Chapter 5. Decimals. Use the calculator.

Size: px
Start display at page:

Transcription

1 Chapter 5. Decimals 5.1 An Introduction to the Decimals 5.2 Adding and Subtracting Decimals 5.3 Multiplying Decimals 5.4 Dividing Decimals 5.5 Fractions and Decimals 5.6 Square Roots 5.7 Solving Equations that Involve Decimals Use the calculator. 1

2 5.1 An Introduction to the Decimals 1. Identify the place value of a digit in a decimal number 2. Write decimals in expanded form 3. Read decimals and write them in standard form 4. Compare decimal using inequality symbols 5. Graph decimals on a number line 6. Round decimals 7. Read tables and graphs involving decimals 2

3 5.1 An Introduction to the Decimals 1. Identify the place value of a digit in a decimal number This is a review. e.g.1 Consider the decimal number: 8, a. What is the place value of the digit 5? Ans. hundred thousandths b. Which digit tells the the number of hundredths? Ans. 6 3

4 5.1 An Introduction to the Decimals 2. Write decimals in expanded form This is a review. e.g.2 Write the decimal number in expanded form Ans , ,000 4

5 5.1 An Introduction to the Decimals 3. Read decimals and write them in standard form This is a review. e.g.3 Write each decimal in words and then as a fraction or mixed numbers. a. One gallon of milk weighs 8.6 lbs Ans. eight and sixth Ans b. One meter is about inches Ans. thirty-nine and three thousand, seven hundred one ten-thousandths Ans. 39 3,701 10,000 5

6 5.1 An Introduction to the Decimals 3. Read decimals and write them in standard form Mostly review. e.g.3 Write each decimal in words and then as a fraction or mixed numbers. c. The smallest freshwater fish is the dwarf pygmy goby. Adult males weigh ounce. Ans. fourteen hundred-thousandths Ans ,000 d. Ocean salt water freezes at 1.94 Celsius Ans. negative one and ninety-four hundredths 94 Ans

7 5.1 An Introduction to the Decimals 3. Read decimals and write them in standard form This is a review. e.g.4 Write each number in standard form a. Sixty-seven and thirty-eight hundredths Ans b. Nineteen and twenty-five thousandths Ans

8 5.1 An Introduction to the Decimals 4. Compare decimals using inequality symbols Align decimal point. Compare digits, column by column, from left to right The first time when two digits are different If decimals are positive, the decimal with greater digit is the greater of two decimals If decimals are negative, the decimal with the smaller digit is the greater of two decimals 8

9 5.1 An Introduction to the Decimals 4. Compare decimals using inequality symbols Mostly review. e.g.5 Place an < or > symbols in the box to make a true statement: a > b < c <

10 5.1 An Introduction to the Decimals 5. Graph decimals on a number line Negative number on a number line. e.g.6 Graph 1.37, 0.9, 1.7, and

11 5.1 An Introduction to the Decimals 6. Round decimals Same rule for rounding negative numbers. e.g.8 Round each decimal to the indicated place value: a to the nearest tenth Ans b to the nearest hundredth Ans e.g.9 UTILITY BILLS A utility company calculates a homeowner s monthly natural gas bill by multiplying the unit cost of \$ by the number of therms used that month. Found the unit cost to the nearest cent. Ans. \$

12 5.1 An Introduction to the Decimals 6. Round decimals e.g.9 A plumber earned \$76, dollars in on year. Round his income to the nearest dollar. Ans. \$76,351 12

13 5.1 An Introduction to the Decimals 7. Read tables and graphs involving decimals The table shows the number of pounds of trash generated daily per person in the U.S. for selected years from 1960 through Pound of trash generated daily (per person) Year pounds Pounds year 13

14 5.2 Adding and Subtracting Decimals 1. Add decimals 2. Subtract decimals 3. Add and subtract signed decimals 4. Estimate sums and differences of decimals 5. Solve application problems by adding and subtracting decimals 14

15 5.2 Adding and Subtracting Decimals 1. Add decimals (review) e.g.1 Add: Ans Subtract decimals (review) e.g.2 Subtract: Ans e.g.3 Subtract from 45.6 Ans

16 5.2 Adding and Subtracting Decimals 3. Add and subtract signed decimals Sign rule is exactly the same as in integer case! e.g.4 Add: ( 8.3) Ans e.g.5 Add: ( 29.8) Ans e.g.6 Subtract: Ans

17 5.2 Adding and Subtracting Decimals 3. Add and subtract signed decimals Sign rule is exactly the same as in integer case! e.g.7 Subtract: 2.98 ( 27.3) Ans e.g.8 Evaluate: 33.5 ( ) Ans

18 5.2 Adding and Subtracting Decimals 4. Estimate sums and differences of decimals e.g.9 Estimate a. Estimate by rounding the addends to the nearest ten: b. Estimate by front-end rounding: Ans. 880 Ans. 650 Note: front-end rounding means that each number is rounded to its largest place value. 18

19 5.2 Adding and Subtracting Decimals 5. Solve application problems by adding and subtracting decimals e.g.10 PRICING Find the retail price of an electric stapler if an office supply company buys them for \$29.50 each and then marks them up \$12.95 to sell in its stores. Ans. \$42.45 Note: retail price = cost + markup 19

20 5.2 Adding and Subtracting Decimals 5. Solve application problems by adding and subtracting decimals e.g.11 TABLES A kitchen table has a 20-gauge stainless steel top that is inch thick and legs made of 16-gauge stainless steel that is in thick. How much thicker is the 16-gauge stainless steel? Ans inch 20

21 5.2 Adding and Subtracting Decimals 5. Solve application problems by adding and subtracting decimals e.g.12 CONDITIONING PROGRAM A 180-pound baseball player lost 4.2 pounds during the first week of spring training. He gained back 1.9 pounds the second week. Find his weight after two weeks of spring training. Ans lb 21

22 5.3 Multiplying Decimals 1. Multiplying decimals (review) 2. Multiply decimals by power of 10 (review) 3. Multiply signed decimals 4. Evaluate exponential expression that have decimal base 5. Use the order of operations rule 6. Evaluate formulas 7. Estimate product of decimals 8. Solve application problems by multiplying decimals 22

23 5.3 Multiplying Decimals 1. Multiplying decimals (review) e.g.2 Multiply: 0.004(2.3) e.g.3 Multiply: 286(3.9) Ans Ans. 1, Multiply decimals by powers of 10 (review) Comment: when multiplying a decimal by 10, 100, 1000, and so on, move decimal point to right e.g.4 Multiply: a (100) b. 46.3(100,000) Ans Ans. 4,630,000 23

24 5.3 Multiplying Decimals 2. Multiply decimals by powers of 10 (review) Comment: when multiplying a decimal by 0.1, 0.01, 0.001, and so on, move decimal point to left e.g.4 Multiply: a (0.0001) b. 0.83(0.01) Ans Ans

25 5.3 Multiplying Decimals 2. Multiply decimals by powers of 10 (review) What is million? (10 6 ), billion? (10 9 ), and trillion? (10 12 ) Write each number in standard notation: a. In 2007, the U.S had million acres of farmland. b. Americans took 10.7 billion trips on public transportation in c. It would take about trillion pennies to fill the Empire State Building. Ans. 930,900,000 Ans. 10,700,000,000 Ans. 1,818,000,000,000 25

26 5.3 Multiplying Decimals 3. Multiply signed decimals Sign rule is exactly the same as in integer case! e.g.7 Multiply a. 3.6(2.8) Ans b. ( 10,000)( 63.11) Ans. 631,100 26

27 5.3 Multiplying Decimals 4. Evaluate exponential expression that have decimal base (like integers) e.g.8 Evaluate: a. (4.2) 2 b. ( 0.07) 2 Ans

28 5.3 Multiplying Decimals 5. Use the order of operations rule (like integers) e.g.9 Evaluate: ( 0.9) Ans Estimate Formulas (review) e.g.10 Evaluate: A = P + Prt for P = 75.50, r = 0.12, t = 2 Ans

29 5.3 Multiplying Decimals 7. Estimate product of decimals e.g.11 Estimate product. a. Estimate using front-end rounding 2.371(76) Ans. 160 b. Evaluate by rounding all factors to the nearest tenth: (7.344) Ans c. Estimate by rounding: (97.89) (hint: ) Ans

30 5.3 Multiplying Decimals 8. Solve application problems by multiplying decimals e.g.12 COINS Banks wrap dimes in rolls of 50 cents. If a dime is 1.35 millimeters thick, how tall is a stack of 50 dimes? Ans mm e.g.13 WEEKLY EARNINGS An iron worker s basic workweek is 40 hours. After his daily shift is over, he can work overtime at a rate of 1.5 times his regular rate of \$18.08 per hour. How much money will he earn in a week if he works 2hours of overtime? Ans. \$

31 5.4 Dividing Decimals 1. Divide a decimal by a whole number 2. Divide a decimal by a decimal 3. Round a decimal quotient 4. Estimate quotients of decimals 5. Divide decimals by power of Divide signed decimals 7. Use the order of operations rule 8. Evaluate formulas 9. Solve application problems by dividing decimals 31

32 5.4 Dividing Decimals 1. Divide a decimal by a whole number (review) e.g.2 Divide: e.g.3 Divide: Ans Ans Divide a decimal by a decimal (review) e.g.4 Divide: Ans Question: how to check the result? 32

33 5.4 Dividing Decimals 3. Round a decimal quotient (review) e.g.5 Divide: , round the quotient to the nearest hundredth Ans Estimate quotients of decimals Rule of thumb: round both up or round both down e.g.6 Estimate the quotient: Ans. 8 33

34 5.4 Dividing Decimals 5. Divide decimals by power of 10 Comment: when dividing a decimal by 10, 100, 1000, and so on, move decimal point to left when dividing a decimal by 0.1, 0.01, 0.001, and so on, move decimal point to right e.g.7 Find each quotient: 1.67 a b. c ,000 Ans Ans. 498,

35 5.4 Dividing Decimals 6. Divide signed decimals Sign rule: just like dividing integers e.g.8 Divide: a Ans b Ans

36 5.4 Dividing Decimals 7. Use the order of operations rule Just like integers e.g.9 Evaluate: 2(0.932 ) Ans Evaluate formulas (review) e.g.10 Evaluate the formula h = for V = and B = 2.4 3V B Ans

37 5.4 Dividing Decimals 9. Solve application problems by dividing decimals Like review e.g.11 PEPPERONI A meat slicing machine cuts 12-inch-long pepperoni sausages into inch-thick slices. How many slices are there in one sausage? Ans. 96 slices 37

38 5.4 Dividing Decimals 9. Solve application problems by dividing decimals e.g.12 BROADWAY SHOWS Use the following data to determine the average number of tickets that were sold per year to Broadway shows in New York City for years 2004 through season tickets sold (in millions) Ans millions 38

39 5.5 Fractions and Decimals 1. Write fractions as equivalent terminating decimals 2. Write fractions as equivalent repeating decimal 3. Round repeating decimals 4. Graph fractions and decimals on a number line 5. Compare fractions and decimals 6. Evaluate expressions containing fractions and decimals 7. Solve application problems involving fractions and decimals 39

40 5.5 Fractions and Decimals 1. Write fractions as equivalent terminating decimals 2. Write fractions as equivalent repeating decimal This is review To write fractions as decimal, just divide. The quotient is either terminating decimal or repeating decimal. e.g.1 b. Write as a decimal. e.g.3 Write mixed number in decimal form. e.g.5 Write as a decimal Ans Ans Ans

41 5.5 Fractions and Decimals 3. Round repeating decimals (review) 11 e.g.7 Write as a decimal and round to the nearest 12 thousandth. Ans Graph fractions and decimals on a number line Change fraction to decimal then plot all decimal points. 41

42 5.5 Fractions and Decimals 5. Compare fractions and decimals (review) Change fraction to decimal e.g.8 Place an <, > or = symbol in the box to make a true statement. 3 5 a b c < > = e.g.9 Write the numbers in order from smallest to largest: , 3, Ans., ,

43 5.5 Fractions and Decimals 6. Evaluate expressions containing fractions and decimals (partly review) e.g.10 Evaluate 0.11 by working in terms of fractions Ans e.g.11 Evaluate 0.11 by working in terms of decimals. Ans e.g.12 Evaluate: ( 1.75) (0.6) + Ans

44 5.5 Fractions and Decimals 7. Solve application problems involving fractions and decimals e.g.13 SHOPPING A shopper purchased pound of fruit, 3 1 priced at \$0.99 per pound, and pound of fresh-ground coffee, selling for \$7.60 per pound. Find the total cost of these items. Ans. \$

45 5.6 Square Roots 1. Find the square root of a perfect square 2. Find the square root of fractions and decimals 3. Evaluate expressions that contain square roots 4. Evaluate formulas involving square roots 5. Approximate square roots 45

46 5.6 Square Roots (very new) 1. Find the square root of a perfect square A square root of a given number is a number whose square is the given number. e.g.1 Find two square roots of 4. Ans. 2 and 2 why? In this example, we denote that 4 = 2 In word, the positive square root of 4 is 2. 46

47 5.6 Square Roots (very new) 1. Find the square root of a perfect square In general, given a positive number a, the positive square root of a is denoted by and the negative square root of a is denoted by a a e.g. Find square root of 5. Ans. No explicit solutions. However we denote square roots of 5 by, 5 and 5 e.g. Find square root of 8. Ans. Again no explicit solutions. we denote square roots of 8 by, 8 and 8 47

48 5.6 Square Roots (very new) 1. Find the square root of a perfect square e.g. Find square root of 9. Ans. 3 and 3 We see that only perfect squares have explicit square roots. The following are first 16 perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225 e.g.2 Evaluate each square root: a. b. Ans. 5 Ans

49 5.6 Square Roots (very new) 1. Find the square root of a perfect square Expression 4 represents the positive square root of 4, here 4 is called radical expression 4 is called radicand is called radical symbol 49

50 5.6 Square Roots 2. Find the square root of fractions and decimals e.g.3 Evaluate each square root: 81 a. b. 4 9 Ans Ans

51 5.6 Square Roots 3. Evaluate expressions that contain square roots e.g.4 Evaluate: a. 144 b. Ans. 21 Ans e.g.5 Evaluate: a. 49 b. 5 Ans Ans. 2 e.g.6 Evaluate: [4 2 (4 + 1) ] Ans

52 5.6 Square Roots 4. Evaluate formulas involving square roots 2 2 e.g.7 Evaluate c = b for a = 3 and b = 4. a + Ans. 3 52

53 5.6 Square Roots 5. Approximate square roots (use calculator) e.g.8 Use calculator to approximate each square root. Round to the nearest hundredth. a. b. c Ans Ans Ans

54 5.7 Solving Equations that Involve Decimals 1. Simplify products 2. Use the distributive property 3. Simplify expressions by combining like terms 4. Use one property of equality to solve equations that involve decimals 5. Use more than one property of equality to solve equations that involve decimals 6. Use equations to solve application problems that involve decimals 54

55 5.7 Solving Equations that Involve Decimals 1. Simplify products (Like integers ) e.g.1 Multiply a y Ans. 29.2y b. 6.52b( 3) Ans b c. 2.8( 7.7r) Ans r d. 3(5.09n)2 Ans n 55

56 5.7 Solving Equations that Involve Decimals 2. Use the distributive property (Like integers ) e.g.2 Multiply a. 7.3(8t + 9) Ans. 56.4t b. 5(8.5n 6.9) Ans. 42.5n c. (m 2.4)0.09 Ans. 0.09m

57 5.7 Solving Equations that Involve Decimals 3. Simplify expressions by combining like terms (Like integers ) e.g.3 Simplify by combining like terms a. 4.5a + 3.3a b. 5.1b + ( 9.7b) + 4.9b Ans. 7.8a Ans. 9.9b c. 0.33h h 2 d. 5.02y y 1.31 Ans. 0.54h 2 Ans. 7.99y e.g.4 Simplify: 3.8(y + 2) 4.9 (1.4y + 7.9) Ans. 2.4y

58 5.7 Solving Equations that Involve Decimals 4. Use one property of equality to solve equations that involve decimals (Like integers ) e.g.5 Solve each equation and check the result: a. x = 10.9 b. x 2.31 = 5.68 Ans. x = 7.2 Ans. x = 3.37 e.g.6 Solve: x 4 = 9.9 Ans. x = 39.6 e.g.7 Solve: = 5.6x Ans. x =

59 5.7 Solving Equations that Involve Decimals 5. Use more than one property of equality to solve equations that involve decimals (Like integers ) e.g.8 Solve: 7.1m 1.03 = 6.71 Ans. m = 0.8 e.g.9 Solve the equation and check the result: 0.1m 4 = 0.9m Ans. m = 7 e.g.10 Solve: 5(m + 1.9) = 11.8 Ans. m =

60 5.7 Solving Equations that Involve Decimals 6. Use equations to solve application problems that involve decimals(like integers ) e.g.11 GRADUATION A printer charges a setup fee of \$16 and then 85 cents for each graduation announcement printed (tax included). If a student wants to spend \$50 on her announcements, how many can she have printed? Note: 5 step process. Ans. 40 graduation announcements 60

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

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

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

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.

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

FSCJ PERT. Florida State College at Jacksonville. assessment. and Certification Centers

FSCJ Florida State College at Jacksonville Assessment and Certification Centers PERT Postsecondary Education Readiness Test Study Guide for Mathematics Note: Pages through are a basic review. Pages forward

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

Math and FUNDRAISING. Ex. 73, p. 111 1.3 0. 7

Standards Preparation Connect 2.7 KEY VOCABULARY leading digit compatible numbers For an interactive example of multiplying decimals go to classzone.com. Multiplying and Dividing Decimals Gr. 5 NS 2.1

20(-1) - (-4) (-5) 10)

Pre-Algebra Final Exam Review Name Write the whole number in words. 1) 9,300,695 1) Add. 2) 58,142 30,645 + 5,300,621 2) Round the whole number to the given place. 3) 49,815,425 to the nearest million

Learning Objectives for Section 1.1 Linear Equations and Inequalities

Learning Objectives for Section 1.1 Linear Equations and Inequalities After this lecture and the assigned homework, you should be able to solve linear equations. solve linear inequalities. use interval

4 th Grade Summer Mathematics Review #1. Name: 1. How many sides does each polygon have? 2. What is the rule for this function machine?

. How many sides does each polygon have? th Grade Summer Mathematics Review #. What is the rule for this function machine? A. Pentagon B. Nonagon C. Octagon D. Quadrilateral. List all of the factors of

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

Regents Exam Questions A2.S.7: Exponential Regression www.jmap.org

A2.S.7: Exponential Regression: Determine the function for the regression model, using appropriate technology, and use the regression function to interpolate/extrapolate from data 1 A cup of soup is left

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

Unit 6 Number and Operations in Base Ten: Decimals

Unit 6 Number and Operations in Base Ten: Decimals Introduction Students will extend the place value system to decimals. They will apply their understanding of models for decimals and decimal notation,

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

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

Algebra 1: Basic Skills Packet Page 1 Name: Integers 1. 54 + 35 2. 18 ( 30) 3. 15 ( 4) 4. 623 432 5. 8 23 6. 882 14

Algebra 1: Basic Skills Packet Page 1 Name: Number Sense: Add, Subtract, Multiply or Divide without a Calculator Integers 1. 54 + 35 2. 18 ( 30) 3. 15 ( 4) 4. 623 432 5. 8 23 6. 882 14 Decimals 7. 43.21

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

A.2. Exponents and Radicals. Integer Exponents. What you should learn. Exponential Notation. Why you should learn it. Properties of Exponents

Appendix A. Exponents and Radicals A11 A. Exponents and Radicals What you should learn Use properties of exponents. Use scientific notation to represent real numbers. Use properties of radicals. Simplify

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.

Math Refresher. Book #2. Workers Opportunities Resources Knowledge

Math Refresher Book #2 Workers Opportunities Resources Knowledge Contents Introduction...1 Basic Math Concepts...2 1. Fractions...2 2. Decimals...11 3. Percentages...15 4. Ratios...17 Sample Questions...18

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

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

9.3 Solving Quadratic Equations by Using the Quadratic Formula 9.3 OBJECTIVES 1. Solve a quadratic equation by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation

5.1 Radical Notation and Rational Exponents

Section 5.1 Radical Notation and Rational Exponents 1 5.1 Radical Notation and Rational Exponents We now review how exponents can be used to describe not only powers (such as 5 2 and 2 3 ), but also roots

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

7-2 Solving Exponential Equations and Inequalities. Solve each equation. 1. 3 5x = 27 2x 4 SOLUTION:

7-2 Solving Exponential Equations and Inequalities Solve each equation. 1. 3 5x = 27 2x 4 3. 2 6x = 32 x 2 12 2. 16 2y 3 = 4 y + 1 10 4. 49 x + 5 = 7 8x 6 3. 2 6x = 32 x 2 5. SCIENCE Mitosis is a process

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.

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.

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

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

1 Decimals Adding and Subtracting Decimals are a group of digits, which express numbers or measurements in units, tens, and multiples of 10. The digits for units and multiples of 10 are followed by a decimal

Chapter 7 - Roots, Radicals, and Complex Numbers

Math 233 - Spring 2009 Chapter 7 - Roots, Radicals, and Complex Numbers 7.1 Roots and Radicals 7.1.1 Notation and Terminology In the expression x the is called the radical sign. The expression under the

Assessment For The California Mathematics Standards Grade 3

Introduction: Summary of Goals GRADE THREE By the end of grade three, students deepen their understanding of place value and their understanding of and skill with addition, subtraction, multiplication,

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

Irrational Numbers. A. Rational Numbers 1. Before we discuss irrational numbers, it would probably be a good idea to define rational numbers.

Irrational Numbers A. Rational Numbers 1. Before we discuss irrational numbers, it would probably be a good idea to define rational numbers. Definition: Rational Number A rational number is a number that

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

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%

Solving Equations With Fractional Coefficients

Solving Equations With Fractional Coefficients Some equations include a variable with a fractional coefficient. Solve this kind of equation by multiplying both sides of the equation by the reciprocal of

PERT Computerized Placement Test

PERT Computerized Placement Test REVIEW BOOKLET FOR MATHEMATICS Valencia College Orlando, Florida Prepared by Valencia College Math Department Revised April 0 of 0 // : AM Contents of this PERT Review

Figure 1. A typical Laboratory Thermometer graduated in C.

SIGNIFICANT FIGURES, EXPONENTS, AND SCIENTIFIC NOTATION 2004, 1990 by David A. Katz. All rights reserved. Permission for classroom use as long as the original copyright is included. 1. SIGNIFICANT FIGURES

Grade 4 Unit 3: Multiplication and Division; Number Sentences and Algebra

Grade 4 Unit 3: Multiplication and Division; Number Sentences and Algebra Activity Lesson 3-1 What s My Rule? page 159) Everyday Mathematics Goal for Mathematical Practice GMP 2.2 Explain the meanings

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,

Quarterly Cumulative Test 2

Select the best answer. 1. Find the difference 90 37.23. A 67.23 C 52.77 B 57.77 D 32.23 2. Which ratio is equivalent to 3 20? F 5 to 100 H 140 to 21 G 100 to 5 J 21 to 140 3. Alonda purchased 8 for \$2.00.

8. Simplification of Radical Expressions 8. OBJECTIVES 1. Simplify a radical expression by using the product property. Simplify a radical expression by using the quotient property NOTE A precise set of

(c) Nine thousand nineteen in standard form is. [1] In 4598, the digit is in the hundreds place, and its value is.

Assessment Test for Singapore Primary Mathematics 3A Standards Edition This test covers material taught in Primary Mathematics 3A, Standards Edition (http://www.singaporemath.com/) 1. Fill in the blanks.

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

Math 120 Final Exam Practice Problems, Form: A

Math 120 Final Exam Practice Problems, Form: A Name: While every attempt was made to be complete in the types of problems given below, we make no guarantees about the completeness of the problems. Specifically,

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

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

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.

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

MATH COMPUTATION. Part 1. TIME : 15 Minutes

MATH COMPUTATION Part 1 TIME : 15 Minutes This is a practice test - the results are not valid for certificate requirements. A calculator may not be used for this test. MATH COMPUTATION 1. 182 7 = A. 20

Dr Brian Beaudrie pg. 1

Multiplication of Decimals Name: Multiplication of a decimal by a whole number can be represented by the repeated addition model. For example, 3 0.14 means add 0.14 three times, regroup, and simplify,

Section 5.4 Multiplying Decimals

Section 5.4 Multiplying Decimals Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Multiply a decimal by a decimal. Multiplying whole numbers

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

Definition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.

8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent

Session 29 Scientific Notation and Laws of Exponents. If you have ever taken a Chemistry class, you may have encountered the following numbers:

Session 9 Scientific Notation and Laws of Exponents If you have ever taken a Chemistry class, you may have encountered the following numbers: There are approximately 60,4,79,00,000,000,000,000 molecules

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

Whole Number and Decimal Place Values

Whole Number and Decimal Place Values We will begin our review of place values with a look at whole numbers. When writing large numbers it is common practice to separate them into groups of three using

MEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile.

MEASUREMENTS A measurement includes a number and a unit. 3 feet 7 minutes 12 gallons Standard units of measurement have been established to simplify trade and commerce. TIME Equivalences between units

Five daily lessons. Page 23. Page 25. Page 29. Pages 31

Unit 4 Fractions and decimals Five daily lessons Year 5 Spring term Unit Objectives Year 5 Order a set of fractions, such as 2, 2¾, 1¾, 1½, and position them on a number line. Relate fractions to division

Autumn - 12 Weeks. Spring 11 Weeks. Summer 12 Weeks. Not As We Know It Limited 2014

A Year 5 Mathematician Planning of coverage and resources. Autumn - 12 Weeks Spring 11 Weeks Summer 12 Weeks TARGETS NHM YR 5 Collins 5 Abacus 5 Abacus 6 LA Prior Step NHM 4 CPM 4 Ginn 4 Number, place

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

Word Problems Involving Systems of Linear Equations

Word Problems Involving Systems of Linear Equations Many word problems will give rise to systems of equations that is, a pair of equations like this: 2x+3y = 10 x 6y = 5 You can solve a system of equations

SUNY ECC. ACCUPLACER Preparation Workshop. Algebra Skills

SUNY ECC ACCUPLACER Preparation Workshop Algebra Skills Gail A. Butler Ph.D. Evaluating Algebraic Epressions Substitute the value (#) in place of the letter (variable). Follow order of operations!!! E)

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

COMPETENCY TEST SAMPLE TEST. A scientific, non-graphing calculator is required for this test. C = pd or. A = pr 2. A = 1 2 bh

BASIC MATHEMATICS COMPETENCY TEST SAMPLE TEST 2004 A scientific, non-graphing calculator is required for this test. The following formulas may be used on this test: Circumference of a circle: C = pd or

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

Algebra I Sample Questions. 1 Which ordered pair is not in the solution set of (1) (5,3) (2) (4,3) (3) (3,4) (4) (4,4)

1 Which ordered pair is not in the solution set of (1) (5,3) (2) (4,3) (3) (3,4) (4) (4,4) y 1 > x + 5 and y 3x 2? 2 5 2 If the quadratic formula is used to find the roots of the equation x 2 6x 19 = 0,

1) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-1) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = 7) (5)(-4) = 8) (-3)(-6) = 9) (-1)(2) =

Extra Practice for Lesson Add or subtract. ) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = Multiply. 7) (5)(-4) = 8) (-3)(-6) = 9) (-)(2) = Division is

Linear Equations and Inequalities

Linear Equations and Inequalities Section 1.1 Prof. Wodarz Math 109 - Fall 2008 Contents 1 Linear Equations 2 1.1 Standard Form of a Linear Equation................ 2 1.2 Solving Linear Equations......................

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

\$566.30. What is the monthly interest rate on the account? (Round to the nearest hundredth of a percent.) 4 = x 12. 7)

Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1)What percent of 6 is 27? 1) 2)64.288 is 28.7% of what number? 2) 3)112% of what number is

The symbols indicate where the topic is first introduced or specifically addressed.

ingapore Math Inc. cope and equence U: U.. Edition : ommon ore Edition : tandards Edition : ommon ore tandards 1 2 3 4 5 Reviews in ommon ore Edition cover just the unit whereas those in U.. and tandards

Powers and Roots. 20 Sail area 810 ft 2. Sail area-displacement ratio (r) 22 24 26 28 30 Displacement (thousands of pounds)

C H A P T E R Powers and Roots Sail area-displacement ratio (r) 1 16 14 1 1 Sail area 1 ft 4 6 Displacement (thousands of pounds) ailing the very word conjures up images of warm summer S breezes, sparkling

ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES

ARE YOU A RADICAL OR JUST A SQUARE ROOT? EXAMPLES 1. Squaring a number means using that number as a factor two times. 8 8(8) 64 (-8) (-8)(-8) 64 Make sure students realize that x means (x ), not (-x).

Rational Exponents. Squaring both sides of the equation yields. and to be consistent, we must have

8.6 Rational Exponents 8.6 OBJECTIVES 1. Define rational exponents 2. Simplify expressions containing rational exponents 3. Use a calculator to estimate the value of an expression containing rational exponents

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

ALGEBRA I (Common Core)

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, June 17, 2015 1:15 to 4:15 p.m. MODEL RESPONSE SET Table of Contents Question 25..................

7.1 Graphs of Quadratic Functions in Vertex Form

7.1 Graphs of Quadratic Functions in Vertex Form Quadratic Function in Vertex Form A quadratic function in vertex form is a function that can be written in the form f (x) = a(x! h) 2 + k where a is called

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

Day 1. 1. What number is five cubed? 2. A circle has radius r. What is the formula for the area of the circle?

Mental Arithmetic Questions 1. What number is five cubed? KS3 MATHEMATICS 10 4 10 Level 7 Questions Day 1 2. A circle has radius r. What is the formula for the area of the circle? 3. Jenny and Mark share

12) 13) 14) (5x)2/3. 16) x5/8 x3/8. 19) (r1/7 s1/7) 2

DMA 080 WORKSHEET # (8.-8.2) Name Find the square root. Assume that all variables represent positive real numbers. ) 6 2) 8 / 2) 9x8 ) -00 ) 8 27 2/ Use a calculator to approximate the square root to decimal

NWT Apprenticeship Support Materials

NWT Apprenticeship Support Materials Math Reading Comprehension Science * Module 1 Foundations * Module 2 Patterns and Relations * Module 3 Variables and Equations * Module 4 Measuring Time, Shapes and

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

Test 4 Sample Problem Solutions, 27.58 = 27 47 100, 7 5, 1 6. 5 = 14 10 = 1.4. Moving the decimal two spots to the left gives

Test 4 Sample Problem Solutions Convert from a decimal to a fraction: 0.023, 27.58, 0.777... For the first two we have 0.023 = 23 58, 27.58 = 27 1000 100. For the last, if we set x = 0.777..., then 10x

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

Using Proportions to Solve Percent Problems I

RP7-1 Using Proportions to Solve Percent Problems I Pages 46 48 Standards: 7.RP.A. Goals: Students will write equivalent statements for proportions by keeping track of the part and the whole, and by solving

a. 3.452 x 10 = 34.52 b. 3.452 x 100 = c. 3.452 x 1000 = d. Explain how and why the value of the 5 changed in (a), (b), and (c). 1.A.

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 1 Problem Set 5 1 1. Record the digits of the first factor on the top row of the place value chart. Draw arrows to show how the value of each digit changes

Reading Writing Small Numbers Objective To read write small numbers in stard exped notations wwweverydaymathonlinecom epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment

Quarter One: August-October

Quarter One: August-October (Chapters 1 3, 5-6, 10) August - December Quarterly Addition facts with sums through 20 General Math Content 1. Write sums through 20. 1. Choose and enter the appropriate answer.

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,

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.

CALCULATIONS. Understand the operation of addition and the associated vocabulary, and its relationship to subtraction

CALCULATIONS Pupils should be taught to: Understand the operation of addition and the associated vocabulary, and its relationship to subtraction As outcomes, Year 4 pupils should, for example: Use, read