MATHEMATICAL OPERATIONS

DUFF’S MATH STUFF…MAKING SENSE OF NUMBER SENSE

LESSON 2

WHAT ARE OPERATIONS ???

ALTHOUGH NUMBERS ARE THE MOST IMPORTANT PART OF MATH, WE WOULDN’T BE ABLE TO DO ANYTHING WITH THEM WITHOUT OPERATIONS!

+ - x ÷+ - x ÷ + - x ÷ + - x ÷ + - x ÷

SYMBOLS THAT CONNECT NUMBERS TO FORM MATHEMATICAL EXPRESSIONS ARE REPRESENT

THESE OPERATIONS. THE FOUR MOST BASIC OPERATIONS ARE

ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION

OPERATIONS AND KEY TERMS

OPERATION SYMBOL KEY TERMS

ADDITION + ADD, PLUS, TOTAL, SUM

SUBTRACTION − SUBTRACT, MINUS, LESS THAN, GREATER THAN, DIFFERENCE

MULTIPLICATION x

MULTIPLY, MULTIPLE, TIMES, DOUBLE, TRIPLE, TWICE, PRODUCT

DIVISION ÷ DIVIDE, DIVIDEND, DIVISOR, HALF, PER, EACH, QUOTIENT

OTHER IMPORTANT OPERATIONS IN MIDDLE SCHOOL MATH

EXPONENTS # EXPONENT, POWER, SQUARED, CUBED

SQUARE ROOTS √# SQUARE ROOT

WHEN SOLVING WORD PROBLEMS, THE FOLLOWING KEY TERMS WILL INDICATE WHICH OPERATION WILL HELP YOU FIND A SOLUTION

EXPONENTS

WHEN A SINGLE NUMBER IS MULTIPLIED BY ITSELF REPEATEDLY, EXPONENTS CAN BE

USED TO SIMPLIFY THE WAY THE EXPRESSION LOOKS. THE NUMBER ITSELF

IS CALLED A BASE NUMBER AND THE AMOUNT OF TIMES IT APPEARS IS

REPRESENTED BY THE EXPONENT, SMALL TO THE UPPER RIGHT CORNER

3 x 3 x 3 x 3 x 3 x 3 ≈ 3, SIX TIMES ≈ 36

SQUARE ROOTSPERFEC

T SQUARE

‘WORK’ ROOT

√1 1 ÷ 1 = 1 1

√4 4 ÷ 2 = 2 2

√9 9 ÷ 3 = 3 3

√16 16 ÷ 4 = 4 4

√25 25 ÷ 5 = 5 5

√36 36 ÷ 6 = 6 6

√49 49 ÷ 7 = 7 7

√64 64 ÷ 8 = 8 8

√81 81 ÷ 9 = 9 9

√100100 ÷ 10

= 10 10

A SPECIAL KIND OF DIVISION, IN WHICH THE DIVISOR AND

QUOTIENT ARE THE SAME NUMBER, IS CALLED A SQUARE

ROOT. SQUARE ROOTS ARE THE INVERSE OF SQUARING A NUMBER (EXPONENTS OF 2)

A NUMBER WHOSE SQUARE ROOT IS A WHOLE NUMBER IS CALLED A PERFECT SQUARE – SINCE WHOLE NUMBERS ARE RATIONAL, PERFECT SQUARES

HAVE RATIONAL ROOTS.

ALL TH E NUMBERS ‘SKIPPED’ ON THE LIST OF PERFECT

SQUARES (2,3,5,6,7,8,10, 11…) HAVE DECIMAL ROOTS, WHICH

MAKES THEM IRRATIONAL

THE ORDER OF OPERATIONSEXPRESSIONS CONTAINING MANY OPERATIONS MUST BE SOLVED IN AN ORGANIZED WAY. THE ACRONYM IS USED TO REPRESENT

THE CORRECT ORDER OF PERFORMING OPERATIONS

P.E.M.D.A.S.…IT STANDS FOR:

PARENTHESIS, EXPONENTS, MULTIPLICATION & DIVISION, ADDITION & SUBTRACTION

*PARENTHESIS IS NOT AN OPERATION, IT MEANS THAT ANY OPERATIONS INSIDE PARENTHESIS SHOULD BE DONE FIRST

*SINCE EXPONENTS AND SQUARE ROOTS ARE INVERSES, THEY SHOULD BE DONE SECOND IN EVALUATING AN EXPRESSION

*MULTIPLICATION AND DIVISION SHOULD BE DONE AS THEY APPEAR IN A MATHEMATIC SENTENCE FROM LEFT TO RIGHT

LESSON 2 VOCABULARY REVIEWTERM DEFINITION

OPERATION

NON-NUMERIC SYMBOLS INDICATING HOW TO COMBINE OR SEPARATE THE VALUES IN A MATHEMATICAL EXPRESSION (ADDITION AND SUBTRACTION ARE OPERATIONS, REPRESENTED BY THE SYMBOLS ‘+’ AND ‘–‘ )

SUMSOLUTION TO AN ADDITION PROBLEM (4 +3 IS 7, OR THE SUM OF 4 AND 3 IS 7)

DIFFERENCESOLUTION TO A SUBTRACTION PROBLEM (8 – 2 = 6 OR THE DIFFERENCE OF 8 AND 2 IS 6)

PRODUCTSOLUTION TO A MULTIPLICATION PROBLEM (4X7 IS 28 OR THE PRODUCT OF 4 AND 7 IS 28)

QUOTIENTSOLUTION TO A DIVISION PROBLEM (10÷5=2 OR THE QUOTIENT OF 10 AND 5 IS 2)

EXPONENT

A SMALL NUMBER LOCATED TO THE UPPER RIGHT OF A BASE NUMBER; IT INDICATES THE AMOUNT OF TIMES TO MULTIPLY THE BASE TIMES ITSELF (IN 43, THE EXPONENT IS 3…IT TELLS US TO MULTIPLY 4 TIMES ITSELF 3 TIMES)

TERM DEFINITION

BASE NUMBER

LARGE NUMBER WITH EXPONENT TO THE UPPER RIGHT; IT WILL BE MULTIPLIED TIMES ITSELF BASED ON THE NUMBER IN THE EXPONENT (IN 73, THE BASE NUMBER IS SEVEN)

SQUARE ROOT

“SPECIAL DIVISION” IN WHICH THE DIVISOR AND QUOTIENT ARE THE SAME NUMBER (64 DIVIDED BY 8 IS 8, SO THE SQUARE ROOT OF 64 IS 8)’√’IS THE SYMBOL TO REPRESENT THIS OPERATION

PERFECT SQUARE

ANY NUMBER WHOSE SQUARE ROOT IS A COUNTING NUMBER (1, 4, 9, 16, AND 25 ARE THE FIRST FIVE PERFECT SQUARES IN THE REAL NUMBER SYSTEM, THEIR SQUARE ROOTS ARE 1, 2, 3, 4, AND 5)

EXPRESSIONANY MATHEMATICAL SENTENCE CONTAINING OPERATIONS, NUMBERS, AND/OR VARIABLES (3+7 IS AN EXPRESSION; SO IS 5n – 13)

ORDER OF OPERATIONS

THE PROCEDURE FOR PERFOMING OPERATIONS WHEN A MATHEMATICAL EXPRESSION CONTAINS MORE THAN ONE OPERATION: ANYTHING INSIDE OF PARENTHESIS, FOLLOWED BY ANY EXPONENTS (OR SQUARE ROOTS), THEN MULTIPLICATION AND/OR DIVISION AS IT APPEARS FROM LEFT TO RIGHT, AND FINALLY ANY ADDITION OR SUBTRACTION FROM LEFT TO RIGHT

PEMDAS

THIS ACRONYM REPRESENTS THE ORDER OF OPERATIONS: ‘P’ IS PARENTHESIS, ‘E’ IS EXPONENTS, ‘M’ AND ‘D’ ARE MULTIPLICATION AND DIVISION, ‘A’ AND ‘S’ ARE ADDITION AND SUBTRACTION

LESSON 2 VOCABULARY REVIEW