# Decimals are absolutely amazing We have only 10 symbols, yet can represent any number, large or small We use zero (0) as a place holder to allow us

Size: px
Start display at page:

Download "Decimals are absolutely amazing We have only 10 symbols, yet can represent any number, large or small We use zero (0) as a place holder to allow us"

Transcription

1 Decimals 1

2 Decimals are absolutely amazing We have only 10 symbols, yet can represent any number, large or small We use zero (0) as a place holder to allow us to do this 2

3 Some Older Number Systems 3

4 Can you imagine doing arithmetic with Roman Numerals? 29 plus 28 becomes: XXIX+ XXVII =? How do you put together the X, V, and I? 4

5 5

6 We Use Place Value vs : What does the position of the 2 say about the value of the number? For numbers greater than one we have: ones tens hundreds For numbers less than one we have: tenths hundredths We separate those less than one by using a decimal point; one is the focus point, not zero! 6

7 One tenth is 1/10 is 0.1 For Numbers Less Than One One thousandth is 1/1000 is What is 0.321? 7

8 We can think in terms of adding is 3 hundreds tens 40 5 ones 5 2 tenths 2/10 6 hundredths 6/ /10 + 6/100 =

9 Examples 9

10 Decimals to Fractions We can write decimals as fractions (and/or mixed numbers) 0.51 = 51/ = 126/1000 We could also write as 1/10 + 2/ /1000, find a common denominator, and add the fractions! 10

11 Mixed Numbers 5.7 = 5 7/ = /

12 Fractions as Decimals 6/10 = /100 = /10 = /100 = 3.06 How do I know that there is something to the left of the decimal point? If the numerator is larger than the denominator 12

13 Examples/Review Three and nine tenths in decimals = Eight hundred four and three hundred ninety-nine thousandths in decimals = in words = 3601/1000 in decimals = 13

14 Solution Three and nine tenths in decimals = 3.9 Eight hundred four and three hundred ninety-nine thousandths in decimals = in words = forty seven and 65 hundredths 3601/1000 in decimals =

15 Place Value Our base-ten place-value numeration system is adequate for expressing all whole numbers and decimal numbers. The value of each digit in a numeral is determined by the position of the digit in the numeral. Digits in different places have different values. Finally, the number 1, not the decimal point, serves as the focal point of decimal numbers. 15

16 Order and Rounding 16

17 Which is larger? or ? or 3.405? 25.1 or 25.13? 0.61 or 0.076? or ? 17

18 Solution or ? or 3.405? 25.1 or 25.13? 0.61 or 0.076? or ? It is less negative, so larger 18

19 Note: 76 = 76.0 = , etc. Similarly 0.35 =.35, etc. and 02 (which makes no sense) is still 2 19

20 Rounding Remember If we round 56 to the nearest ten, we have 60 If we round 3465 to the nearest thousand we have 3000 Rule: if the number in the place to the right of where we are rounding to is <5, drop it: 343 rounded to the nearest 10 is 340 If the number in the place to the left of where we are rounding to is 5, go up: 345 rounded to the nearest 10 is

21 Rounding Similarly, rounded to the nearest hundredth is 2.95 What is rounded to the nearest tenth??? Nearest one? 21

22 Solution What is rounded to the nearest tenth??? 3.0 Nearest one? 3 (or 3.0, they are the same) 22

23 Examples Suzie has an annual income of \$41, She is paying her taxes, and the tax table use amounts to the nearest dollar. What income value should she use in determining her tax? Jane has an income of \$154, For her income bracket, the tax tables use amounts to the nearest hundred dollars. What income value should she use in determining her tax? 23

24 Solution \$41, to the nearest dollar is \$41,569 \$154, to the nearest hundred dollars is \$154,300 24

25 More Examples Which number(s) round to 0.06?

26 Solution and

27 Adding and Subtracting Decimals 27

28 How? Can think of in two ways: need a common denominator, or line up the decimal points = 2385/ /1000; common denominator is 1000, ( )/1000 = 25454/1000 =

29 Estimating =? We know that this has to be close to or 530. This helps us figure out where the decimal point goes If the number seems wrong, check where your decimal point is. The exact answer is , which is near 530 This is especially useful for division! 29

30 Examples: Estimate and Solve = = = What is wrong with:

31 = 6.6; estimate = 6 Solutions = ; estimate = = = ; estimate = = 115 What is wrong with: The decimal points were not kept straight! 31

32 Subtraction Same as addition, but may need to borrow: Get a common denominator or Line up the decimal points = change the 82 to 81 and make the one into 10/

33 Examples: Estimate and Solve = = = 33

34 Solutions = 5.5; estimate = = 24.7; estimate 28 3 = = 3.36; estimate =

35 Example Find the total cost of owning this car: monthly car payment \$ monthly car insurance \$47.52 average gas per month \$

36 Solution To find the total monthly cost, we need to add up all the monthly expenses =? estimate: = 400 actual \$

37 Example The average temperature throughout the US, for many years is F. In 1998, the warmest year, the average was F. How much warmer than usual was it in 1998? 37

38 Solution = 2.23 F 38

39 Example To send a 2 lb package by parcel post cost \$4.90. To send it express mail costs \$ How much more does it cost to send the package by express mail than by regular mail? 39

40 Solution To send a 2 lb package by parcel post cost \$4.90. To send it express mail costs \$ How much more does it cost to send the package by express mail than by regular mail? = \$

41 Example; Mean Chocolate Consumption Which country has the most chocolate consumption per person? The least? How much more chocolate do Austrians eat than Germans? Pounds of Chocolate/yr Austria Germany Norway Switzerland Ireland Country 41

42 Solution Which country has the most chocolate consumption per person? Switzerland The least? Norway How much more chocolate do Austrians eat than Germans? 2.09 lb 42

43 Example The screen of the 2007 iphone was 4.5 by 2.4. What was its perimeter 43

44 Solution The screen of the 2007 iphone was 4.5 by 2.4. What was its perimeter Perimeter = 2 L + 2 W = 2 (4.5) + 2( 2.4) = =

45 Multiplying and Dividing Decimals 45

46 It is like multiplying fractions: 0.6 x 0.03 = 6/10 x 3/100 = 18/1000 = Or a rule: Count the number of digits to the right of the decimal point in the problem, and you need that many in the answer; just multiply the numbers as if they are whole 0.6 x 0.03: 1 place plus 2 places = 3 places; 6 x 3 = 18, but need three decimal places, so

47 Estimation Figuring out how big the number should be is a helpful check x 0.6 = You have 1/10 time 6/10, so you know it is near 6/ x 6 = 672, but it has to be near 6/100, so Or, 112/1000 x 6/100 Or, there are four decimals in the problem, four in the answer 47

48 x 10 = Multiplying by Power of Ten x 0.1 = Just move the decimal point to the right or left, depending on how many decimal places there are in the power of ten 48

49 Examples 23.7 x 10 = x 100 = 7.62 x 0.1 = 1.9 x 0.01 = 7682 x = 49

50 Solutions 23.7 x 10 = x 100 = 20, x 0.1 = x 0.01 = x =

51 Examples 0.7 x 0.9 = 6.8 x 0.3 = x 5.5 = x 3.71 = 51

52 Solutions 0.7 x 0.9 = x 0.3 = 2.04 (estimate 7 x 0.3) x 5.5 = (estimate 2 x 5.5) x 3.71 = (estimate 31 x 4) 52

53 Example The circumference of a circle is 2π times the radius, where π = Approximating π as 3.14, find the circumference of a circle that has a diameter of 10 cm. 53

54 Solution If the diameter is 10, the radius is 5 2 π r = 2 x π x 5 = 10 π =

55 Example In 2010 the average US airplane passenger paid \$ per mile to fly. If it is 905 mils from Atlanta to Minneapolis, find the fare. (Round to the nearest cent) 55

56 Solution In 2010 the average US airplane passenger paid \$ per mile to fly. If it is 905 mils from Atlanta to Minneapolis, find the fare. (Round to the nearest cent) x 905 = \$ Estimate: 0.14 x

57 Dividing Decimals and Order of Operations 57

58 Dividing by a Whole Number The key is to fix the decimal point! Estimation can help / 7 Estimate 270/7 ~ 40; you can check your result against this Write the problem, but fix the decimal point above where it should be! xxx.xxxxx 7)270.6 Do the long division. 7 doesn t divide 2, 7 divides 27, 3 times, 7 divides 60, 8 times, THEN PUT THE DECIMAL POINT / 7 =

59 Examples 8.32 / 32 = / 48 = 59

60 Solutions 8.32 / 32 = 0.26; estimate 8/32 ~ / 48 = 0.71; estimate 34/48 ~ 3/4 =

61 Dividing by a Decimal DON T!!!! Multiply the numerator and denominator by the same power of 10 so that the denominator is no longer a decimal / 2.3 =? Multiply top and bottom (numerator and denominator) by / 23 Then divide a decimal by a whole number 61

62 Examples 17.5 / 0.48 = 1750 / 48 = 23.4 / 0.57= / 28.4 = 62

63 Solution 17.5 / 0.48 = 1750 / 48 = 36.46; estimate 1750/50 = 175/5 = / 0.57= 41.05; rewrite 2340 / 57; estimate 2400/60 = 240/ / 28.4 = 9.59; rewrite / 284; estimate 3000/300 = 30/3 = 10 63

64 Order of Operations PEMDAS: Please Excuse My Dear Aunt Sally P: Parentheses; simplify quantities in parentheses, inside to outside, and remove the parentheses E: Exponents; evaluate any expressions with exponents M and D: Multiplication and Division; perform any multiplication and division from left to right A and S: Addition and Subtraction; perform any addition and subtraction from left to right M and D are done at the same time, as are A and S; My and Dear are adjectives, Aunt and Sally are nouns; they stay together. 64

65 Examples / 1000 x 10 = No P, no E, M & D, working from left to right Step 1: 723.6/1000 = Step 2: x 10 = What happens if we mix the order? if we multiply 1000 x 10 = 10, / 10,000 = : WRONG!!! 65

66 Example 0.5 ( ) = P first: = 7.4 No E M and D: 0.5 x 7.4 =

67 [ (0.9) 2 / 100 ] / 0.2 = Example 67

68 Solution [ (0.9) 2 / 100 ] / 0.2 = P: can t simplify [ ] until we do some work Inside the [ ] first E: (0.9) 2 = 0.81 M & D: 0.81 / 100 = A & S: = Now we have [ ] evaluated [ ] / 0.2 = / 0.2 = / 2 =

69 Example / 100 x 10 = 8.69 ( ) = [ (1.2) 2 / 10 ] / 0.02 = 69

70 897.8 / 100 x 10 = Solution 8.69 ( ) = [ (1.2) 2 / 10 ] / 0.02 =

71 Fractions as Decimals Writing decimals as fractions is easy: denominator is a power of 10 Writing fractions as decimals is a bit harder may not have a finite number of digits. To make a fraction a decimal, just divide: 1/4 = 1 4 = /5 = 4 5 =

72 When it Doesn t Come out Even 2/3 =? : The means keep writing 6 for a long as you want; it will never end _ You can also write 0.6 =

73 Example Write as a decimal, round to nearest thousandth: 28/13 = 2 3/16 = 3 5/16 = 7/9 = 73

74 Solution 28/13 = /16 = /16 = /9 = =

75 Which is Larger? 1/2 or 0.54? 0.44 or 4/9? 5/7 or 0.72? 75

76 Solution 1/2 or 0.54? 0.44 or 4/9? Same 5/7 or 0.72? 76

77 Summary Decimal Arithmetic: Estimate the result Multiplication: You can make decimals fractions and multiply, or Count the number of decimal places (riskier) Division: When dividing by a hole number, mark the decimal point When dividing by decimals, GET RID OF THE DECIMALS IN THE DENOMINATOR! 77

78 Summary Cont. Order of operations Clear parentheses, inside to out Clear exponents Multiplication and Division, from left to right Addition and Subtraction, from left to right PEMDAS: Please Excuse My Dear Aunt Sally M and D go together (adjectives) Aunt and Sally go together (nouns) 78

79 Solution 8.32 / / 48 79

### Exponents. Exponents tell us how many times to multiply a base number by itself.

Exponents Exponents tell us how many times to multiply a base number by itself. Exponential form: 5 4 exponent base number Expanded form: 5 5 5 5 25 5 5 125 5 625 To use a calculator: put in the base number,

### How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

### Math 0306 Final Exam Review

Math 006 Final Exam Review Problem Section Answers Whole Numbers 1. According to the 1990 census, the population of Nebraska is 1,8,8, the population of Nevada is 1,01,8, the population of New Hampshire

### Pre-Algebra Lecture 6

Pre-Algebra Lecture 6 Today we will discuss Decimals and Percentages. Outline: 1. Decimals 2. Ordering Decimals 3. Rounding Decimals 4. Adding and subtracting Decimals 5. Multiplying and Dividing Decimals

### Revision Notes Adult Numeracy Level 2

Revision Notes Adult Numeracy Level 2 Place Value The use of place value from earlier levels applies but is extended to all sizes of numbers. The values of columns are: Millions Hundred thousands Ten thousands

### Fractions to decimals

Worksheet.4 Fractions and Decimals Section Fractions to decimals The most common method of converting fractions to decimals is to use a calculator. A fraction represents a division so is another way of

### Pre-Algebra - Order of Operations

0.3 Pre-Algebra - Order of Operations Objective: Evaluate expressions using the order of operations, including the use of absolute value. When simplifying expressions it is important that we simplify them

### The gas can has a capacity of 4.17 gallons and weighs 3.4 pounds.

hundred million\$ ten------ million\$ million\$ 00,000,000 0,000,000,000,000 00,000 0,000,000 00 0 0 0 0 0 0 0 0 0 Session 26 Decimal Fractions Explain the meaning of the values stated in the following sentence.

### Multiplying and Dividing Signed Numbers. Finding the Product of Two Signed Numbers. (a) (3)( 4) ( 4) ( 4) ( 4) 12 (b) (4)( 5) ( 5) ( 5) ( 5) ( 5) 20

SECTION.4 Multiplying and Dividing Signed Numbers.4 OBJECTIVES 1. Multiply signed numbers 2. Use the commutative property of multiplication 3. Use the associative property of multiplication 4. Divide signed

### Arithmetic Review ORDER OF OPERATIONS WITH WHOLE NUMBERS

Arithmetic Review The arithmetic portion of the Accuplacer Placement test consists of seventeen multiple choice questions. These questions will measure skills in computation of whole numbers, fractions,

### DATE PERIOD. Estimate the product of a decimal and a whole number by rounding the Estimation

A Multiplying Decimals by Whole Numbers (pages 135 138) When you multiply a decimal by a whole number, you can estimate to find where to put the decimal point in the product. You can also place the decimal

### Order of Operations More Essential Practice

Order of Operations More Essential Practice We will be simplifying expressions using the order of operations in this section. Automatic Skill: Order of operations needs to become an automatic skill. Failure

### 1 3 7 5. 2 3 1 6. The pattern going to the right or the left from the decimal point is the same but there are two big differences:

Review of Place Values in Decimal Numbers A decimal number includes a decimal point and digit(s) to the right of the decimal point. Saying a decimal number aloud is very similar to saying a whole number

### BASIC MATHEMATICS. WORKBOOK Volume 2

BASIC MATHEMATICS WORKBOOK Volume 2 2006 Veronique Lankar A r ef resher o n t he i mp o rt a nt s ki l l s y o u l l ne e d b efo r e y o u ca n s t a rt Alg e b ra. This can be use d a s a s elf-teaching

### 1.6 The Order of Operations

1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative

### MATH-0910 Review Concepts (Haugen)

Unit 1 Whole Numbers and Fractions MATH-0910 Review Concepts (Haugen) Exam 1 Sections 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4, and 2.5 Dividing Whole Numbers Equivalent ways of expressing division: a b,

### Introduction to Decimals

Introduction to Decimals Reading and Writing Decimals: Note: There is a relationship between fractions and numbers written in decimal notation. Three-tenths 10 0. 1 zero 1 decimal place Three- 0. 0 100

### Quick Reference ebook

This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

### Florida 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

### Beginning Algebra Math 100B. Math Study Center BYU-Idaho

Beginning Algebra Math 100B Math Study Center BYU-Idaho Preface This math book has been created by the BYU-Idaho Math Study Center for the college student who needs an introduction to Algebra. This book

### Decimals and other fractions

Chapter 2 Decimals and other fractions How to deal with the bits and pieces When drugs come from the manufacturer they are in doses to suit most adult patients. However, many of your patients will be very

### Accuplacer Arithmetic Study Guide

Accuplacer Arithmetic Study Guide Section One: Terms Numerator: The number on top of a fraction which tells how many parts you have. Denominator: The number on the bottom of a fraction which tells how

### **Unedited Draft** Arithmetic Revisited Lesson 5: Decimal Fractions or Place Value Extended Part 3: Multiplying Decimals

1. Multiplying Decimals **Unedited Draft** Arithmetic Revisited Lesson 5: Decimal Fractions or Place Value Extended Part 3: Multiplying Decimals Multiplying two (or more) decimals is very similar to how

### To Multiply Decimals

4.3 Multiplying Decimals 4.3 OBJECTIVES 1. Multiply two or more decimals 2. Use multiplication of decimals to solve application problems 3. Multiply a decimal by a power of ten 4. Use multiplication by

### Chapter 3 Review Math 1030

Section A.1: Three Ways of Using Percentages Using percentages We can use percentages in three different ways: To express a fraction of something. For example, A total of 10, 000 newspaper employees, 2.6%

### Welcome to Basic Math Skills!

Basic Math Skills Welcome to Basic Math Skills! Most students find the math sections to be the most difficult. Basic Math Skills was designed to give you a refresher on the basics of math. There are lots

### Representing Decimals (pages 102 105)

A Representing Decimals (pages 102 105) Decimals are numbers that are expressed using a decimal point. The decimal point separates the whole number part of the decimal from the part that is less than one.

### LESSON 5 - DECIMALS INTRODUCTION

LESSON 5 - DECIMALS INTRODUCTION Now that we know something about whole numbers and fractions, we will begin working with types of numbers that are extensions of whole numbers and related to fractions.

### Math. Rounding Decimals. Answers. 1) Round to the nearest tenth. 8.54 8.5. 2) Round to the nearest whole number. 99.59 100

1) Round to the nearest tenth. 8.54 8.5 2) Round to the nearest whole number. 99.59 100 3) Round to the nearest tenth. 310.286 310.3 4) Round to the nearest whole number. 6.4 6 5) Round to the nearest

### 5.1 Introduction to Decimals, Place Value, and Rounding

5.1 Introduction to Decimals, Place Value, and Rounding 5.1 OBJECTIVES 1. Identify place value in a decimal fraction 2. Write a decimal in words 3. Write a decimal as a fraction or mixed number 4. Compare

### Introduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman

Introduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman hundredths tenths ones tens Decimal Art An Introduction to Decimals Directions: Part 1: Coloring Have children

### DECIMAL COMPETENCY PACKET

DECIMAL COMPETENCY PACKET Developed by: Nancy Tufo Revised: Sharyn Sweeney 2004 Student Support Center North Shore Community College 2 In this booklet arithmetic operations involving decimal numbers are

### Section 1.5 Exponents, Square Roots, and the Order of Operations

Section 1.5 Exponents, Square Roots, and the Order of Operations Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Identify perfect squares.

### 10-4-10 Year 9 mathematics: holiday revision. 2 How many nines are there in fifty-four?

DAY 1 Mental questions 1 Multiply seven by seven. 49 2 How many nines are there in fifty-four? 54 9 = 6 6 3 What number should you add to negative three to get the answer five? 8 4 Add two point five to

### Charlesworth School Year Group Maths Targets

Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve

### Section 4.1 Rules of Exponents

Section 4.1 Rules of Exponents THE MEANING OF THE EXPONENT The exponent is an abbreviation for repeated multiplication. The repeated number is called a factor. x n means n factors of x. The exponent tells

### DIVISION OF DECIMALS. 1503 9. We then we multiply by the

Tallahassee Community College 0 DIVISION OF DECIMALS To divide 9, we write these fractions: reciprocal of the divisor 0 9. We then we multiply by the 0 67 67 = = 9 67 67 The decimal equivalent of is. 67.

### 1004.6 one thousand, four AND six tenths 3.042 three AND forty-two thousandths 0.0063 sixty-three ten-thousands Two hundred AND two hundreds 200.

Section 4 Decimal Notation Place Value Chart 00 0 0 00 000 0000 00000 0. 0.0 0.00 0.000 0.0000 hundred ten one tenth hundredth thousandth Ten thousandth Hundred thousandth Identify the place value for

### Addition Methods. Methods Jottings Expanded Compact Examples 8 + 7 = 15

Addition Methods Methods Jottings Expanded Compact Examples 8 + 7 = 15 48 + 36 = 84 or: Write the numbers in columns. Adding the tens first: 47 + 76 110 13 123 Adding the units first: 47 + 76 13 110 123

### Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B

Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced

### LESSON PLANS FOR PERCENTAGES, FRACTIONS, DECIMALS, AND ORDERING Lesson Purpose: The students will be able to:

LESSON PLANS FOR PERCENTAGES, FRACTIONS, DECIMALS, AND ORDERING Lesson Purpose: The students will be able to: 1. Change fractions to decimals. 2. Change decimals to fractions. 3. Change percents to decimals.

### Characteristics of the Four Main Geometrical Figures

Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.

### 3.3 Addition and Subtraction of Rational Numbers

3.3 Addition and Subtraction of Rational Numbers In this section we consider addition and subtraction of both fractions and decimals. We start with addition and subtraction of fractions with the same denominator.

### Basic numerical skills: FRACTIONS, DECIMALS, PROPORTIONS, RATIOS AND PERCENTAGES

Basic numerical skills: FRACTIONS, DECIMALS, PROPORTIONS, RATIOS AND PERCENTAGES. Introduction (simple) This helpsheet is concerned with the ways that we express quantities that are not whole numbers,

### 5 Mathematics Curriculum

New York State Common Core 5 Mathematics Curriculum G R A D E GRADE 5 MODULE 1 Topic B Decimal Fractions and Place Value Patterns 5.NBT.3 Focus Standard: 5.NBT.3 Read, write, and compare decimals to thousandths.

### CHAPTER 4 DIMENSIONAL ANALYSIS

CHAPTER 4 DIMENSIONAL ANALYSIS 1. DIMENSIONAL ANALYSIS Dimensional analysis, which is also known as the factor label method or unit conversion method, is an extremely important tool in the field of chemistry.

### Lesson 1: Fractions, Decimals and Percents

Lesson 1: Fractions, Decimals and Percents Selected Content Standards Benchmarks Addressed: N-2-H Demonstrating that a number can be expressed in many forms, and selecting an appropriate form for a given

### MathSphere MATHEMATICS. Equipment. Y6 Fractions 6365 Round decimals. Equivalence between decimals and fractions

MATHEMATICS Y6 Fractions 6365 Round decimals. Equivalence between decimals and fractions Paper, pencil, ruler Fraction cards Calculator Equipment MathSphere 6365 Round decimals. Equivalence between fractions

### ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers Basic Math 1.2 - The Number Line Basic Math 1.3 - Addition of Whole Numbers, Part I

ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers 1) Read whole numbers. 2) Write whole numbers in words. 3) Change whole numbers stated in words into decimal numeral form. 4) Write numerals in

### Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. Solve word problems that call for addition of three whole numbers

### Multiplying and Dividing Fractions

Multiplying and Dividing Fractions 1 Overview Fractions and Mixed Numbers Factors and Prime Factorization Simplest Form of a Fraction Multiplying Fractions and Mixed Numbers Dividing Fractions and Mixed

Arithmetic 1 Progress Ladder Maths Makes Sense Foundation End-of-year objectives page 2 Maths Makes Sense 1 2 End-of-block objectives page 3 Maths Makes Sense 3 4 End-of-block objectives page 4 Maths Makes

### Paramedic Program Pre-Admission Mathematics Test Study Guide

Paramedic Program Pre-Admission Mathematics Test Study Guide 05/13 1 Table of Contents Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page

### Exponential Notation and the Order of Operations

1.7 Exponential Notation and the Order of Operations 1.7 OBJECTIVES 1. Use exponent notation 2. Evaluate expressions containing powers of whole numbers 3. Know the order of operations 4. Evaluate expressions

### Chapter 4 -- Decimals

Chapter 4 -- Decimals \$34.99 decimal notation ex. The cost of an object. ex. The balance of your bank account ex The amount owed ex. The tax on a purchase. Just like Whole Numbers Place Value - 1.23456789

### Chapter 2: Linear Equations and Inequalities Lecture notes Math 1010

Section 2.1: Linear Equations Definition of equation An equation is a statement that equates two algebraic expressions. Solving an equation involving a variable means finding all values of the variable

### Integers, I, is a set of numbers that include positive and negative numbers and zero.

Grade 9 Math Unit 3: Rational Numbers Section 3.1: What is a Rational Number? Integers, I, is a set of numbers that include positive and negative numbers and zero. Imagine a number line These numbers are

### Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.

Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material

### REVIEW SHEETS BASIC MATHEMATICS MATH 010

REVIEW SHEETS BASIC MATHEMATICS MATH 010 A Summary of Concepts Needed to be Successful in Mathematics The following sheets list the key concepts that are taught in the specified math course. The sheets

### MULTIPLICATION AND DIVISION OF REAL NUMBERS In this section we will complete the study of the four basic operations with real numbers.

1.4 Multiplication and (1-25) 25 In this section Multiplication of Real Numbers Division by Zero helpful hint The product of two numbers with like signs is positive, but the product of three numbers with

### numerical place value additional topics rounding off numbers power of numbers negative numbers addition with materials fundamentals

Math Scope & Sequence fundamentals number sense and numeration of the decimal system Count to 10 by units Associate number to numeral (1-10) KN 1 KN 1 KN 2 KN 2 Identify odd and even numbers/numerals and

### PREPARATION FOR MATH TESTING at CityLab Academy

PREPARATION FOR MATH TESTING at CityLab Academy compiled by Gloria Vachino, M.S. Refresh your math skills with a MATH REVIEW and find out if you are ready for the math entrance test by taking a PRE-TEST

### 5.1 Simple and Compound Interest

5.1 Simple and Compound Interest Question 1: What is simple interest? Question 2: What is compound interest? Question 3: What is an effective interest rate? Question 4: What is continuous compound interest?

### Tenths, Hundredths, and Thousandths

Mastery Drill Tenths, Hundredths, and Thousandths You remember that and can be written as common fractions or as decimal fractions. = 0. 0 = 0.0 two two Mixed numbers in or can also be written both ways.

### Keystone National High School Placement Exam Math Level 1. Find the seventh term in the following sequence: 2, 6, 18, 54

1. Find the seventh term in the following sequence: 2, 6, 18, 54 2. Write a numerical expression for the verbal phrase. sixteen minus twelve divided by six Answer: b) 1458 Answer: d) 16 12 6 3. Evaluate

### Training Manual. Pre-Employment Math. Version 1.1

Training Manual Pre-Employment Math Version 1.1 Created April 2012 1 Table of Contents Item # Training Topic Page # 1. Operations with Whole Numbers... 3 2. Operations with Decimal Numbers... 4 3. Operations

### Exponents, Radicals, and Scientific Notation

General Exponent Rules: Exponents, Radicals, and Scientific Notation x m x n = x m+n Example 1: x 5 x = x 5+ = x 7 (x m ) n = x mn Example : (x 5 ) = x 5 = x 10 (x m y n ) p = x mp y np Example : (x) =

What five coins add up to a nickel? five pennies (1 + 1 + 1 + 1 + 1 = 5) Which is longest: a foot, a yard or an inch? a yard (3 feet = 1 yard; 12 inches = 1 foot) What do you call the answer to a multiplication

### HFCC Math Lab Arithmetic - 4. Addition, Subtraction, Multiplication and Division of Mixed Numbers

HFCC Math Lab Arithmetic - Addition, Subtraction, Multiplication and Division of Mixed Numbers Part I: Addition and Subtraction of Mixed Numbers There are two ways of adding and subtracting mixed numbers.

### Circumference and Area of a Circle

Overview Math Concepts Materials Students explore how to derive pi (π) as a ratio. Students also study the circumference and area of a circle using formulas. numbers and operations TI-30XS MultiView two-dimensional

### Decimal Notations for Fractions Number and Operations Fractions /4.NF

Decimal Notations for Fractions Number and Operations Fractions /4.NF Domain: Cluster: Standard: 4.NF Number and Operations Fractions Understand decimal notation for fractions, and compare decimal fractions.

### Exercise Worksheets. Copyright. 2002 Susan D. Phillips

Exercise Worksheets Copyright 00 Susan D. Phillips Contents WHOLE NUMBERS. Adding. Subtracting. Multiplying. Dividing. Order of Operations FRACTIONS. Mixed Numbers. Prime Factorization. Least Common Multiple.

UNDERSTANDING ALGEBRA JAMES BRENNAN Copyright 00, All Rights Reserved CONTENTS CHAPTER 1: THE NUMBERS OF ARITHMETIC 1 THE REAL NUMBER SYSTEM 1 ADDITION AND SUBTRACTION OF REAL NUMBERS 8 MULTIPLICATION

### Primary Curriculum 2014

Primary Curriculum 2014 Suggested Key Objectives for Mathematics at Key Stages 1 and 2 Year 1 Maths Key Objectives Taken from the National Curriculum 1 Count to and across 100, forwards and backwards,

### Part 1 Expressions, Equations, and Inequalities: Simplifying and Solving

Section 7 Algebraic Manipulations and Solving Part 1 Expressions, Equations, and Inequalities: Simplifying and Solving Before launching into the mathematics, let s take a moment to talk about the words

### 3. ROUNDING OFF DECIMAL NUMBERS TO THE NEAREST TENTH

3. ROUNDING OFF DECIMAL NUMBERS TO THE NEAREST TENTH Material: Decimal Board and materials Small gold circle Prepared problems Paper and pencil Presentation: 1. Form a number on the board with discs: 0.68.

### All the examples in this worksheet and all the answers to questions are available as answer sheets or videos.

BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com Numbers 3 In this section we will look at - improper fractions and mixed fractions - multiplying and dividing fractions - what decimals mean and exponents

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

### Sunny Hills Math Club Decimal Numbers Lesson 4

Are you tired of finding common denominators to add fractions? Are you tired of converting mixed fractions into improper fractions, just to multiply and convert them back? Are you tired of reducing fractions

### Maths Assessment Year 4: Fractions

Name: Maths Assessment Year : Fractions 1. Recognise and show, using diagrams, families of common equivalent fractions. 2. Count up and down in hundredths. 3. Solve problems involving increasingly harder

### Algebra 1. Practice Workbook with Examples. McDougal Littell. Concepts and Skills

McDougal Littell Algebra 1 Concepts and Skills Larson Boswell Kanold Stiff Practice Workbook with Examples The Practice Workbook provides additional practice with worked-out examples for every lesson.

### To Evaluate an Algebraic Expression

1.5 Evaluating Algebraic Expressions 1.5 OBJECTIVES 1. Evaluate algebraic expressions given any signed number value for the variables 2. Use a calculator to evaluate algebraic expressions 3. Find the sum

### What are the place values to the left of the decimal point and their associated powers of ten?

The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything

### NUMBER SYSTEMS. William Stallings

NUMBER SYSTEMS William Stallings The Decimal System... The Binary System...3 Converting between Binary and Decimal...3 Integers...4 Fractions...5 Hexadecimal Notation...6 This document available at WilliamStallings.com/StudentSupport.html

### Negative Integral Exponents. If x is nonzero, the reciprocal of x is written as 1 x. For example, the reciprocal of 23 is written as 2

4 (4-) Chapter 4 Polynomials and Eponents P( r) 0 ( r) dollars. Which law of eponents can be used to simplify the last epression? Simplify it. P( r) 7. CD rollover. Ronnie invested P dollars in a -year

### Contents. Subtraction (Taking Away)... 6. Multiplication... 7 by a single digit. by a two digit number by 10, 100 or 1000

This booklet outlines the methods we teach pupils for place value, times tables, addition, subtraction, multiplication, division, fractions, decimals, percentages, negative numbers and basic algebra Any

### Chapter 2 Measurement and Problem Solving

Introductory Chemistry, 3 rd Edition Nivaldo Tro Measurement and Problem Solving Graph of global Temperature rise in 20 th Century. Cover page Opposite page 11. Roy Kennedy Massachusetts Bay Community

### Lesson 4. Factors and Multiples. Objectives

Student Name: Date: Contact Person Name: Phone Number: Lesson 4 Factors and Multiples Objectives Understand what factors and multiples are Write a number as a product of its prime factors Find the greatest

### Calculation Policy Fractions

Calculation Policy Fractions This policy is to be used in conjunction with the calculation policy to enable children to become fluent in fractions and ready to calculate them by Year 5. It has been devised

### ROUND(cell or formula, 2)

There are many ways to set up an amortization table. This document shows how to set up five columns for the payment number, payment, interest, payment applied to the outstanding balance, and the outstanding

### c sigma & CEMTL

c sigma & CEMTL Foreword The Regional Centre for Excellence in Mathematics Teaching and Learning (CEMTL) is collaboration between the Shannon Consortium Partners: University of Limerick, Institute of Technology,

### WSMA Decimal Numbers Lesson 4

Thousands Hundreds Tens Ones Decimal Tenths Hundredths Thousandths WSMA Decimal Numbers Lesson 4 Are you tired of finding common denominators to add fractions? Are you tired of converting mixed fractions

### Grade 5 Common Core State Standard

2.1.5.B.1 Apply place value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals. M05.A-T.1.1.1 Demonstrate an understanding that 5.NBT.1 Recognize

### Accentuate the Negative: Homework Examples from ACE

Accentuate the Negative: Homework Examples from ACE Investigation 1: Extending the Number System, ACE #6, 7, 12-15, 47, 49-52 Investigation 2: Adding and Subtracting Rational Numbers, ACE 18-22, 38(a),

### Summary Of Mental Maths Targets EYFS Yr 6. Year 3. Count from 0 in multiples of 4 & 8, 50 & 100. Count back in 100s, 10s, 1s eg.

Autumn 1 Say the number names in order to 10. Read and write from 1 to 20 in numerals and words. Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward. Count from 0 in

### Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used