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MATH TIPS. for PARENTS. 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) In Algebra: (a + b) + c = a + (b + c).

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Math tips




Number properties the operation called addition

Associative property of 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)In Algebra:(a + b) + c = a + (b + c)

Commutative property of addition
Commutative Property of Addition

  • Changing the order of the numbers (addends) will not change the sum (answer in addition).In Arithmetic:8 + 4 = 4 + 8In Algebra:a + b = b + a

Identity 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 = 6In Algebra:a + 0 = a

Inverse operation of addition
Inverse Operation of Addition

  • Subtraction undoes the operation called addition.In Arithmetic:If 7 + 4 = 11, then11 - 7 = 4 and11 - 4 = 7In Algebra:a + b = c, thenc - a = b and c - b = a

Inverse operation of subtraction
Inverse Operation of Subtraction

  • Addition undoes the operation called subtraction.In Arithmetic:If16 - 9 = 7, then9 + 7 = 16 and 7 + 9 = 16In Algebra:c - b = a, thenb + a = cand a + b = c

Inverse operation of division
Inverse Operation of Division

  • Multiplication undoes the operation called division.In Arithmetic:If 48 / 8 = 6, then8 x 6 = 48and 6 x 8 = 48In Algebra:c / b = a, thenb x a = canda x b = c

Associative property of multiplication
Associative Property of Multiplication

  • Changing the grouping of the factors will not change the product (answer in multiplication).In Arithmetic:(5 x 4) x 2 = 5 x (4 x 2) In Algebra:(a x b) x c = a x (b x c) or (ab) c = a (bc)

Commutative property of multiplication
Commutative Property of Multiplication

  • Changing the order of the factors (multiplicand and multiplier) will not change the product (answer in multiplication).In Arithmetic:6 x 9 = 9 x 6 In Algebra:a x b = b x a or ab = ba

Identity Property of Multiplication

  • The product (answer in multiplication) and 1 is the original number.In Arithmetic:7 x 1 = 7In Algebra:a x 1 = a or a • 1 = a

Multiplication property of zero
Multiplication Property of Zero

  • The product (answer in multiplication) of any number and zero is zero.In Arithmetic:9 x 0 = 0In Algebra:a x 0 = 0 or a • 0 = 0Multiplication is repeated addition.8 x 4 = 8 + 8 + 8 + 8

Distributive Property of Multiplicationover Addition or Subtraction

  • 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.In Arithmetic:OVER ADDITION 5(90 + 10) = (5 x 90) + (5 x 10)OVER SUBTRACTION 5(90 - 10) = (5 x 90) - (5 x 10)In Algebra:OVER ADDITION a(b + c) = (a x b) + (a x c) ora(b + c) = ab + acOVER SUBTRACTION a(b - c) = (a x b) - (a x c)

Glossary of mathematical terms


Add addend addition array

ADDTo put one thing, set or group with another thing, set or group.

ADDENDNumbers to be added.Example: 12 + 23 = 25 a + b + c = abc

ADDITIONThe operation of putting together two or more numbers, things, groups or sets.Example: 8 + 2 + 4 = 14 is an addition problem

ARRAYAn orderly arrangement of persons or things, rows and columns. The number of elements in an array can be found by multiplying the number of rows by the number of columns.Example: * * * * * * * * * * * * * * * * * * 3 x 6 = 18

Associative property of addition multiplication attribute
Associative Property of Addition-Multiplication/Attribute

ASSOCIATIVE PROPERTY OF ADDITIONThe way in which three numbers to be added are grouped two at a time does not affect the sum.Example: 3 + (5 + 6) = (3 + 5) + 6 3 + 11 = 8 + 6 14 = 14

ASSOCIATIVE PROPERTY OF MULTIPLICATIONThe way in which three numbers to be multiplied are grouped two at a time does not affect the product.Example: 3 x (2 x 6) = (3 x 2) x 6 3 x 12 = 6 x 6 36 = 36

ATTRIBUTEA quality that is thought of as belonging to a person of thing. Characteristics; such as, size, shape, color and/or thickness.

Average axis

AVERAGEA 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.STEP 1 STEP 2

86 68is the average 54 How many addends? 4) 272 39 Quantity is 4 - 24 + 93 32272sum or total - 32 0

AXIS (axes)Horizontal and vertical number lines in a number plane.

Bar graph braces
Bar Graph/Braces

Colors the Class Likes

BAR GRAPHA picture in which number informationis shown by means of bars of different lengths.

BRACESBraces are symbols { }. They are used to list names of numbers (elements) of a set.Example: { Pauline, April, Joni, Jackie}is a set of secretaries.

{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}is a set of the days of the week.

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






Capacity cardinal number centigrade cent centimeter
Capacity/Cardinal Number/Centigrade/Cent/Centimeter

CAPACITYThe amount that can be held in a space.

CARDINAL NUMBERA number that tells how many there are.Example: There are five squares

CENTIGRADEDivided 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

CENTA coin of the United States and Canada. One hundred cents make a dollar.

CENTIMETERA unit of length in the metric system. A centimeter is equal to one hundredths of a meter or .39 of an inch.

Century closed figure closure
Century/Closed Figure/Closure

CENTURYA period of one hundred years.

CLOSED FIGUREA geometric figure that entirely encloses part of the plane.

CLOSUREA property of a set of numbers such that the operation with two or more numbers of that set results in a number of the set.Example: In addition and multiplication with counting numbers, the results is a counting numbers. 2 + 4 = 6; 2 x 4 = 8

Thus, the counting numbers are closed under 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.

Combine common common factor common multiple
Combine/Common/Common Factor/Common Multiple

COMBINETo put (join) together.

COMMONBelonging equally to all.

COMMON FACTORA common factor of two or more numbers is a number which is a factor of each of the numbers.Example: 8 = {1, 2, 4, 8} 32 = {1, 2, 4, 8, 16, 32} 1, 2, 4 and 8 are the common factors of 8 and 32

COMMON MULTIPLEA 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

Commutative property of addition multiplication compare composite number
Commutative Property of (Addition)(Multiplication)/Compare/Composite Number

COMMUTATIVE PROPERTY OF ADDITIONThe order of two numbers (addends) may be switched around and the answer (total, sum) is the same.Example: 7 + 4 = 11 and 4 + 7 = 11; therefore, 7 + 4 = 4 + 7

COMMUTATIVE PROPERTY OF MULTIPLICATIONThe order of two numbers (factors) may be switched around and the answer (total product) is the same.Example: 8 x 6 = 48 and 8 x 6 = 48; therefore, 8 x 6 = 6 x 8

COMPARETo study, discover and/or find out how persons or things are alike or different.

COMPOSITE NUMBERA 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.

Conditional sentence congruent figure conjecture conjunction
Conditional Sentence/Congruent Figure/Conjecture/Conjunction

CONDITIONAL SENTENCE (In logically thinking)A sentence of the form “if. . ., then. . .?Example: If 6 x 7 = 42 and 7 x 6 = 42, Then 42  6 = 7 and 42  6 = 7

CONGRUENT FIGUREGeometric shapes consisting of the same shape and size.Example: 8 x 6 = 48 and 8 x 6 = 48; therefore, 8 x 6 = 6 x 8

CONJECTUREA guess resulting from an experiment.Example: 2, 4, 6, 8, 10 are even numbers; therefore, 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.Example: 1/4 + 1/4 = 2/4 = 1/2

Coordinates counting number decade decimal
Coordinates/Counting Number/Decade/Decimal

COORDINATESTo 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.Example: 1, 2, 3, 4, 5. . . *There is no longest number. Counting numbers are infinite.

DECADEA period of ten years.

DECIMALNames the same number as a fraction when the denominator is 10, 100, 1000. . . It is written with a decimal point.Example: .75

Decimal system diagonal degree denominator
Decimal System/Diagonal/Degree/Denominator

DECIMAL SYSTEMA plan for naming numbers that is based on ten is called a decimal system of numeration. The Hindu-Arabic system is a decimal system.

DIAGONALA straight line that connects the opposite corners of a rectangle.Example:

DEGREEA unit of angle measurement.

DENOMINATORIn 3/5 the denominator is 5. It tells the number of equal parts, groups or sets the whole was divided.

Difference digit disjoint sets
Difference/Digit/Disjoint Sets

DIFFERENCEThe number which results when one number is subtracted from another is called the difference. It is a missing addend in addition.Example: 7 - 4 = 3 the difference is 3

DIGITAny one of the basic numerals, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, is a digit.The numeral 12 is a two-digit numeral and the numeral 354 is a three digit numeral.

DISJOINT SETSSets that have no members in common are disjoint sets.Example: Set A = {a, b}, Set B {1, 2, 3}. Sets A and B are disjoint

Distributive property of multiplication over addition divide dividend
Distributive Property of Multiplication over Addition/Divide/Dividend

DISTRIBUTIVE PROPERTY OFMULTIPLICATION OVER ADDITIONMultiplication by the same factor may be distributed over two or more addends.Example: 3 x (6 + 4) = (3 x 6) + (3 x 4) = 18 + 12 = 30

DIVIDETo separate into equal parts, pieces, groups or sets..Example: x x x x x x x x x x 10  2 = 5

DIVIDENDA number that shows the total amount to be separated into equal parts, groups of sets by another number.Example: 100  25 = 4, the dividend is 100

Divisible divisor element element of a set empty set
Divisible/Divisor/Element/Element of a Set/Empty Set Addition/Divide/Dividend

DIVISIBLECapability of being separated equally without a remainder.Example: 18 is divisible by 1, 2, 3, 6, 9 and 18

DIVISORA number that tells what kind of equal parts, groups or sets the dividend is to be separated.

ELEMENTA member of a set.

ELEMENT OF A SETA member of a set.

EMPTY SETThe set which has no members. The number of the empty set is zero. A symbol for the empty set is { }.

Equal endpoint equal sets equal sign
Equal/Endpoint/Equal Sets/Equal Sign Addition/Divide/Dividend

EQUALA relationship between two expressions denoting exactly the same or equivalent quantities.Example: The two expressions 2 + 6 and 3 + 5 are said to be equal because they both denote exactly the same quantity.

ENDPOINTA point at the end of a line segment or ray.

EQUAL SETSTwo sets with exactly the same things, elements or members.Example: A = {1, 2, 3} and B = {3, 2, 1}

EQUAL SIGNThe equal sign shows that two numerals or expressions name the same number.Example: 10 + 9 = 19In a true sentence, the equal sign shows that the numerals on each side of the sign name the same number.

Equation equivalent sets estimate
Equation/Equivalent Sets/Estimate Addition/Divide/Dividend

EQUATIONA number sentence in which the equal sign = is used in an equation.Example: 6 + = 10 and 8 - 3 = are equations

EQUIVALENT SETSIf the members of two sets can be matched one to one, the sets are equivalent. Equivalent sets have the same number of members/elements.

ESTIMATEAn estimate is an approximate answer found by rounding numbers.Example: 22 + 39 = , 22 may be rounded to 20, 39 may be rounded to 40. The estimated sum is 20 + 40 or 60

Even number expanded numeral exponent
Even Number/Expanded Numeral/Exponent Addition/Divide/Dividend

EVEN NUMBERAn integer that is divisible by 2 without a remainder.Example: 0, 2, 4, 6. . . Are even numbers

EXPANDED NUMERALAn expanded numeral is a name for a number which shows the value of the digits.Example: An expanded number for 35 is 30 + 5 or ( 3 x 10) + (5 x 1)

EXPONENTA number which tells how many times a base number issued as a factor. In the example below the base numbers are 10, 3, and 9.Example: 10 = 10 x 10 3 = 3 x 3 x 3 10 = 10 x 10 x 10 x 10 x 10 x 10 9 = 9 x 9 x 9 x 9

Factors factor tree fahrenheit
Factors/Factor Tree/Fahrenheit Addition/Divide/Dividend

FACTORSNumbers to be multiplied. In 2 x 4 = 8, the factor are 2 and 4.FACTOR TREEA diagram used to show the prime factors of a number. Example: 24

6 x 4

2 x 3 2 x 2

24 = 2 x 3 x 2 x 2 or 2 x 3

FAHRENHEITOf 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.

Fraction fractional numbers greater than greatest common factor
Fraction-Fractional Numbers/Greater Than/ Addition/Divide/DividendGreatest Common Factor

FRACTION FRACTIONAL NUMBEREqual 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 THANLarger 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.Example: 8 > 3 is a true sentence

GREATEST COMMON FACTORThe greatest common factor (GCF) of two or more counting numbers is the largest counting which is a factor of each of the counting numbers.Example: 10 = {1, 2, 5} 12 = {1, 2, 3, 4, 6, 12} 2 is the G.C.F. for 10 and 12

Graph Addition/Divide/Dividend

GRAPHA 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.


MonthGirls Present 20

April 10


June 0

Each symbol represents 3 girls 10 11 12 1 2 3

Graphs continued on next page

Graph hindu arabic numeration system
Graph/Hindu Arabic Numeration System Addition/Divide/Dividend


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. . .)Example: 96,5200 = (9 x 10,000) + (6 x 1,000) + (5 x 100) + (2 x 10) + (0 x 1)or (9 x 10) + (6 x 10) + (5 x 10) + (2 x 10) + (0 x 1)

Horizontal identity element of addition multiplication inequality integer
Horizontal/Identity Element of (Addition)(Multiplication)/Inequality/Integer

HORIZONTALStraight across. Travels from west to east and east to west.Example: 965 x 4 = 3,860

IDENTITY ELEMENT OF ADDITIONThe sum of any number and zero is the other number.Example: 6 + 0 = 6

IDENTITY ELEMENT OF MULTIPLICATIONThe sum of any number and one is that number.Example: 6 x 1 = 6

INEQUALITYA mathematical sentence which states that two expressions de not name the same number. The signs < and > are usually used.

INTEGERThe integers consist of the counting numbers, zero and the negatives of the counting numbers.Example: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. . .

Intersection of sets joining sets kilometer
Intersection of Sets/Joining Sets/Kilometer (Addition)(Multiplication)/Inequality/Integer

INTERSECTION OF SETSThe set consisting of all members which are common to two or more sets.Example: 12 14 3 1 7 4 2 6 12 14

JOINING SETSForming one set which contains all the members of two or more sets.Example: If Set A = {a, b} and Set B = {3, 4}, Sets A and B may be joined to form the set C = {a, b, 3, 4}

KILOMETERA unit of length in the metric system. A kilometer (KM) is equal to 1000 meters, or about .62 of a mile.

Least common multiple length
Least Common Multiple/Length (Addition)(Multiplication)/Inequality/Integer

LEAST COMMON MULTIPLEThe 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).

LENGTHThe distance from one end to the other end. Long represents how long something is from the beginning to the end. Endpoint to endpoint.

Less than lowest terms measure measure of a set
Less Than/Lowest Terms/Measure/Measure of a Set (Addition)(Multiplication)/Inequality/Integer

LESS THANSmaller than something else. In less than the symbol “<“ means that the number to the left of the symbol is smaller than the number to the right of the symbol.Example: 104 < 140; 5 + 6 < 6 + 6; 1/6 < 1/4

LOWEST TERMSA fraction is in the lowest or simplest form if the numerator and denominator have no other common factors besides 1.Example: The lowest terms of 8/32 is 1/4

MEASURETo find or show the size, weight or amount of something.

MEASURE OF A SETEach thing belonging to a set is a member of the set. It is also called an element of the set.Example: In a set, A = {R, S, T}, R, S, and T are members/elements of set A.

Meter metric system minuend minus
Meter/Metric System/Minuend/Minus (Addition)(Multiplication)/Inequality/Integer

METERThe basic unit of measure is the metric system. The meter is about 39 inches long.

METRIC SYSTEMA decimal system used for practically all scientific measurement. The standard unit of length is the meter.

MINUENDThe number of things, members or elements in all (whole set) before subtracting.Example: 904 is the minuend of 904 - 756 = 148 The number from which another number is taken away (subtracted).

MINUSDecreased by. Lower or less than.Example: 12 - 5 = 7 The numeral 12 is decreased by 5 or minus 5.

Mixed numeral multiple multiplicand multiplication
Mixed Numeral/Multiple/Multiplicand/Multiplication (Addition)(Multiplication)/Inequality/Integer

MIXED NUMERALA numeral which consists of numerals for a whole number and a fractional number.Example: 3

MULTIPLE A number that is multiplied a certain number of times.Example: Multiples of 10 are 10, 20, 30, 40, 50. . . Multiples of 3 are 6, 9, 12, 15, 18. . .

MULTIPLICAND A number that is to be multiplied by another number.Example: 36 x 14, 36 is the multiplicand

MULTIPLICATIONThe operation of taking a number and adding it to itself a certain number of times.Example: 4 x 3 = 4 + 4 +4 25 x 6 = 25 + 25 + 25 + 25 + 25 + 25

Multiplier multiply natural numbers negative numbers number sentence
Multiplier/Multiply/Natural Numbers/ (Addition)(Multiplication)/Inequality/IntegerNegative Numbers/Number Sentence

MULTIPLIERA number that tells how many times to multiply anotherExample: 7 x 4 means that 7 will be multiplied 4 times.

MULTIPLYTo add a number to itself a certain number of times. Shortcut to addition.

NATURAL NUMBERSCounting numbers.

NEGATIVE NUMBERSNumbers less than 0.Example: -5, -6, -7, -4, -3, -2. . .

NUMBER SENTENCEA sentence of numerical relationship.Example: 2 + 5 = 1 + 6 3 + 8 > 6 1 x 3 < 9 - 2

Numeral numeration numerator
Numeral/Numeration/Numerator (Addition)(Multiplication)/Inequality/Integer

NUMERALA symbol for a number.Example: The number word six may be denoted by 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.

Odd number one to one correspondence
Odd Number/One-to-One Correspondence (Addition)(Multiplication)/Inequality/Integer

ODD NUMBERAn integer which is divisible by 2 with a remainder.Example: ///

ONE-TO-ONE CORRESPONDENCE A one -to-one matching relationship. If to every member in one set there corresponds one and only one member in a second set, and to every member in the second set there corresponds one and only member in the first set, the sets are said to be in one-to-one correspondence.Example: If every seat in a room is occupied by a person, and no person is standing, there is a one-to-one correspondence between the number of persons and the number of seats.

Open sentence operation order
Open Sentence/Operation/Order (Addition)(Multiplication)/Inequality/Integer

OPEN SENTENCEA mathematical sentence which contains a variable such as n, x, , or.Example: 3 + = 8An 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.Example: Addition, subtraction, multiplication, division

ORDER The way in which something is arranged.Example: 1, 2, 3, 4. . . A, B, C, D. . . 9, 8, 7, 6. . . 3, 6, 9, 12. . . Z, Y, X, W. . . First, Second, Third, Fourth. . .

Ordinal number pair per percent
Ordinal Number/Pair/Per/Percent (Addition)(Multiplication)/Inequality/Integer

ORDINAL NUMBERA number which indicates the order place of a member of a set in relation to other members of the same set. Example: 1st, 2nd, 3rd. . .

PAIR Two persons, animals, or things that are alike/ that go together.Example: A pair of gloves

PER For each. Similar and are matched to go together.Example: eggs per dozen

PERCENTRatio with 100 as its second number. Percent means per hundred.Example: % = /100

Picture graph place value prime number
Picture Graph/Place Value/Prime Number (Addition)(Multiplication)/Inequality/Integer

PICTURE GRAPHA graph which uses picture symbols to show number information.Example: The pictograph shows how much money 4 children earned last week. Each means 10 cent.Cierra  Alex      Paul     Calin    

PLACE VALUE 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.

Product product set quotient related sentences or equations
Product/Product Set/Quotient/Related Sentences or Equations (Addition)(Multiplication)/Inequality/Integer

PRODUCTThe number that results when two or more numbers are multiplied. The answer in a multiplication problem.Example: 2 x 3 = 6, the product is 6

PRODUCT SET The set of all couples formed by pairing every member of one set with every member of a second set.

QUOTIENT 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 EQUATIONSRelated sentences give the same number relation in different ways. Example: 4 + 3 = 7, 3 + 4 = 7, 7 - 4 = 3, 7 - 3 = 4 are all related sentences

Remainder scale drawing
Remainder/Scale Drawing (Addition)(Multiplication)/Inequality/Integer

REMAINDERThe difference of the dividend and the greatest multiple of the divisor which is less than the dividend.Example: 17 = (3 x 5) + 2, 3 ) 17 The remainder is 2

The part that’s left over. (xxx) (xxx) (xxx) xxremainder

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.

Score set simplest forms of a fractional numeral standard statistics
Score/Set/Simplest Forms of a Fractional Numeral/Standard/Statistics

SCOREA 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.

STANDARDAnything used to set an example or serve as something to be copied.

STATISTICSCollection data expressed through numerical facts.

Subtract subtraction subtrahend sum
Subtract/Subtraction/Subtrahend/Sum Numeral/Standard/Statistics

SUBTRACTTo take away from the whole group or set.Example: Take Away     5 subtract 2 = 3

SUBTRACTION The act of taking away some things, members or elements in the whole group or set.Example: 202 - 197 = problem

SUBTRAHEND The number of things, members or elements in the whole group or set.

SUMThe number that results when two or more numbers are added is the sum.Example: 3 + 2 = 5, the sum is 5

Symbol total variable
Symbol/Total/Variable Numeral/Standard/Statistics

SYMBOLA letter, numeral or mark which represents quantities, number, operations, or relations.Example: +, -, x,  are symbols for operations =, <, > are symbols for relations The symbol (numeral), 67, may be used to represent the number word, sixty-seven.

TOTAL The whole amount.

VARIABLE A letter or symbol that represents a number. The unknown.Example: N x 20 = 100 - 8 = 5

Vertical weigh weight whole numbers width
Vertical/Weigh/Weight/Whole Numbers/Width Numeral/Standard/Statistics

VERTICALStraight up and down.Example: 567 493+48

WEIGH To measure the heaviness of a person or thing.

WEIGHT The amount of heaviness of a person or thing.

WHOLE NUMBERSThe 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.


GEOMETRY Numeral/Standard/Statistics

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

Common geometric symbols
Common Geometric Symbols Numeral/Standard/Statistics









FOR ANGLE Illustration:ABC

FOR CONGRUENT Illustration:A B C D



FOR PARALLEL Illustration:A B C D



Glossary of geometric terms
Glossary of Geometric Terms Numeral/Standard/Statistics

Adjacent alphabet angle
Adjacent/Alphabet/Angle Numeral/Standard/Statistics




ADJACENTNear or close to something; adjoining.

ALPHABETLetters to name geometric ideas.

ANGLEA model to indicate that a line extends indefinitely in both directions.Illustration:

Area area of a rectangle
Area/Area of a Rectangle Numeral/Standard/Statistics

AREA•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.

AREA OF A RECTANGLE:•The number of square inches in a rectangle equals the number of rows one inch wide times the number of square inches in a row.Illustration:

• The number of square centimeters or square feet in a rectangle is its area.

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


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


Area = Length times width (formula)or

A = L x W orA = LW


Area = One-half the base times the height or A =  bh orA =


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

A = + orA = 2 or A = bh





Arrow bisect common congruent constructions curves
Arrow/Bisect/Common/Congruent/Constructions/Curves (square)(rectangle)(triangle)(parallelogram)

ARROWA model to indicate that a line extends indefinitely in both directions.

BISECTSeparate into two congruent parts.

COMMONThe same.

CONGRUENTFigures, in geometry, that have the same size and shape.

CONSTRUCTIONSGeometric drawings made with only a compass and a straight edge.

CURVESA line having no straight part; bend having no angular part.

Degree diagonal dimension edge enclose
Degree/Diagonal/Dimension/Edge/Enclose (square)(rectangle)(triangle)(parallelogram)

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

DIAGONALIn a polygon, a line segment that joins two non-adjacent vertices; extending slantingly between opposite corners.


DIMENSIONThe measurement of the length and width.

EDGEA line segment formed by the intersection of two faces of a solid figure such as a prism.

ENCLOSEShut in all around; surrounded.

Endpoint face geometric figure geometry intersection
Endpoint/Face/Geometric Figure/Geometry/Intersection (square)(rectangle)(triangle)(parallelogram)






ENDPOINTIn a line segment, the two points at the end of the segment used to name it.

FACEA plane surface of a space figure.

GEOMETRIC FIGUREEvery set of points in space.

GEOMETRYThe study of space and figures in space.

INTERSECTIONA set that contains all the members common to two other sets no other members. The intersection of the model.Illustration:

The intersection of angles AYD and CYD is “Y.”

Line line segment or segment
Line/Line Segment or Segment (square)(rectangle)(triangle)(parallelogram)

LINEA 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.Illustration:



Line of symmetry midpoint of a line
Line of Symmetry/Midpoint of a Line (square)(rectangle)(triangle)(parallelogram)






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.Illustration:

MIDPOINT ON A LINE:The point on a line segment which is the same distance from the endpoints; midway between the endpoints of a line segment.Illustration:

Point symmetry parallel lines
Point Symmetry/Parallel Lines (square)(rectangle)(triangle)(parallelogram)























POINT SYMMETRY:Can be fitted onto itself by making 1/2 turn about a point.Illustration:

PARALLEL LINES:Two lines in the same plane that do not intersect.Illustration:

Perpendicular parallel
Perpendicular/Parallel (square)(rectangle)(triangle)(parallelogram)






PERPENDICULAR BISECTOR:A line which bisects a segment and is perpendicular to it.Illustration:

PARALLELTravel the same direction apart of every point, so as never to meet, as lines, planes, etc.

Perimeter (square)(rectangle)(triangle)(parallelogram)

PERIMETER• 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.1. PERIMETER OF A RECTANGLE:Perimeter = 2 x Length + 2 x Width or P = 2 x L + 2 x W orP = 2 x (L + W)

2. PERIMETER OF A SQUARE:Perimeter = 4 x length of one side or P = S + S + S + S orP = 4S3. PERIMETER OF A TRIANGLE:Perimeter = Side + Side + Side or P = S + S + S

Plane plane figure point
Plane/Plane Figure/Point (square)(rectangle)(triangle)(parallelogram)

PLANETravel the same direction apart of every point, so as never to meet, as lines, planes, etc.Illustration:

PLANE FIGUREAll the points of a figure lying on the same plane.Illustration:a b c d e

POINTAn idea about an exact location; it has no dimensions whatsoever but is represented by a dot (•) There is an unlimited number of lines through a point.






Polygon regular polygon figure plane figures simple closed figure
Polygon (square)(rectangle)(triangle)(parallelogram)(Regular Polygon/Figure/Plane Figures/Simple Closed Figure)

POLYGONA simple closed figure that consists only of line segments.

REGULAR POLYGON:A polygon with congruent sides and congruent angles.

FIGURE:In Geometry, any sets of points.

PLANE FIGURES:Rectangle, square and circle are the most common.

SIMPLE CLOSED FIGURE:A Simple Closed Figure is one that does not intersect (cross) itself. If it is made up of line segments it is called a polygon. Illustration:

Polygon parallelogram pentagon octagon quadrilateral rectangle
Polygon (Parallelogram/Pentagon/Octagon/Quadrilateral/Rectangle)





PARALLELOGRAM:A quadrilateral in which opposite sides are parallel.

PENTAGON:A polygon with five sides.

OCTAGON:An eight-sided polygon.

QUADRILATERAL:A polygon(simple closed figure) formed by four line segments.

RECTANGLE:A quadrilateral (polygon) with two pairs of parallel sides and four right angles (4 sides and 4 square corners). Illustration:

Polygon square trapezoid
Polygon (Square/Trapezoid) (Parallelogram/Pentagon/Octagon/Quadrilateral/Rectangle)




SQUARE:A quadrilateral (polygon) with congruent sides the same length and four right angles. Also, the product when a number is multiplied by itself.Example:3 x 3 = 9, The square of 3 or 3


TRAPEZOID:A quadrilateral (polygon) with only one pair of parallel sides. Illustration:





Polygon triangle
Polygon (Triangle) (Parallelogram/Pentagon/Octagon/Quadrilateral/Rectangle)

















TRIANGLE:A figure (polygon) with three sides.KINDS:1. EQUILATERAL TRIANGLE: A triangle all of whose sides are congruent.

2. ISOSCELES TRIANGLE: A triangle with at least two sides congruent.

3. RIGHT TRIANGLE: A triangle with one right angle.

4. SCALENE TRIANGLE: A triangle with no congruent sides.

• LEGS (of a right triangle): The two sides in a right triangle that are also sides of the right angles.


• HYPOTENUSE: The side opposite the right angle in a right triangle.

Protractor prism ray
Protractor/Prism/Ray (Parallelogram/Pentagon/Octagon/Quadrilateral/Rectangle)










FIGURE 1:RS and SQ are used to form the Acute Angle RSQ

FIGURE 2:DE and EG are used to form the Obtuse Angle DEG

PROTRACTORAn instrument for measuring angles just as a ruler is an instrument for measuring line segments.

PRISMA closed space figure. The bases are congruent polygons in parallel planes.

RAY • A point on a line and all the points in one direction from the point.

• Has infinite length and only one endpoint (vertex).

• The sides of the angle.


Region size space figure straight edge vertex
Region/Size/Space Figure/Straight Edge/Vertex (Parallelogram/Pentagon/Octagon/Quadrilateral/Rectangle)











FIGURE 1:Point B is the Vertexof angle CBA.

FIGURE 2:Point R is the Vertex of Angles QRS, SRT and TRQ.

REGIONA closed curve and all the points inside it.

SIZERefers to the amount of opening between the side (rays) of the angle.

SPACE FIGUREA figure encloses a part of space.

STRAIGHT EDGEHas no marks on it with which measurements can be made; by tracing along its edge one can construct a line segment.

VERTEXA common endpoint of two rays, two segments, or three or more edges of a space figure.Illustration:

Units of measure

UNITS OF MEASURE (Parallelogram/Pentagon/Octagon/Quadrilateral/Rectangle)

Length liquid weight
Length/Liquid/Weight (Parallelogram/Pentagon/Octagon/Quadrilateral/Rectangle)



12 inches (in.) = 1 foot (ft.) 1000 milliliters (mm) = 1 meter 3 feet (ft.) = 1 yard (yd.) 100 centiliters (cm) = 1 meter 36 inches = 1 yard (yd.) 10 deciliters (dm) = 1 meter 5280 feet = 1 mile (MI.) 1000 liters = 1 kilometer



2 cups (c.) = 1 pint (pt.) 1000 milliliters (ml) = 1 liter (l) 2 pints = 1 quart (qt.) 100 centiliters (cl) = 1 liter (l) 4 quarts = 1 gallon (gal.) 10 deciliters (dl) = 1 liter (l) 1000 liters (l) = 1 kiloliter (kl)



16 ounces (oz.) = 1 pound (lb.) 1000 milligrams (mg) = 1 gram (g)2000 pounds = 1 ton (T.) 100 centigrams (cg) = 1 gram 10 decigrams (dg) = 1 gram 1000 grams = 1 kilogram

Equivalent units time
Equivalent Units/Time (Parallelogram/Pentagon/Octagon/Quadrilateral/Rectangle)



2.5 centimeters is about 1 inch. .95 liter is about 1 quart. 28.35 grams is about 1 ounce. .9 meter is about 1 yard. 3.79 liters is about 1 gallon. .45 kilogram is about 1 pound.1.6 kilometers is about 1 mile.


60 seconds (sec.) = 1 minute 60 minutes (min.) = 1 hour 24 hours (hr.) = 1 day 7 days = 1 week (wk.) 365 days = 1 year (yr.) 366 days = 1 leap year 10 years = 1 decade 20 years = 1 score 100 years = 1 century