NUMBER PROPERTIES THE OPERATION CALLED ADDITION

NUMBER PROPERTIESTHE OPERATION CALLED ADDITION... Identity Property of Addition• Zero added to any given number given addend, the sum will equal the given number given addend... Distribu

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NUMBER PROPERTIES

THE OPERATION CALLED ADDITION

Associative Property of Addition:

• Changing the grouping of the terms (addends) will not

change the sum (answer in addition).

In Arithmetic: (5 + 3) + 2 = (3 + 2)

• Changing the order of the numbers (addends) will not

change the sum (answer in addition).

In Arithmetic: 8 + 4 = 4 + 8

Commutative Property of Addition

Identity Property of Addition

• Zero added to any given number (given addend), the sum will equal the given number (given addend).

In Arithmetic: 6 + 0 = 6

• Subtraction undoes the operation called addition.

THE OPERATION CALLED SUBTRACTION

• Addition undoes the operation called subtraction.

THE OPERATION CALLED DIVISION

• Multiplication undoes the operation called division.

THE OPERATION CALLED MULTIPLICATION

• Changing the grouping of the factors will not change the

product (answer in multiplication).

• Changing the order of the factors (multiplicand and

multiplier) will not change the product (answer in

• The product (answer in multiplication) and 1 is the original

• The product (answer in multiplication) of any number and

• Multiplication by the same factor may be distributed over

two or more addends This property allows you to multiply each term inside a set of parentheses by a term inside the parentheses *In many cases this is an excellent vehicle for mental math.

Distributive Property of Multiplication

over Addition or Subtraction Distributive Property of Multiplication

over Addition or Subtraction

GLOSSARY of

MATHEMATICAL TERMS

* * * * * *

Add/Addend/Addition/Array

ASSOCIATIVE PROPERTY OF ADDITION

The way in which three numbers to be added are grouped two at a time does not affect the sum

3 + 11 = 8 + 6

14 = 14

ASSOCIATIVE PROPERTY OF MULTIPLICATION

The way in which three numbers to be multiplied are grouped two

at a time does not affect the product

3 x 12 = 6 x 6

36 = 36

ATTRIBUTE

A quality that is thought of as belonging to a person of thing

Characteristics; such as, size, shape, color and/or thickness

Associative Property of Addition-Multiplication/Attribute

A number found by dividing the sum (total) of two or the sum

(total) of two or more quantities by the number of quantities

The average of 86, 54, 9 and 93 is 68

BAR GRAPH

A picture in which number information

is shown by means of bars of

{1, 2, 3, 4, 5, 6, 7, 8, 9} is a set of counting numbers from 1 to 9.

Colors the Class Likes

25 20 15 10 0

Bar Graph/Braces

The amount that can be held in a space

CARDINAL NUMBER

A number that tells how many there are

CENTIGRADE

Divided into one hundred degrees (100%) On the centigrade

temperature scale, freezing point is at zero degrees (0%) The boiling point water is at one hundred degrees (100º)

* Celsius scale is the official name of the temperature

Example: In addition and multiplication with counting

numbers, the results is a counting numbers.

2 + 4 = 6; 2 x 4 = 8

these two operations.

In subtraction, if 4 is subtracted from 2, the result (-2) is not a counting number Also in dividing a

2 by 4, the results (1/2) is not a counting number Thus, the counting numbers are not closed with respect to subtraction and division.

Century/Closed Figure/Closure

A common multiple of two or more numbers is a number which is

a multiple of each of the numbers

Example: 12 = {12, 24, 36, 48, 72, 84, 96, 108, 120}

15 = {15, 30, 45, 60, 75, 90, 105, 120, 135, 150}

60 and 120 are the common multiples

Combine/Common/Common Factor/Common Multiple

COMMUTATIVE PROPERTY OF ADDITION

The order of two numbers (addends) may be switched around and the answer (total, sum) is the same

therefore, 7 + 4 = 4 + 7

COMMUTATIVE PROPERTY OF MULTIPLICATION

The order of two numbers (factors) may be switched around and the answer (total product) is the same

A number which has factors other than itself and one

Since 16 = 1 x 16, 2 x 8 and 4 x 4, it is a composite number.

Commutative Property of (Addition)(Multiplication)/

Compare/Composite Number

CONDITIONAL SENTENCE (In logically thinking)

A sentence of the form “if ., then .?

A guess resulting from an experiment

even numbers must have 0, 2, 4, 5, or 8

in the ones’ place.

CONJUNCTION (In logically thinking)

A two-part sentence joined by “and” to form true parts

Conditional Sentence/Congruent Figure/Conjecture/Conjunction

To numbers, an ordered pair, used to plot a point in a number

plane

COUNTING NUMBER (Natural Numbers)

To numbers, an ordered pair, used to plot a point in a number

plane

*There is no longest number.

Counting numbers are infinite.

DECADE

A period of ten years

DECIMAL

Names the same number as a fraction when the denominator is

10, 100, 1000 It is written with a decimal point

Coordinates/Counting Number/Decade/Decimal

DECIMAL SYSTEM

A plan for naming numbers that is based on ten is called a

decimal system of numeration The Hindu-Arabic system is a

In 3/5 the denominator is 5 It tells the number of equal parts,

groups or sets the whole was divided

Decimal System/Diagonal/Degree/Denominator

DISJOINT SETS

Sets that have no members in common are disjoint sets

Sets A and B are disjoint

Difference/Digit/Disjoint Sets

DISTRIBUTIVE PROPERTY OF

MULTIPLICATION OVER ADDITION

Multiplication by the same factor may be distributed over two or more addends

Distributive Property of Multiplication over Addition/Divide/Dividend

Capability of being separated equally without a remainder

A relationship between two expressions denoting exactly the same

or equivalent quantities

said to be equal because they both denote exactly the same quantity.

In a true sentence, the equal sign shows that the numerals on

Equal/Endpoint/Equal Sets/Equal Sign

EVEN NUMBER

An integer that is divisible by 2 without a remainder

Of or according to the temperature scale of which 32 degrees

(32º) is the freezing point of water and 212 degrees is the boiling point of water

Factors/Factor Tree/Fahrenheit

FRACTION FRACTIONAL NUMBER

Equal parts of a whole thing, group or set A number named by a numeral such as 1/2, 2/3, 6/2, 8/4

GREATER THAN

Larger than or bigger than something else In greater than the

symbol >, means that the number named at the left is greater than the number named at the right

GREATEST COMMON FACTOR

The greatest common factor (GCF) of two or more counting

numbers is the largest counting which is a factor of each of the counting numbers

12 = {1, 2, 3, 4, 6, 12}

2 is the G.C.F for 10 and 12

Fraction-Fractional Numbers/Greater Than/

Greatest Common Factor

A graph shows two sets of related information by the use of

pictures, bars, lines or a circle Graphs may be constructed using horizontal or vertical positions

April

10

May

Each symbol represents 3 girls 10 11 12 1 2 3

Graphs continued on next page

GRAPHS (continued)

10,000 9,000 8,000 7,000 6,000 5,000 4,000 3,000 2,000 1,000 0

Caribbean Red North Japan

HINDU ARABIC NUMERATION SYSTEM

(Base Ten Decimal Numeration System)

There are 10 digits; namely, 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 All

whole numbers may be represented by using the digits and Base Ten place value (one, tens, hundreds .)

Straight across Travels from west to east and east to west

IDENTITY ELEMENT OF ADDITION

The sum of any number and zero is the other number

IDENTITY ELEMENT OF MULTIPLICATION

The sum of any number and one is that number

The integers consist of the counting numbers, zero and the

negatives of the counting numbers

Horizontal/Identity Element of (Addition)

(Multiplication)/Inequality/Integer

Sets A and B may be joined to form the set C = {a, b, 3, 4}

KILOMETER

A unit of length in the metric system A kilometer (KM) is equal to

1000 meters, or about 62 of a mile

Intersection of Sets/Joining Sets/Kilometer

LEAST COMMON MULTIPLE

The least common multiple of two or more counting numbers is the smallest counting numbers which is a multiple of each of the counting numbers

Example: What are some multiples of both 4 and 6?

Set of multiples of 4 = {4, 8, 12, 16, 20, 24, 28, 32, .} Set of multiples of 6 = {6, 12, 18, 24, 30, 36, .}

12 is multiple of both 4 and 6 Another multiple of both 4 and 6

is 24 Therefore, 12 and 24 are called common multiples of 4

and 6 12 is the Least Common Multiple (LCM).

Less Than/Lowest Terms/Measure/Measure of a Set

The basic unit of measure is the metric system The meter is

about 39 inches long

The number from which another number

is taken away (subtracted).

A number that is multiplied a certain number of times.

Multiples of 3 are 6, 9, 12, 15, 18 .

MULTIPLICAND

A number that is to be multiplied by another number

A number that tells how many times to multiply another

will be multiplied 4 times.

A symbol for a number

the symbol 6; thus, 6 is a numeral.

NOTE: The fundamental operations(addition, subtraction,

multiplication, division) are performed with numbers, not with numerals.

The word “numeral” is used only when referring to the whether to use the word “number” or “numeral,” use the word

NUMERATION

A system to name numbers in various ways

NUMERATOR

In 3/5, the numerator is 3 The numerator tells the number of

equal parts, groups or sets that is being used

Numeral/Numeration/Numerator

person, and no person is standing, there

is a one-to-one correspondence between the number of persons and the number

of seats.

Odd Number/One-to-One Correspondence

OPEN SENTENCE

A mathematical sentence which contains a variable such as n, x,

, or .

An open sentence cannot be judged true or false When the

variable is replaced by a numeral, the open sentence becomes a statement

OPERATION

A specific process for combining quantities

Two persons, animals, or things that are alike/ that go together.

PER

For each Similar and are matched to go together

PICTURE GRAPH

A graph which uses picture symbols to show number information

Place value is the value of each place in a plan for naming

numbers The value of the first place on the right, in our system of naming whole numbers is one The value of the place to the left of ones place is then [Tens/Ones]

PRIME NUMBER

A number greater than one which has factors of only itself and

one 2, 3, 5, 7, 11 and 13 are just a few of the prime numbers

Picture Graph/Place Value/Prime Number

In 6 - 2 = 3, 3 is the quotient For 13  2, 13 = 2 x 6 + 1;

6 is the quotient and 1 is the remainder

RELATED SENTENCES OR EQUATIONS

Related sentences give the same number relation in different

ways

7 - 4 = 3, 7 - 3 = 4 are all related sentences

Product/Product Set/Quotient/Related Sentences or Equations

The difference of the dividend and the greatest multiple of the

divisor which is less than the dividend

The remainder is 2 The part that’s left over.

(xxx) (xxx) (xxx) xx remainder

3 Remainder 2

3 )11

- 9 2

SCALE DRAWING

A drawing the same shape as an object, but which may be larger, the same size, or smaller than the object

Remainder/Scale Drawing

A period of twenty years

SET

A set is a collection or group of objects which may be physical

things, points, numbers, and so on

SIMPLEST FORMS OF A FRACTIONAL NUMERAL

In simplest form, the greatest common factor of the numerator and the denominator is one

STANDARD

Anything used to set an example or serve as something to be

copied

STATISTICS

Collection data expressed through numerical facts

Score/Set/Simplest Forms of a Fractional

Numeral/Standard/Statistics

To take away from the whole group or set

A letter, numeral or mark which represents quantities, number, operations, or relations

=, <, > are symbols for relations The symbol (numeral), 67, may be used

Straight up and down

493 +48

The numbers which tell “how many” are whole numbers The set

of whole numbers contains the counting numbers and zero

Set of Whole Numbers = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 .} They are infinite.

WIDTH

The distance from one side of something to the other side How wide something is from one side to the other side

Vertical/Weigh/Weight/Whole Numbers/Width

Our environment contains many physical objects for which mathematicians have developed geometric ideas These objects then serve as models of the geometric ideas.

TO NAME A LINE. Illustration: AB MEANS LINE AB.

TO NAME A LINE SEGMENT Illustration: AB MEANS LINE SEGMENT AB

TO NAME A RAY Illustration: AB MEANS RAY AB.

FOR ANGLE Illustration: ABC

FOR CONGRUENT Illustration: A B C D

AB CD

FOR TRIANGLE Illustration: ABC

FOR PARALLEL Illustration: A B

Glossary of Geometric Terms

• The amount of space enclosed by a plane figure (simple closed figure).

• The measure of the interior (region) of a simple closed figure.

NOTE: The measure of the interior of a simple closed figure is called its area-measure.

• The measure of a region is expressed by such terms as: square inches,

square centimeters, square feet, square yard, square meter, etc.

• The area of a square one inch long and one inch wide is a square inch.

• The area of a square one foot long and one foot wide is a square foot.

• The area of a square one yard long and one yard wide is a square yard.

• The area of a square one meter long and one meter wide is a square meter.

TO FIND THE AREA OF A SQUARE:

Area = Side Squared or A = S x S or A = S

TO FIND THE AREA OF A RECTANGLE:

Area = Length times width (formula)

or

A = L x W or A = LW

TO FIND THE AREA OF A TRIANGLE:

Area = One-half the base times the height

or

A =  bh or A =

TO FIND THE AREA OF A PARALLELOGRAM:

Area = Base times height over two plus base times height over two

or

A = + or A = 2 or A = bh

bh 2

bh 2

bh

2 (bh) 2

Finding the area of (square)(rectangle)(triangle)(parallelogram)

A standard unit of measure used in the measurement of angles.

DIAGONAL

In a polygon, a line segment that joins two non-adjacent vertices;

extending slantingly between opposite corners.

A set of points.

Illustration:

• The word “line” means straight line.

• Extends indefinitely in each of its two directions.

• A geometric line is the property these models of lines have

in common; it has length but no thickness and no width;

it is an idea.

• The edge of a ruler, a taut string or wire or an edge of this page

is a model of a line.

LINE SEGMENT or SEGMENT:

• A part of a straight line consisting of two points, called endpoints, and all the points that are between these points on the line.

• Has definite length.

LINE OF SYMMETRY:

A line which divides a figure into two congruent parts When a figure is folded along a line symmetry, the parts fit exactly on one another.

D C

Y S

X R

Z Y

X W

Point Symmetry/Parallel Lines

Perpendicular/Parallel

• The distance around a figure (polygon).

• The perimeter of any polygon can be found by adding the measures of the sides of the polygon, if they are given in the same unit.

• When you find the perimeter of a figure, the length and the width must be in the same units.

1 If the dimensions of a figure are in inches , the perimeter will be in inches

2 If the dimensions of a figure are in centimeters , the perimeter will be in

centimeters

3 If the dimensions of a figure are in feet , the perimeter will be in feet

• Finding the perimeter of any polygon is based on addition of measures.

• The perimeter of some polygons can be expressed by a formula.