Multiply Decimals Multiply # s, Ignore Decimals, Count # of Decimals, Place in Product from right counting in to left
|
|
- Noah Hopkins
- 6 years ago
- Views:
Transcription
1 Multiply Decimals Multiply # s, Ignore Decimals, Count # of Decimals, Place in Product from right counting in to left Dividing Decimals Quotient (answer to prob), Dividend (the # being subdivided) & Divisor (# of equal parts dividend is to be subdivided into) Decimal always placed after ones in dividend, zeros can be added indefinitely to the right Terminating Decimal (an exact answer is achieved) Repeating Non-Terminating Decimal (a bar is used over the repeat to show, never use fractions in a decimal, don t round unless specifically asked or need to for a real-world application) Non-Repeating Non-Terminating Decimals are irrational numbers and can t be achieved by dividing one # by another Division by decimal: Move decimal out of divisor, moving it the same number of places (to the right) in the dividend Multiplication Property of Zero Anything times zero is zero: a 0 = 0 Sets of Numbers A group or collection of things (elements or members); In math numbers form sets Real Numbers (R) Natural Numbers (N): subset of real, whole, integers, rationals Whole Numbers (W): subset of real, integers, rationals Integers (Z): can be subdivided into positive (whole numbers) and negative integers; subset of reals & rationals Rational Numbers (Q): subset of reals; mutually exclusive of irrationals Irrational Numbers (I): subset of reals; mutually exclusive of rationals Subset is a set contained within another set Comparison of Numbers < is less than, > is greater than, is less than or equal to & is greater than or equal to How to tell apart: Old way is little eats big, new way is point out the small guy Order Property of Real # s: On # line left gets smaller & right gets bigger (neg. are all smaller than pos.) Decimals: Compare number by number, find the smaller, you ve found the smaller Fractions: Cross mult. up (denom to num) and the larger product is larger fraction Neg. # s: Larger the number looks without it s sign the smaller it is! Adding Fractions Must have an LCD to add Find LCD by prime factorization and unique primes to highest exponent (find product) Build higher terms by using Fundamental Theorem of Fractions (mult. old denom by constant to get LCD & mult. old num by same constant to get new num) All fractional answer are in lowest terms/reduce. Fundamental Thm of Fractions to divide out GCF Improper Fractions should be changed to mixed # s Integer Addition Subtraction is not allowed, change to addition by adding the opposite of the number following the subtraction symbol Like Signs when adding the numbers add and you keep the sign Unlike Signs when adding the big minus the small and bigger # s sign is sign of answer Absolute Value The distance from zero regardless of direction (the number w/out its sign) Absolute values DON T distribute ; they are grouping symbols do problem inside and then take abs. val Y. Butterworth Translation Problems Review 1
2 Order of Operations PEMDAS Parentheses, Exponents, Mult/Division (left to right order), Add/Subt. (left to right order) Parentheses is generic for grouping symbols which include parentheses, brackets, braces, absolute values, radicals, fractions bars Most common errors: add/subt. before mult. divide & mult. before dividing Adding/Subtracting Decimals Line up decimal places and add/subtract as normal, bringing down the decimal as it is crossed Multiplying Integers + + = +, = +, + = or + = Multiplying Fractions Cancel if possible (dividing out a common factor from num & denom) Mult. numerators & mult. denominators If improper change to mixed number Check for common factors, especially if you didn t try to cancel Exponents Represents repeated multiplication (base used as a factor number of times indicated by exponent) Fractions: numerator & denominator to exponent (if lowest terms to start will be in lowest terms in end) Decimals: see mult. decimals Grouping Symbols: Simplify inside 1 st then take single number to power One to any power is one: 1 n = 1 Negative number to even power (parentheses around the negative #) is always positive Neg. # to odd power (parentheses around neg. #) is always negative -a n (-a) n when n is even -a n is read as: The opposite of a to the n th power (-a) n is read as: A negative number used as a factor n times Anything to the zero power is one: a 0 = 1 Evaluation Put in the values given for the variables, using parentheses to replace the variables with the values Simplify using order of operations Distributive property should never be used in lieu of order of operations This is taught as a first step in a check for an equation, and it s use in many solution methods Properties of the Real Numbers Commutative Property of Addition and of Multiplication (move addend/factors around) Associate Property of Addition and of Multiplication (group addends/factors in different orders) Identity Property of Addition and of Multiplication (gives back the identity using identity element) Identity Element of Addition: ZERO Identity Element of Multiplication: ONE Inverse Property of Addition and of Multiplication (inverse is used to give back identity element) Distributive Property (Multiplication distributes over add/subt) Division by Zero: UNDEFINED Zero Divided by Anything: ZERO (division is multiplication by a recip so becomes zero times anything) Multiplication by Zero: ZERO Translation There is a whole separate sheet with all the translation nuances Y. Butterworth Translation Problems Review 2
3 Solving Equations Simplify: 1) Distribute 1 st 2) Clear fractions/decimals 3) Combine like terms Addition Property of Equality used to move things that are add/subt. from one another across the equal sign (can be used twice) Multiplication Property of Equality used to remove numeric coefficient of variable (last step used only once) Give answers as x = #, or as a solution set in roster form 3 Types of Equations: 1) Conditional 2) Identity 3) Contradictions 3 Types of Solutions from 3 Types of Eq.: 1) Single Solution 2) All Real Numbers 3) No Solution Solving an Equation for 1 Variable Follow the process for solving an equation, only focusing on the variable of interest Percentage Problems Percentage to decimal conversion: Move the decimal 2 places left (remember that decimal always comes after ones position) Decimal to Fraction Conversion: Read the decimal and write what you read or count the number of decimal places and put the number in the decimal over a factor of 10 with the number of decimal places that you just counted Set up as algebra problem: % of (whole) is (part) where percent as a decimal is multiplied by the whole and is equal to the part Set up as a proportion: is over of equals some part of one hundred Simple Interest: PRT = I % Increase/Decrease Problems: Original Price (op) is unknown and % is a known, and final result is known (price after increase or decrease) % of (op) is (increase/decrease) and then an equation results: op ± increase/decrease = price after which can be solved for op This is not all the concepts in Chapter 1, but this is an adequate review. I do not have time to cover every concept in the detail that I would like. I will leave it to you to review on your own and to look over my supplementary notes (Ch. 1 on my web page). Please do not put the review on the back burner, for it may become very important sometime in the very near future! Y. Butterworth Translation Problems Review 3
4 Addition Word Phrasing Symbols Sum The sum of 7 and more than 5 more than added to 6 added to greater than 7 greater than increased by 4 increased by years older than 15 years older than John. John is total of The total of 6 and plus 8 plus Subtraction Word Phrasing Symbols difference of The difference of 5 and 2 The difference of 2 and *years younger than Sam's age if he is 3 years younger than John. John is diminished by 15 diminished by 9 21 diminished by *less than 17 less than 49 7 less than decreased by 29 decreased by decreased by *subtract(ed) from Subtract 13 from 51 Subtract 51 from take away 79 take away subtract 54 subtract less 16 less * - Means that the numbers come in opposite order than they appear in the sentence. Multiplication Word Phrasing Symbols product The product of 6 and times 24 times 7 24(7) twice Twice 24 2(24) multiplied by 8 multiplied by 15 8*15 at 9 items at $5 a piece ($5)9 "fractional part" of A quarter of 8 (¼)(8) or 8 / 4. "Amount" of "$" or Amount of money in 25 dimes ($0.1)(25) or (10)(25) " " (nickels, quarters, pennies, etc.) percent of 3 percent of (15) Division Word Phrasing Symbols divide Divide 81 by quotient The quotient of 6 and 3 The quotient of 24 and divided by 100 divided by divided by ratio of The ratio of 16 to 8 The ratio of 8 to shared equally among 65 apples shared equally among 5 people 65 5 Note: Division can also be written in the following equivalent ways, i.e. x 6 = x/6 = 6 x = x 6 Y. Butterworth Translation Problems Review 4
5 Exponents Words Phrasing Algebraic Expression squared Some number squared x 2 square of The square of some number x 2 cubed Some number cubed x 3 cube of The cube of some number x 3 (raised) to the power of Some number (raised) to the power of 6 x 6 Equality Words Phrasing Algebraic Equation yields A number and 7 yields 17. Let x = #. x + 7 = 17 equals 7 and 9 equals = 16 is The sum of 5 and 4 is = 9 will be 12 decreased by 4 will be = 8 was The quotient of 12 and 6 was = 2 Note: Any form of the word is can be used to mean equal. Parentheses Parentheses are indicated in four ways. The first is the use of a comma, such as: The product of 5, and 16 less than a number. The second is the use of two operators' phrases next to one another, such as: 17 decreased by the sum of 9 and 2. *Notice how decreased by is followed by the sum of and not a number, this indicates that we will be doing the sum first; hence a set of parentheses will be needed. Next, you may notice that the expected 'and' between the two numbers being operated on is after a prepositional phrase [A phrase that consists of a preposition (usually of in our case) and the noun it governs (usually number in our case) and acts like an adjective or adverb]. Such as: The sum of 9 times a number and the number. *Usually we would see the 'and' just after the number 9, but it does not appear until after the prepositional phrase 'of 9 times a number'. If you think of this in a logical manner, what you should see is that you have to have two numbers to operate on before you can complete the operation, which would require the use of parentheses to tell you to find a number first! Finally, you may notice a phrase containing another operator after the 'and' where you would expect a number. An example here might be: The difference of 51 and the product of 9 and a number. *The note about thinking in a logical manner applies here too! You must have two numbers to operate on! Y. Butterworth Ch. 1 Concepts Review Int. Alg. FTHL 5
6 Chapter 1 Pretest Circle the best answer. Support with work whenever possible. 1. (-6.4)(3)(0) = (5)(0)(5) a) True b) False < -13 a) True b) False 3. Simplify: (- 4 / 9 ) (- 3 / 4 ) a) 11 / 36 b) -1 7 / 36 c) - 1 / 9 d) 19 / Simplify: a) 18 b) 12 c) 32 d) Simplify: 5(-0.2) (0.1)(2) a) -1.2 b) 0.8 c) -0.8 d) Simplify: (3) a) 0 b) -4 c) 14 d) Simplify: 4(- 4 / 5 ) 3 2 (2) + ( 2 / 3 ) 2 a) / 9 b) 1 / 81 c) - 7 / 36 d) / Simplify: (-3 + 1) (4) a) - 1 / 2 b) - 1 / 6 c) 3 / 5 d) 1 / 2 9. Evaluate when x = 6, y = -1 and z = 0: x + 6y z 6x y + z a) 1 / 37 b) 0 c) 5 12 / 37 d) undefined Y. Butterworth Ch. 1 Concepts Review Int. Alg. FTHL 6
7 10. Name the property illustrated: 3(x + y) = 3(y + x) a) associative prop. of mult. b) communtative prop. of add. c) distributive property d) associative prop. of add. 11. Name the property illustrated: (a + b) 0 = 0 a) multiplicative identity prop. b) assoiciative prop. of add. c) multiplicative prop. of zero d) distributive prop. 12. Translate the statement using mathematical symbols. The quotient of seven and the sum of x and two is equal to four. a) 7 = 4 b) 7(x + 2) = 4 x + 2 c) 7 = 4 d) 7 = 4 x 2 x Translate the statement using mathematical symbols. The difference of 3 and twice x, multiplied by 4, is 12. a) 4(3 2x) = 12 b) 3 2x = 4(12) c) 3 4(2x) = 12 d) 4(3 + 2x) = Translate the statement using mathematical symbols. Eight less than x is twice x. a) 8 x = 2x b) x 8 = x 2 c) x 8 = 2x d) 8 x = x Translate the statement using mathematical symbols. Three times x squared subtracted from 5 is the product of 8 and x. a) 3x 2 5 = 8x b) 3(x 2 5) = 8x c) 5 3x 2 = 8x c) 3(5 x 2 ) = 8 / x 16. Solve: -4(2 3x) = -(4 + x) 3(x + 2) a) x = - 1 / 8 b) x = -1 c) x = 5 / 7 d) x = 1 Y. Butterworth Ch. 1 Concepts Review Int. Alg. FTHL 7
8 17. Solve: 3x 5 + 8(x 4) = 5(2x 7) a) x = 4 b) x = -26 c) x = -4 d) x = Solve: 2x + 5 = 4x a) x = -3 3 / 8 b) x = -7 3 / 4 c) x = / 4 d) x = -1 3 / Solve: 6 5m = 5 3(m + 1) 2m + 4 a) No Sol.or b) m = 5 / 6 c) m = 0 d) All Real # s 20. Solve for y: 5x + 11y = 6 a) y = 5x / / 11 b) y = 11 / 6 5x / 6 c) y = 6 / 11 5x / 11 d) y = 11 / 5 6x / Solve for y: 4 / x + 3 / y = 1 / z a) y = 4xz b) y = 3xz z 3x 4z x c) y = 3xz b) y = 3xz 4x z x 4z 22. Jose is deciding whether to accept a sales position at an electronics store. He is offered a salary of $1200 monthly plus a 8% commission on his sales. If his sales are $12,000, what is his pay? a) $2160 b) $960 c) $1056 d) $2560 Y. Butterworth Ch. 1 Concepts Review Int. Alg. FTHL 8
Integers are whole numbers; they include negative whole numbers and zero. For example -7, 0, 18 are integers, 1.5 is not.
What is an INTEGER/NONINTEGER? Integers are whole numbers; they include negative whole numbers and zero. For example -7, 0, 18 are integers, 1.5 is not. What is a REAL/IMAGINARY number? A real number is
More informationGateway Regional School District VERTICAL ALIGNMENT OF MATHEMATICS STANDARDS Grades 3-6
NUMBER SENSE & OPERATIONS 3.N.1 Exhibit an understanding of the values of the digits in the base ten number system by reading, modeling, writing, comparing, and ordering whole numbers through 9,999. Our
More informationAlgebra Homework: Chapter 1 (Homework is listed by date assigned; homework is due the following class period) Day Date In-Class Homework
Algebra Homework: Chapter 1 (Homework is listed by date assigned; homework is due the following class period) Day Date In-Class Homework 1 T 8/30 Introductions Operations on Decimals Converting Decimals
More informationMath Glossary Numbers and Arithmetic
Math Glossary Numbers and Arithmetic Version 0.1.1 September 1, 200 Next release: On or before September 0, 200. E-mail edu@ezlink.com for the latest version. Copyright 200 by Brad Jolly All Rights Reserved
More informationInteger Operations. Summer Packet 7 th into 8 th grade 1. Name = = = = = 6.
Summer Packet 7 th into 8 th grade 1 Integer Operations Name Adding Integers If the signs are the same, add the numbers and keep the sign. 7 + 9 = 16-2 + -6 = -8 If the signs are different, find the difference
More informationFraction to Percents Change the fraction to a decimal (see above) and then change the decimal to a percent (see above).
PEMDAS This is an acronym for the order of operations. Order of operations is the order in which you complete problems with more than one operation. o P parenthesis o E exponents o M multiplication OR
More informationAccuplacer Arithmetic Study Guide
Accuplacer Arithmetic Study Guide I. Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole (the number on the bottom) Example: parts
More informationWHOLE NUMBER AND DECIMAL OPERATIONS
WHOLE NUMBER AND DECIMAL OPERATIONS Whole Number Place Value : 5,854,902 = Ten thousands thousands millions Hundred thousands Ten thousands Adding & Subtracting Decimals : Line up the decimals vertically.
More informationRational Number is a number that can be written as a quotient of two integers. DECIMALS are special fractions whose denominators are powers of 10.
PA Ch 5 Rational Expressions Rational Number is a number that can be written as a quotient of two integers. DECIMALS are special fractions whose denominators are powers of 0. Since decimals are special
More informationHOW TO DIVIDE: MCC6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE
MCC6.NS. Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE Dividend A number that is divided by another number. Divisor A number by which another number
More informationCHAPTER 1B: : Foundations for Algebra
CHAPTER B: : Foundations for Algebra 0-: Rounding and Estimating Objective: Round numbers. Rounding: To round to a given place value, do the following Rounding Numbers Round each number to the given place
More informationSUMMER REVIEW PACKET 2 FOR STUDENTS ENTERING ALGEBRA 1
SUMMER REVIEW PACKET FOR STUDENTS ENTERING ALGEBRA Dear Students, Welcome to Ma ayanot. We are very happy that you will be with us in the Fall. The Math department is looking forward to working with you
More informationMini-Lectures by Section
Mini-Lectures by Section BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture 1.1 1. Learn the definition of factor.. Write fractions in lowest terms.. Multiply and divide fractions.. Add and subtract fractions..
More informationKNOWLEDGE OF NUMBER SENSE, CONCEPTS, AND OPERATIONS
DOMAIN I. COMPETENCY 1.0 MATHEMATICS KNOWLEDGE OF NUMBER SENSE, CONCEPTS, AND OPERATIONS Skill 1.1 Compare the relative value of real numbers (e.g., integers, fractions, decimals, percents, irrational
More informationName: Date: Review Packet: Unit 1 The Number System
Name: Date: Math 7 Ms. Conway Review Packet: Unit 1 The Number System Key Concepts Module 1: Adding and Subtracting Integers 7.NS.1, 7.NS.1a, 7.NS.1b, 7.NS.1c, 7.NS.1d, 7.NS.3, 7.EE.3 To add integers with
More informationIs the statement sufficient? If both x and y are odd, is xy odd? 1) xy 2 < 0. Odds & Evens. Positives & Negatives. Answer: Yes, xy is odd
Is the statement sufficient? If both x and y are odd, is xy odd? Is x < 0? 1) xy 2 < 0 Positives & Negatives Answer: Yes, xy is odd Odd numbers can be represented as 2m + 1 or 2n + 1, where m and n are
More informationPre-Algebra Notes Unit Five: Rational Numbers and Equations
Pre-Algebra Notes Unit Five: Rational Numbers and Equations Rational Numbers Rational numbers are numbers that can be written as a quotient of two integers. Since decimals are special fractions, all the
More informationSection 1.2 Fractions
Objectives Section 1.2 Fractions Factor and prime factor natural numbers Recognize special fraction forms Multiply and divide fractions Build equivalent fractions Simplify fractions Add and subtract fractions
More informationMath 7 Notes Unit Three: Applying Rational Numbers
Math 7 Notes Unit Three: Applying Rational Numbers Strategy note to teachers: Typically students need more practice doing computations with fractions. You may want to consider teaching the sections on
More informationFlorida Math 0018 Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower
Florida Math 0018 Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower Whole Numbers MDECL1: Perform operations on whole numbers (with applications, including
More informationWhat is a Fraction? Fractions. One Way To Remember Numerator = North / 16. Example. What Fraction is Shaded? 9/16/16. Fraction = Part of a Whole
// Fractions Pages What is a Fraction? Fraction Part of a Whole Top Number? Bottom Number? Page Numerator tells how many parts you have Denominator tells how many parts are in the whole Note: the fraction
More informationCIV Module Unit Session Learning Objectives
CIV Module Unit Session Learning Objectives C IV Module: Essentials of Recognizing a Fraction 1. Learning that a fraction is a part of a whole through the use of area models C IV Module: Essentials of
More informationStudent Success Center Arithmetic Study Guide for the ACCUPLACER (CPT)
Fractions Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole (the number on the bottom) is parts have a dot out of Proper fraction:
More information(-,+) (+,+) Plotting Points
Algebra Basics +y (-,+) (+,+) -x +x (-,-) (+,-) Plotting Points -y Commutative Property of Addition/Multiplication * You can commute or move the terms * This only applies to addition and multiplication
More informationALGEBRA I Summer Packet
ALGEBRA I Summer Packet 2018-2019 Name 7 th Grade Math Teacher: Objectives for Algebra I Summer Packet I. Variables and translating (Problems #1 5) Write Algebraic Expressions Writing Algebraic Equations
More informationSection 1.8. Simplifying Expressions
Section 1.8 Simplifying Expressions But, first Commutative property: a + b = b + a; a * b = b * a Associative property: (a + b) + c = a + (b + c) (a * b) * c = a * (b * c) Distributive property: a * (b
More information8 th Grade Math Reference Sheet
8 th Grade Math Reference Sheet Number Sense DECIMALS NS 1 To change a DECIMAL FRACTION, use the place value of the decimal as the denominator of the fraction; simplify if. 1. Line up decimal points 2.
More information6th Grade Arithmetic (with QuickTables)
6th Grade Arithmetic (with QuickTables) This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence
More informationNUMBER SENSE AND OPERATIONS. Competency 0001 Understand the structure of numeration systems and multiple representations of numbers.
SUBAREA I. NUMBER SENSE AND OPERATIONS Competency 0001 Understand the structure of numeration systems and multiple representations of numbers. Prime numbers are numbers that can only be factored into 1
More informationMathematics LV 5 (with QuickTables)
Mathematics LV 5 (with QuickTables) This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence
More informationTable of Contents. Foundations 5p Vocabulary List
Table of Contents Objective 1: Review (Natural Numbers)... 3 Objective 2: Reading and Writing Natural Numbers... 5 Objective 3: Lines: Rays, and Line Segments... 6 Objective 4: Comparing Natural Numbers...
More informationAlignment to the Texas Essential Knowledge and Skills Standards
Alignment to the Texas Essential Knowledge and Skills Standards Contents Kindergarten... 2 Level 1... 4 Level 2... 6 Level 3... 8 Level 4... 10 Level 5... 13 Level 6... 16 Level 7... 19 Level 8... 22 High
More informationSUPER MATH GLOSSARY. 1. Addition- The mathematical operation used to find a sum. The problem =1.5 is an example.
SUPER MATH GLOSSARY 1. Addition- The mathematical operation used to find a sum. The problem 0.2+1.3=1.5 is an example. 2. Area- A measurement of the amount of a surface on a flat figure. A tabletop that
More informationFractions. There are several terms that are commonly used when working with fractions.
Chapter 0 Review of Arithmetic Fractions There are several terms that are commonly used when working with fractions. Fraction: The ratio of two numbers. We use a division bar to show this ratio. The number
More informationSection 2.3 Rational Numbers. A rational number is a number that may be written in the form a b. for any integer a and any nonzero integer b.
Section 2.3 Rational Numbers A rational number is a number that may be written in the form a b for any integer a and any nonzero integer b. Why is division by zero undefined? For example, we know that
More informationLearning Log Title: CHAPTER 3: ARITHMETIC PROPERTIES. Date: Lesson: Chapter 3: Arithmetic Properties
Chapter 3: Arithmetic Properties CHAPTER 3: ARITHMETIC PROPERTIES Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 3: Arithmetic Properties Date: Lesson: Learning Log Title:
More informationExample: Which of the following expressions must be an even integer if x is an integer? a. x + 5
8th Grade Honors Basic Operations Part 1 1 NUMBER DEFINITIONS UNDEFINED On the ACT, when something is divided by zero, it is considered undefined. For example, the expression a bc is undefined if either
More informationChapter 1: Number and Operations
Chapter 1: Number and Operations 1.1 Order of operations When simplifying algebraic expressions we use the following order: 1. Perform operations within a parenthesis. 2. Evaluate exponents. 3. Multiply
More informationSummer Packet 7 th into 8 th grade. Name. Integer Operations = 2. (-7)(6)(-4) = = = = 6.
Integer Operations Name Adding Integers If the signs are the same, add the numbers and keep the sign. 7 + 9 = 16 - + -6 = -8 If the signs are different, find the difference between the numbers and keep
More informationPre-Algebra Notes Unit Five: Rational Numbers and Equations
Pre-Algebra Notes Unit Five: Rational Numbers and Equations Rational Numbers Rational numbers are numbers that can be written as a quotient of two integers. Since decimals are special fractions, all the
More informationConverting Between Mixed Numbers & Improper Fractions
01 Converting Between Mixed Numbers & Improper Fractions A mixed number is a whole number and a fraction: 4 1 2 An improper fraction is a fraction with a larger numerator than denominator: 9 2 You can
More informationHundred-thousands. Millions. Ten-thousands
Place Value, Names for Numbers, and Reading Tables The digits used to write numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Unit 1 Lesson 1a Natural numbers are positive numbers only {1, 2, 3, 4, 5, 6, 7,
More informationLesson 1: Arithmetic Review
In this lesson we step back and review several key arithmetic topics that are extremely relevant to this course. Before we work with algebraic expressions and equations, it is important to have a good
More informationAdding and Subtracting Integers
Quarterly 1 Review Sheet (NOTE: This may not include everything you need to know for tomorrow about every topic. It is student created and I am just sharing it in case you find it helpful) Page 1: Adding
More informationPre Algebra 2. Student Goals. Curriculum Sample
Pre Algebra 2 Curriculum Sample A Grade Ahead s rigorous, year-round math enrichment program is designed to challenge your child to a higher academic standard. Our monthly curriculum includes mathematical
More informationDiocese of Boise Math Curriculum 5 th grade
Diocese of Boise Math Curriculum 5 th grade ESSENTIAL Sample Questions Below: What can affect the relationshi p between numbers? What does a decimal represent? How do we compare decimals? How do we round
More informationAccuplacer Arithmetic Review
Accuplacer Arithmetic Review Hennepin Technical College Placement Testing for Success Page Overview The Arithmetic section of ACCUPLACER contains 7 multiple choice questions that measure your ability to
More informationMini-Lesson 1. Section 1.1: Order of Operations PEMDAS
Name: Date: 1 Section 1.1: Order of Operations PEMDAS If we are working with a mathematical expression that contains more than one operation, then we need to understand how to simplify. The acronym PEMDAS
More informationMontana City School GRADE 5
Montana City School GRADE 5 Montana Standard 1: Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and applications, and using appropriate
More informationEXAMPLE 1. Change each of the following fractions into decimals.
CHAPTER 1. THE ARITHMETIC OF NUMBERS 1.4 Decimal Notation Every rational number can be expressed using decimal notation. To change a fraction into its decimal equivalent, divide the numerator of the fraction
More informationPre-Algebra Notes Unit Five: Rational Numbers and Equations
Pre-Algebra Notes Unit Five: Rational Numbers and Equations Rational Numbers Rational numbers are numbers that can be written as a quotient of two integers. Since decimals are special fractions, all the
More information6-8 Math Adding and Subtracting Polynomials Lesson Objective: Subobjective 1: Subobjective 2:
6-8 Math Adding and Subtracting Polynomials Lesson Objective: The student will add and subtract polynomials. Subobjective 1: The student will add polynomials. Subobjective 2: The student will subtract
More informationUnit 1. Word Definition Picture. The number s distance from 0 on the number line. The symbol that means a number is greater than the second number.
Unit 1 Word Definition Picture Absolute Value The number s distance from 0 on the number line. -3 =3 Greater Than The symbol that means a number is greater than the second number. > Greatest to Least To
More information0001 Understand the structure of numeration systems and multiple representations of numbers. Example: Factor 30 into prime factors.
NUMBER SENSE AND OPERATIONS 0001 Understand the structure of numeration systems and multiple representations of numbers. Prime numbers are numbers that can only be factored into 1 and the number itself.
More informationReteaching. Comparing and Ordering Integers
- Comparing and Ordering Integers The numbers and - are opposites. The numbers 7 and -7 are opposites. Integers are the set of positive whole numbers, their opposites, and zero. 7 6 4 0 negative zero You
More informationMath 7 Glossary Terms
Math 7 Glossary Terms Absolute Value Absolute value is the distance, or number of units, a number is from zero. Distance is always a positive value; therefore, absolute value is always a positive value.
More informationIntegers and Rational Numbers
A A Family Letter: Integers Dear Family, The student will be learning about integers and how these numbers relate to the coordinate plane. The set of integers includes the set of whole numbers (0, 1,,,...)
More informationAlgebra 1 Review. Properties of Real Numbers. Algebraic Expressions
Algebra 1 Review Properties of Real Numbers Algebraic Expressions Real Numbers Natural Numbers: 1, 2, 3, 4,.. Numbers used for counting Whole Numbers: 0, 1, 2, 3, 4,.. Natural Numbers and 0 Integers:,
More informationMAT 003 Brian Killough s Instructor Notes Saint Leo University
MAT 003 Brian Killough s Instructor Notes Saint Leo University Success in online courses requires self-motivation and discipline. It is anticipated that students will read the textbook and complete sample
More informationThousands. Hundreds. Tenths. Ones. Tens. Hundredths. Decimal Point. Thousandths. Place Value. 1000s 100s 10s 1s.
Place Value Thousandths Hundredths Tenths Decimal Point Ones Tens Hundreds Thousands 000s 00s 0s s. 0 00 000 Know the meanings of these column headings is very important. It tells us the value of each
More informationMAT 090 Brian Killough s Instructor Notes Strayer University
MAT 090 Brian Killough s Instructor Notes Strayer University Success in online courses requires self-motivation and discipline. It is anticipated that students will read the textbook and complete sample
More informationMiddle School Math Course 2
Middle School Math Course 2 Correlation of the ALEKS course Middle School Math Course 2 to the Indiana Academic Standards for Mathematics Grade 7 (2014) 1: NUMBER SENSE = ALEKS course topic that addresses
More informationFractions. Dividing the numerator and denominator by the highest common element (or number) in them, we get the fraction in its lowest form.
Fractions A fraction is a part of the whole (object, thing, region). It forms the part of basic aptitude of a person to have and idea of the parts of a population, group or territory. Civil servants must
More information- 0.8.00-0.8. 7 ANSWERS: ) : ) : ) : ) : 8 RATIO WORD PROBLEM EXAMPLES: Ratio Compares two amounts or values; they can be written in ways. As a fraction With a colon : With words to A classroom has girls
More informationTABLE OF CONTENTS. About Finish Line PA Core Math 5. UNIT 1: Big Ideas from Grade 7 7 UNIT 1 REVIEW 38. UNIT 2: The Number System 43 UNIT 2 REVIEW 58
TABLE OF CONTENTS About Finish Line PA Core Math 5 UNIT 1: Big Ideas from Grade 7 7 LESSON 1 CC..1.7.D.1 Understanding Proportional Relationships [connects to CC...8.B.] 8 LESSON CC..1.7.E.1 Operations
More informationRtI 7. Curriculum (219 topics additional topics)
RtI 7 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs. Curriculum
More informationGateway Regional School District VERTICAL ARTICULATION OF MATHEMATICS STANDARDS Grades K-4
NUMBER SENSE & OPERATIONS K.N.1 Count by ones to at least 20. When you count, the last number word you say tells the number of items in the set. Counting a set of objects in a different order does not
More informationPROGRESSION IS HIGHLIGHTED IN THE FOLLOWING DOCUMENT VIA BOLDED TEXT. MATHEMATICAL PROCESSES
Alberta's Program of Studies (Curriculum) - Mathematics - Number (Strand with Achievement Outcomes) Note: These strands are not intended to be discrete units of instruction. The integration of outcomes
More informationChapter 4 Section 2 Operations on Decimals
Chapter 4 Section 2 Operations on Decimals Addition and subtraction of decimals To add decimals, write the numbers so that the decimal points are on a vertical line. Add as you would with whole numbers.
More informationChapter 1: Foundations for Algebra
Chapter 1: Foundations for Algebra Dear Family, The student will follow the order of operations, a set of rules that standardize how to simplify expressions. Order of Operations 1. Perform operations within
More informationSummer 2013 Modules 9-13
Summer 201 Modules 9-1 Mastering the Fundamentals Chris Millett Copyright 201 All rights reserved. Written permission must be secured from the author to use or reproduce any part of this book. Academic
More informationSlide 1 / 180. Radicals and Rational Exponents
Slide 1 / 180 Radicals and Rational Exponents Slide 2 / 180 Roots and Radicals Table of Contents: Square Roots Intro to Cube Roots n th Roots Irrational Roots Rational Exponents Operations with Radicals
More informationBig Mathematical Ideas and Understandings
Big Mathematical Ideas and Understandings A Big Idea is a statement of an idea that is central to the learning of mathematics, one that links numerous mathematical understandings into a coherent whole.
More informationAnadarko Public Schools MATH Power Standards
Anadarko Public Schools MATH Power Standards Kindergarten 1. Say the number name sequence forward and backward beginning from a given number within the known sequence (counting on, spiral) 2. Write numbers
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Math 24 - Study Guide - Chapter 1 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Give one number between -8 and 8 that is a negative real
More informationCollege Readiness (597 topics) Course Name: College Prep Math Spring 2014 Course Code: ARTD4-3N6XJ
Course Name: College Prep Math Spring 2014 Course Code: ARTD4-3N6XJ ALEKS Course: Math for College Readiness Instructor: Ms. Dalton Course Dates: Begin: 01/19/2015 End: 06/18/2015 Course Content: 606 Topics
More informationSection 1.1 Definitions and Properties
Section 1.1 Definitions and Properties Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Abbreviate repeated addition using Exponents and Square
More informationPrime Time (Factors and Multiples)
CONFIDENCE LEVEL: Prime Time Knowledge Map for 6 th Grade Math Prime Time (Factors and Multiples). A factor is a whole numbers that is multiplied by another whole number to get a product. (Ex: x 5 = ;
More informationNFC ACADEMY MATH 600 COURSE OVERVIEW
NFC ACADEMY MATH 600 COURSE OVERVIEW Math 600 is a full-year elementary math course focusing on number skills and numerical literacy, with an introduction to rational numbers and the skills needed for
More informationCommon Core State Standards Mathematics (Subset K-5 Counting and Cardinality, Operations and Algebraic Thinking, Number and Operations in Base 10)
Kindergarten 1 Common Core State Standards Mathematics (Subset K-5 Counting and Cardinality,, Number and Operations in Base 10) Kindergarten Counting and Cardinality Know number names and the count sequence.
More informationMath 96--Radicals #1-- Simplify; Combine--page 1
Simplify; Combine--page 1 Part A Number Systems a. Whole Numbers = {0, 1, 2, 3,...} b. Integers = whole numbers and their opposites = {..., 3, 2, 1, 0, 1, 2, 3,...} c. Rational Numbers = quotient of integers
More informationSection 3.1 Factors and Multiples of Whole Numbers:
Chapter Notes Math 0 Chapter : Factors and Products: Skill Builder: Some Divisibility Rules We can use rules to find out if a number is a factor of another. To find out if, 5, or 0 is a factor look at
More informationTeacher: CORE Math Grade 6 Year: Content Skills VocabularyAssessments Lessons Resources Standards. Diagnostic Math 6 Test 9/10/2011
Teacher: CORE Math Grade 6 Year: 2010-11 Course: Math Grade 6 Month: All Months S e p Essential t Questions e m b e r NUMBER SENSE AND OPERATIONS Content Skills VocabularyAssessments Lessons Resources
More informationWatkins Mill High School. Algebra 2. Math Challenge
Watkins Mill High School Algebra 2 Math Challenge "This packet will help you prepare for Algebra 2 next fall. It will be collected the first week of school. It will count as a grade in the first marking
More informationNativity Catholic School Rising 7th grade IXL Language Arts and Math Summer Homework
Nativity Catholic School Rising 7th grade IXL Language Arts and Math Summer Homework Please work on the following skills listed in the 6 th grade Math and Language Arts IXL program for a minimum of 20
More informationMath 10- Chapter 2 Review
Math 10- Chapter 2 Review [By Christy Chan, Irene Xu, and Henry Luan] Knowledge required for understanding this chapter: 1. Simple calculation skills: addition, subtraction, multiplication, and division
More informationFUNDAMENTAL ARITHMETIC
FUNDAMENTAL ARITHMETIC Prime Numbers Prime numbers are any whole numbers greater than that can only be divided by and itself. Below is the list of all prime numbers between and 00: Prime Factorization
More informationPlace Value. Verbal Form: 30,542 = Thirty thousand, five hundred forty-two. (Notice we don t use the word and.)
WHOLE NUMBERS REVIEW A set is a collection of objects. The set of natural numbers is {1,2,3,4,5,.} The set of whole numbers is {0,1,2,3,4,5, } Whole numbers are used for counting objects (such as money,
More informationOdd-Numbered Answers to Exercise Set 1.1: Numbers
Odd-Numbered Answers to Exercise Set.: Numbers. (a) Composite;,,, Prime Neither (d) Neither (e) Composite;,,,,,. (a) 0. 0. 0. (d) 0. (e) 0. (f) 0. (g) 0. (h) 0. (i) 0.9 = (j). (since = ) 9 9 (k). (since
More informationRational numbers as decimals and as integer fractions
Rational numbers as decimals and as integer fractions Given a rational number expressed as an integer fraction reduced to the lowest terms, the quotient of that fraction will be: an integer, if the denominator
More informationDecimal Binary Conversion Decimal Binary Place Value = 13 (Base 10) becomes = 1101 (Base 2).
DOMAIN I. NUMBER CONCEPTS Competency 00 The teacher understands the structure of number systems, the development of a sense of quantity, and the relationship between quantity and symbolic representations.
More informationRational and Irrational Numbers
LESSON. Rational and Irrational Numbers.NS. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion;... lso.ns.2,.ee.2? ESSENTIL QUESTION
More informationAlgebra II Radical Equations
1 Algebra II Radical Equations 2016-04-21 www.njctl.org 2 Table of Contents: Graphing Square Root Functions Working with Square Roots Irrational Roots Adding and Subtracting Radicals Multiplying Radicals
More information1.1 Review of Place Value
1 1.1 Review of Place Value Our decimal number system is based upon powers of ten. In a given whole number, each digit has a place value, and each place value consists of a power of ten. Example 1 Identify
More informationMath 085 Final Exam Review
Math 08 Final Exam Review Objective : Use the rules of signed number arithmetic to perform operations on integers. These operations include, but are not limited to, addition, subtraction, multiplication,
More informationCarnegie Learning Math Series Course 1, A Florida Standards Program. Chapter 1: Factors, Multiples, Primes, and Composites
. Factors and Multiples Carnegie Learning Math Series Course, Chapter : Factors, Multiples, Primes, and Composites This chapter reviews factors, multiples, primes, composites, and divisibility rules. List
More informationMath 171 Proficiency Packet on Integers
Math 171 Proficiency Packet on Integers Section 1: Integers For many of man's purposes the set of whole numbers W = { 0, 1, 2, } is inadequate. It became necessary to invent negative numbers and extend
More informationUnit 3: Rational Numbers ANSWER KEY
Unit : ANSWER KEY The following unit includes: Adding/Subtracting Integers on a Number Line Adding/Subtracting Integers with Rules Multiplying/Dividing Integers Adding/Subtracting Decimals Multiplying
More informationMATH REVIEW SUPPLEMENT. For The ARITHMETIC SECTION. of the. ACCUPLACER Entry Assessment
Assessment Center MATH REVIEW SUPPLEMENT For The ARITHMETIC SECTION of the ACCUPLACER Entry Assessment Visit The Assessment Center At http://www.stlcc.cc.mo.us/mc/services/assess/index.html This document
More informationChapter 1 Operations With Numbers
Chapter 1 Operations With Numbers Part I Negative Numbers You may already know what negative numbers are, but even if you don t, then you have probably seen them several times over the past few days. If
More information