater than zero

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

Integers

A set of whole numbers and their opposites.

Negative (Integer) Numbers

an integer less than zero

Variables

Terms

Expression

Linear Equations

The letters used to represent numbers eg. x, xy, a

a combination of numbers and variables coonected by multipuca…

Combination of numbers and variables connected by +, -, x, an…

An equation is linear if:... - It has a LHS ,=, RHS

Variables

The letters used to represent numbers eg. x, xy, a

Terms

a combination of numbers and variables coonected by multipuca…

Positive numbers

Negative

Integers the numbers... Absolute value t…

Absolute value

The numbers to the right of zero on the number line

The numbers to the left of zero on the number line

the numbers 3 2 1 0 123

the distance between 0 and a numbe on the number on the numbe…

Positive numbers

The numbers to the right of zero on the number line

Negative

The numbers to the left of zero on the number line

Positive Numbers

Negative numbers

Integers

Absolute value

The numbers to the right of zero on the number line.

The numbers to the left of zero on the number line.

The number...-3,-2, -1, 0, 1, 2, 3.

The distance between 0 and a number on the number line.

Positive Numbers

The numbers to the right of zero on the number line.

Negative numbers

The numbers to the left of zero on the number line.

Positive numbers

Negative numbers

Integers

Absolute value

The numbers to the right of zero on the number line

The numbers to the left of zero on the number line.

The numbers... -3, -2, -1, 0, 1, 2, 3,...

The distance between 0 and a number on the number line.

Positive numbers

The numbers to the right of zero on the number line

Negative numbers

The numbers to the left of zero on the number line.

Positive numbers

Negative numbers

Integers

Absolute value

The numbers to the right of zero on the number line

The numbers to the left of zero on the number line

The numbers -3,-2,-1,0,1,2,3

The distance between 0 and a number on the number line

Positive numbers

The numbers to the right of zero on the number line

Negative numbers

The numbers to the left of zero on the number line

Positive numbers

Negative numbers

Integers

Absolute value

the numbers to the right of zero on the number line.

the numbers to the left of zero on the number line.

the numbers ...-3, -2, -1, 0, 1, 2, 3,...

the distance between 0 and a number on the number line.

Positive numbers

the numbers to the right of zero on the number line.

Negative numbers

the numbers to the left of zero on the number line.

Numerator

Denominator

Add and Subtract Fractions

Multiply Fractions

The number on the top half of a fraction

The number on the bottom half of a fraction

Make denominator the same. Calculate.

Multiply numerators and multiple denominators

Numerator

The number on the top half of a fraction

Denominator

The number on the bottom half of a fraction

Natural numbers

Whole numbers

Integers

Rational numbers

The set of numbers 1, 2, 3, 4, ... Also called counting numbe…

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

The set of whole numbers and their opposites

A number that can be written as a ratio [in the form a/b with…

Natural numbers

The set of numbers 1, 2, 3, 4, ... Also called counting numbe…

Whole numbers

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

positive numbers

negative numbers

integers

absolute value

the numbers to the right of the zero on the number line

the numbers to the left of the zero on the number line

the numbers ...-3, -2, -1, 0, 1, 2, 3...

the distance between 0 and a number on the number line

positive numbers

the numbers to the right of the zero on the number line

negative numbers

the numbers to the left of the zero on the number line

Reflexive Property

Symmetric property

transitive property

Substitution property

any quantity is equal to itself

If one quantity equals a second quantity then the second quan…

if one quantity equals a second quantity and the second quant…

a quantity may be substituted for its equal in any expression

Reflexive Property

any quantity is equal to itself

Symmetric property

If one quantity equals a second quantity then the second quan…

The Fundamental Theorem of Aithmetic

Closure Property of Addition

Inverse Property of Addition

Closure Property of Multiplication

What theorem states that every number with the exception of 1…

If A and B are real numbers, then A + B is a Real number. Wha…

If A is a real number, and A + (-A) = 0, what property is this?

If A and B are real numbers, then AB is a Real number. What p…

The Fundamental Theorem of Aithmetic

What theorem states that every number with the exception of 1…

Closure Property of Addition

If A and B are real numbers, then A + B is a Real number. Wha…

COMMUTATIVE Property of Addition ... (com…

COMMUTATIVE Property of Multiplication…

ASSOCIATIVE Property of Addition ... (ass…

ASSOCIATIVE Property of Multiplication…

3 + 5 = 5 +3

9 x 6 = 6 x 9

4 + (6 + 3) = (4 + 6) + 3

7 x (5 x 3) = (7 x 5) x 3

COMMUTATIVE Property of Addition ... (com…

3 + 5 = 5 +3

COMMUTATIVE Property of Multiplication…

9 x 6 = 6 x 9

complex number

real number

rational number

irrational number

a number of the form a + bi where a and b are real numbers. C…

numbers that are either rational or irrational. A real number…

a number that can be expressed as a/b, the ratio of two integ…

a number that cannot be expressed as a/b, the ratio of two in…

complex number

a number of the form a + bi where a and b are real numbers. C…

real number

numbers that are either rational or irrational. A real number…

Ading a negative is the same as

Subtracting a negative is the same as

Positive x negative=

Negative x positive=

Subtracting the number

Adding a posotive number

Negative

Negative

Ading a negative is the same as

Subtracting the number

Subtracting a negative is the same as

Adding a posotive number

integers

absolute value

opposites

expression

the numbers -3,-2,-1,0,1,2,3

The distance a number is from zero on a number line

two numbers that have the same absolute value but have differ…

A mathematical phrase involving at least one variable and som…

integers

the numbers -3,-2,-1,0,1,2,3

absolute value

The distance a number is from zero on a number line

real numbers

real number line

origin

negative numbers

the set of numbers that includes rational and irrational numb…

real numbers pictured as points on a line

The point labeled 0.

A number less than 0. On a number line, negative numbers are…

real numbers

the set of numbers that includes rational and irrational numb…

real number line

real numbers pictured as points on a line

Imaginary unit

imaginary number

complex number

real part of a complex number

The unit in the imaginary number system, ... sq. root (-1) = i

The square root of a negative number, written in the form bi,…

Any number that can be written as a+bi where a and b are real…

For a number of the form a + bi, a is this part, represented…

Imaginary unit

The unit in the imaginary number system, ... sq. root (-1) = i

imaginary number

The square root of a negative number, written in the form bi,…

Complex Number

Field

Complex Number Formula

Real Numbers

The field of numbers of the form , where and are real numbers…

Any set of elements that satisfies the field axioms for both…

a+bi

The field of all rational and irrational numbers.

Complex Number

The field of numbers of the form , where and are real numbers…

Field

Any set of elements that satisfies the field axioms for both…

Integers

Negative (Integer) Numbers

Positive (Integer) Numbers

Natural Numbers

(Z) positive whole numbers, negative whole numbers and zero

(Z+) an integer less than zero

(Z-) any integer greater than zero

(N) positive whole numbers ( counting numbers)

Integers

(Z) positive whole numbers, negative whole numbers and zero

Negative (Integer) Numbers

(Z+) an integer less than zero

Reflexive Property

Symmetric Property

Transitive Property

Substitution Property

Any quantity is equal to itself

If one quantity equals a second quantity, then the second qua…

If one quantity equals a second quantity and the second quant…

A quantity may be substituted for its equal in any expression.

Reflexive Property

Any quantity is equal to itself

Symmetric Property

If one quantity equals a second quantity, then the second qua…

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

a + b = b + a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

Commutative Property of Addition

a + b = b + a

Commutative Property of Multiplication

ab = ba

positive numbers

negative numbers

integers

absolute value

The numbers to the right of 0 on the number line.

The numbers to the left of 0 on the number line.

The numbers...-3, -2, -2, 0, 1, 2, 3.....

The distance between 0 and a number on the number line.

positive numbers

The numbers to the right of 0 on the number line.

negative numbers

The numbers to the left of 0 on the number line.

closure

identity element

no identity

left identity

start with two elements in a set and end up with an element i…

the intersection of the row and column that remain the same

no column and row stay the same

when a row stays the same but not a coulmn (e@a = a)

closure

start with two elements in a set and end up with an element i…

identity element

the intersection of the row and column that remain the same

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

When adding numbers, changing the order of the numbers doesn'…

When multiplying, changing the order of the factors doesn't c…

When adding numbers, changing the grouping of the numbers doe…

When multiplying, changing the grouping of the doctors doesn'…

Commutative Property of Addition

When adding numbers, changing the order of the numbers doesn'…

Commutative Property of Multiplication

When multiplying, changing the order of the factors doesn't c…

integer

whole

rational

irrational

whole numbers and their opposites (-2, -3, -1, 0, 1, 2, 3)

zero and up (0, 1, 2, 3, 4)

any number that can be written as a ratio (a/b, cannot =0)

cannot be written as a ratio (pi)

integer

whole numbers and their opposites (-2, -3, -1, 0, 1, 2, 3)

whole

zero and up (0, 1, 2, 3, 4)

Natural numbers are

Whole numbers are

Another way to define whole numbers is

Integers are

the counting numbers 1,2,3,...

the NON negative integers 0,1,2,3,...

the counting numbers plus zero!!

whole numbers and their opposite ...-2,-1,0,1,2,...

Natural numbers are

the counting numbers 1,2,3,...

Whole numbers are

the NON negative integers 0,1,2,3,...

Natural Numbers

Whole Numbers

Integers

Real Numbers

positive integers, natural counting numbers (no zero, 1,2,3,4…

natural numbers AND zero (0,1,2,3)

whole numbers and their opposites (-2,-1,0,1,2)

have points on the number line, all numbers including rationa…

Natural Numbers

positive integers, natural counting numbers (no zero, 1,2,3,4…

Whole Numbers

natural numbers AND zero (0,1,2,3)

Real Numbers

Irrational Numbers

Integers

Whole Numbers

all numbers on the number line... We only deal with real numbers…

a number whose decimal never ends and repeats... Ex: pi, square…

...-3, -2, -1, 0, 1, 2, 3...... There are no decimals or fractio…

0, 1, 2, 3...... Whole #s drop the negative #s.

Real Numbers

all numbers on the number line... We only deal with real numbers…

Irrational Numbers

a number whose decimal never ends and repeats... Ex: pi, square…