Algebra 1A and 1B Summer Packet

Size: px
Start display at page:

Download "Algebra 1A and 1B Summer Packet"

Transcription

1 Algebra 1A and 1B Summer Packet Name: Calculators are not allowed on the summer math packet. This packet is due the first week of school and will be counted as a grade. You will also be tested over the material in this packet. Come to school prepared!!! Solve each problem and place the answer on the line to the left of the problem. Adding Integers A. Steps if both numbers are positive. Example: Step 1: Add the two numbers = 7 The answer is 7. B. Steps if both numbers are negative. Example: (-5) + (-2) Step 1: Ignore the negative signs and add the two numbers = 7 Step 2: Put a negative sign on the answer. The answer is -7. C. Steps if one number is positive and one number is negative. Example: (-2) + 9 Step 1: Ignore the negative sign and determine which number is greater. 9 is greater than 2 The answer will have the sign of the greater number so the answer is positive because 9 is positive. Step 2: Subtract the smaller number from the larger number. 2 is smaller and 9 is larger 9 2 = 7 Step 3: Combine the sign of answer with the numeric answer. The answer is (-4) (-17) (-3) + (-6) (-21) (-45) (-34) 8. (-23) + (-12)

2 Subtracting Integers A. Two negative signs in a row = a positive sign. Example: 6 (-11) Step 1: combine the negative signs 6 (-11) = The answer is 17. B. Turn subtraction into adding a negative number. Example: 4 10 = 4 + (-10) The answer is -6. C. Use process for adding integers from the previous page. 9. (-4) (-17) (-3) (-6) (-21) (-45) (-34) 16. (-23) (-12)

3 Multiplying Integers A. The following signs are equivalent multiplication signs: * x ( ) B. If multiplying two positive numbers, answer will be positive. Example: (5) (8) Step 1: Determine the numeric answer by ignoring any negative signs. (5) (8) = 40 Step 2: Determine sign of the answer. Since both numbers are positive, the answer will be positive. The answer is 40. C. If multiplying two negative numbers, answer will be positive. Example: (-5) (-8) Step 1: Determine the numeric answer by ignoring any negative signs. (-5) (-8) = 40 Step 2: Determine sign of the answer. Since both numbers are negative, the answer will be positive. The answer is 40. D. If multiplying one positive number and one negative number, answer will be negative. Example: (-5) (8) Step 1: Determine the numeric answer by ignoring any negative signs. (-5) (8) = 40 Step 2: Determine the sign of the answer. Since one number is positive and one number is negative, the answer will be negative. The answer is (-4) (5) 21. (-17) (34) 18. (-3) (-6) (-21) 19. (13) (9) 23. (23) (-45) 20. (15) (-34) 24. (-23) (-12)

4 Dividing Integers A. The following signs are equivalent division signs: / B. If both numbers are positive, the answer will be positive. C. If both numbers are negative, the answer will be positive. D. If one number is positive and one number is negative, the answer will be negative. E. Steps: Example: 15 / 5 Step 1: Determine the numeric answer by dividing the two numbers and ignoring any negative signs. 15 / 5 = 3 Step 2: Determine the sign of the answer. Since both numbers are positive, the answer will be positive. The answer is 3. Example: (-25) / (-5) Step 1: Determine the numeric answer by dividing the two numbers and ignoring any negative signs. (-25) / (-5) = 5 Step 2: Determine the sign of the answer. Since both numbers are negative, the answer will be positive. The answer is 5. Example: 40 / (-8) Step 1: Determine the numeric answer by dividing the two numbers and ignoring any negative signs. 40 / (-8) = 5 Step 2: Determine the sign of the answer. Since one number is positive and one number is negative, the answer will be negative. The answer is (-12) / (-56) / (-7) 26. (-24) / (-8) 30. (-98) / / (-2) 31. (-28) / / (-16) 32. (-108) / 4

5 Adding Fractions A. The denominators are identical and both fractions are positive. Example: Step 1: Add the numerators = 5 Step 2: Keep the denominator the same, since the denominators for each of the fractions is the same. Answer is 5 9. B. The denominators are identical and both fractions are negative. 1 2 Example: Step 1: Adding the numerators. (-1) + (-2) = -3 Step 2: Keep the denominator the same, since the denominator for each of the fractions is the same. 3 Answer is. 4 C. The denominators are identical and one fraction is positive and one fraction is negative. Example: Step 1: Adding the numerators. 4 + (-5) = -1 Step 2: Keep the denominator the same, since the denominator for each of the fractions is the same. 1 Answer is

6

7 Adding fractions continued D. Denominators are different. You may not add fractions unless they have identical denominators. You must modify the fractions to have identical denominators by finding the Least Common Denominator (LCD). Example: Step 1: Find the LCD. a) Find the prime factors of the denominator. The prime factors of the first denominator (4) are (2) (2) = 2². The prime factors of the second denominator (6) are (2) (3). b) Write the prime factors in exponential format. 4 = = 2 * 3 c) Find the greatest power of each unique prime factor. The unique prime factors are 2 and 3. The greatest power of 2 is 2 2. The greatest power of 3 is 3. d) Multiply these together = LCD. (2²) (3) = (4) (3) = 12 = LCD Step 2: Rewrite the fractions so that each has the LCD as its denominator. 3 5?? + = a) To compute the new numerators, look at each fraction individually. In the first fraction, multiply the old denominator (4) by 3 for it to be equal to the new denominator. Multiply the old numerator by 3 to compute the new numerator: 3 * 3 = 9. In the second fraction, multiply the old denominator (6) by 2 for it to be equal to the new denominator. Multiply the old numerator by 2 to compute the new numerator: (-5) * 2 = Step 3: Now denominators are identical. See previous instructions to add fractions. 1 Answer is

8 Subtracting Fractions Just like subtracting integers, change subtraction of a fraction to adding a negative fraction, remembering that two negative signs in a row equal a positive sign. You may not subtract two fractions unless they have identical denominators. Example: Step 1: Change it to the following: Step 2: Then follow the steps for adding fractions. a) The LCD is b) Add the numerators. 8 Answer is =

9 Multiplying Fractions A. If both numbers are positive, the answer will be positive. B. If both numbers are negative, the answer will be positive. C. If one number is positive and one number is negative, then answer will be negative. D. Fractions should be simplified/reduced/canceled before multiplying. Any numerator may be canceled only with any denominator. Look for a common factor. Example: 3 * Step 1: Reduce. a) The Numerator 3 and denominator 9 have a common factor of 3. Divide each by * 10 3 b) The Numerator 4 and denominator 10 have a common factor of 2. Divide each by * 5 3 Step 2: After simplifying the fractions, multiply numerator by numerator and then multiply denominator by denominator. a) Numerator: 1 * 2 = 2 b) Denominator: 5 * 3 = 15 Answer is * 63. * * 64. * * 65. * * 66. *

10 Dividing Fractions A. If both numbers are positive, the answer will be positive. B. If both numbers are negative, the answer will be positive. C. If one number is positive and one number is negative, then answer will be negative. Example: Step 1: Dividing by a fraction is the same as multiplying by its reciprocal. Change the division operation to multiplication and flip the second fraction. 4 3 * 7 2 Step 2: Determine if the expression can be simplified. a) Numerator 4 and denominator 2 have a common factor of 2. Divide each by * 7 1 Step 3: Multiply the two fractions using the steps in the previous section. Answer is:

11 Properties In Algebra 1, you will be asked to identify certain properties. These are properties that are the rules of Algebra that allow us to work the problems in certain ways. Here is a list of properties that you should be able to recognize: Associative Property: Addition: 1 + (2 + 3) = (1 + 2) + 3 Multiplication: 1 * (2 * 3) = (1 *2* 3) Commutative Property: Addition: = Multiplication: 1 * 2 = 2 * 1 Distributive: 2 (x + 3) = 2x + 6 Additive Inverses: 4 + (-4) = 0 Multiplicative Inverses: Additive Identity: = 1 1 4* 1 4 = Multiplicative Identity: 5 * 1 = 5 Determine if the expressions are True or False. If True, state what property is shown = (2 + 3) + 5 = 2 + (3 + 5) 77. 4(2 + 3) = 4(2) + 4(3) (-5) = (4 2) = (9 4) * (9 2) * 4 = 4 * = = 2

12 Order of Operations Operations are addition, subtraction, multiplication, division, square, etc. There is an order that operations are performed designated by the acronym PEMDAS. Operations are always performed from left to right. P = parentheses E = exponent M = multiplication D = division A = addition S = subtraction Practice: Example: (3 + 6) X 2 Step 1: Order of operations says parentheses is first. (3 + 6) = 9 Equation is now 9 X 2 Step 2: Perform the multiplication 9 X 2 = 18 Answer is ( ) (5 3)² (3 (6 5)) 89. 5² - (12 2) (6 2) (5 1)

13 Evaluating Expressions To evaluate an expression, substitute a number for each variable and perform the operation(s) paying particular attention to the order of operations. Example: 6x + 4y =? when x = 2 and y = 3 Step 1: Substitute 2 for x and 3 for y in the expression Step 2: Order of operations says do multiplication first. 6 2 = 12 and 4 3 = 12 Expression now is Step 3: Perform addition = 24 Answer is j = 5 and k = p = 4 and q = 6 k j 5 (6 + p) (q p) 92. m = 6 and n = x = 3, y = 5 and z = 5 m (n + 1) 2 + y x + z 93. x = 5, y = 5 and z = x = 2 and y = 4 x + y + 2z 5 + yx x

14 Rounding Decimals Rounding means reducing the number of digits while keeping the value similar. Rounding can be to any number of digits. Step 1: Determine the digit to which you are rounding (i.e. whole number, how many decimal places, etc. Step 2: Look at the digit immediately to the right and determine whether to round up or stay the same. a. If the digit to the right is 5-9, round up to the next value. b. If the digit to the right is 0-4, keep the same. Step 3: Eliminate all digits to the right of the rounded digit. Example: Round to the nearest whole number Step 1: Rounding to a whole number means no decimals. Step 2: The number to the right of the whole number is 4 therefore whole number stays the same. Answer is 12. Example: Round to 1 decimal place Step 1: Rounding to 1 decimal place means only 1 digit to the right of the decimal point. Step 2: The number to the right of 1 decimal place is 7 therefore round up the 1 st decimal place to 1. Answer is -2.1 Example: Round to 3 decimal places Step 1: Rounding to 3 decimal places means only 3 digits to the right of the decimal point. Step 2: The number to the right of the 3 rd decimal place is 4 therefore no rounding up. Answer is Round the following to the nearest whole number Round the following to 1 decimal place Round the following to 2 decimal places Round the following to 3 decimal places

15 Answer Key Adding Integers Subtracting Integers Multiplying Integers Dividing Integers Adding Fractions (Identical Denominators) Adding Fractions (Different Denominators)

16 Subtracting Fractions Multiplying Fractions Dividing Fractions Properties True, Commutative Property True, Associative Property True, Distributive Property False False True, Commutative Property False 82. True, Additive Identity Order of Operations

17 Evaluating Expressions Rounding of Decimals

3.1. RATIONAL EXPRESSIONS

3.1. RATIONAL EXPRESSIONS 3.1. RATIONAL EXPRESSIONS RATIONAL NUMBERS In previous courses you have learned how to operate (do addition, subtraction, multiplication, and division) on rational numbers (fractions). Rational numbers

More information

Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704.

Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. The purpose of this Basic Math Refresher is to review basic math concepts so that students enrolled in PUBP704:

More information

Adding and Subtracting Fractions. 1. The denominator of a fraction names the fraction. It tells you how many equal parts something is divided into.

Adding and Subtracting Fractions. 1. The denominator of a fraction names the fraction. It tells you how many equal parts something is divided into. Tallahassee Community College Adding and Subtracting Fractions Important Ideas:. The denominator of a fraction names the fraction. It tells you how many equal parts something is divided into.. The numerator

More information

PREPARATION FOR MATH TESTING at CityLab Academy

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

More information

Solutions of Linear Equations in One Variable

Solutions of Linear Equations in One Variable 2. Solutions of Linear Equations in One Variable 2. OBJECTIVES. Identify a linear equation 2. Combine like terms to solve an equation We begin this chapter by considering one of the most important tools

More information

Algebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions.

Algebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions. Page 1 of 13 Review of Linear Expressions and Equations Skills involving linear equations can be divided into the following groups: Simplifying algebraic expressions. Linear expressions. Solving linear

More information

MATH-0910 Review Concepts (Haugen)

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,

More information

Section 4.1 Rules of Exponents

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

More information

Fractions and Linear Equations

Fractions and Linear Equations Fractions and Linear Equations Fraction Operations While you can perform operations on fractions using the calculator, for this worksheet you must perform the operations by hand. You must show all steps

More information

SIMPLIFYING ALGEBRAIC FRACTIONS

SIMPLIFYING ALGEBRAIC FRACTIONS Tallahassee Community College 5 SIMPLIFYING ALGEBRAIC FRACTIONS In arithmetic, you learned that a fraction is in simplest form if the Greatest Common Factor (GCF) of the numerator and the denominator is

More information

TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers

TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime

More information

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

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.

More information

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. 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,

More information

Radicals - Rational Exponents

Radicals - Rational Exponents 8. Radicals - Rational Exponents Objective: Convert between radical notation and exponential notation and simplify expressions with rational exponents using the properties of exponents. When we simplify

More information

Exponents, Radicals, and Scientific Notation

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) =

More information

This assignment will help you to prepare for Algebra 1 by reviewing some of the things you learned in Middle School. If you cannot remember how to complete a specific problem, there is an example at the

More information

Solving Logarithmic Equations

Solving Logarithmic Equations Solving Logarithmic Equations Deciding How to Solve Logarithmic Equation When asked to solve a logarithmic equation such as log (x + 7) = or log (7x + ) = log (x + 9), the first thing we need to decide

More information

2.6 Exponents and Order of Operations

2.6 Exponents and Order of Operations 2.6 Exponents and Order of Operations We begin this section with exponents applied to negative numbers. The idea of applying an exponent to a negative number is identical to that of a positive number (repeated

More information

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

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

More information

Click on the links below to jump directly to the relevant section

Click on the links below to jump directly to the relevant section Click on the links below to jump directly to the relevant section What is algebra? Operations with algebraic terms Mathematical properties of real numbers Order of operations What is Algebra? Algebra is

More information

Chapter 1: Order of Operations, Fractions & Percents

Chapter 1: Order of Operations, Fractions & Percents HOSP 1107 (Business Math) Learning Centre Chapter 1: Order of Operations, Fractions & Percents ORDER OF OPERATIONS When finding the value of an expression, the operations must be carried out in a certain

More information

Pre-Algebra - Order of Operations

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

More information

2. Simplify. College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key. Use the distributive property to remove the parentheses

2. Simplify. College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key. Use the distributive property to remove the parentheses College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key 1. Multiply 2 3 5 1 Use the distributive property to remove the parentheses 2 3 5 1 2 25 21 3 35 31 2 10 2 3 15 3 2 13 2 15 3 2

More information

0.8 Rational Expressions and Equations

0.8 Rational Expressions and Equations 96 Prerequisites 0.8 Rational Expressions and Equations We now turn our attention to rational expressions - that is, algebraic fractions - and equations which contain them. The reader is encouraged to

More information

2 is the BASE 5 is the EXPONENT. Power Repeated Standard Multiplication. To evaluate a power means to find the answer in standard form.

2 is the BASE 5 is the EXPONENT. Power Repeated Standard Multiplication. To evaluate a power means to find the answer in standard form. Grade 9 Mathematics Unit : Powers and Exponent Rules Sec.1 What is a Power 5 is the BASE 5 is the EXPONENT The entire 5 is called a POWER. 5 = written as repeated multiplication. 5 = 3 written in standard

More information

Answers to Basic Algebra Review

Answers to Basic Algebra Review Answers to Basic Algebra Review 1. -1.1 Follow the sign rules when adding and subtracting: If the numbers have the same sign, add them together and keep the sign. If the numbers have different signs, subtract

More information

Property: Rule: Example:

Property: Rule: Example: Math 1 Unit 2, Lesson 4: Properties of Exponents Property: Rule: Example: Zero as an Exponent: a 0 = 1, this says that anything raised to the zero power is 1. Negative Exponent: Multiplying Powers with

More information

3 cups ¾ ½ ¼ 2 cups ¾ ½ ¼. 1 cup ¾ ½ ¼. 1 cup. 1 cup ¾ ½ ¼ ¾ ½ ¼. 1 cup. 1 cup ¾ ½ ¼ ¾ ½ ¼

3 cups ¾ ½ ¼ 2 cups ¾ ½ ¼. 1 cup ¾ ½ ¼. 1 cup. 1 cup ¾ ½ ¼ ¾ ½ ¼. 1 cup. 1 cup ¾ ½ ¼ ¾ ½ ¼ cups cups cup Fractions are a form of division. When I ask what is / I am asking How big will each part be if I break into equal parts? The answer is. This a fraction. A fraction is part of a whole. The

More information

CAHSEE on Target UC Davis, School and University Partnerships

CAHSEE on Target UC Davis, School and University Partnerships UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 006 Director Sarah R. Martinez,

More information

Lesson Plan -- Rational Number Operations

Lesson Plan -- Rational Number Operations Lesson Plan -- Rational Number Operations Chapter Resources - Lesson 3-12 Rational Number Operations - Lesson 3-12 Rational Number Operations Answers - Lesson 3-13 Take Rational Numbers to Whole-Number

More information

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

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

More information

Accuplacer Arithmetic Study Guide

Accuplacer Arithmetic Study Guide Testing Center Student Success Center 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

More information

MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

More information

Name Date Block. Algebra 1 Laws of Exponents/Polynomials Test STUDY GUIDE

Name Date Block. Algebra 1 Laws of Exponents/Polynomials Test STUDY GUIDE Name Date Block Know how to Algebra 1 Laws of Eponents/Polynomials Test STUDY GUIDE Evaluate epressions with eponents using the laws of eponents: o a m a n = a m+n : Add eponents when multiplying powers

More information

Order of Operations More Essential Practice

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

More information

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

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.

More information

Solving Exponential Equations

Solving Exponential Equations Solving Exponential Equations Deciding How to Solve Exponential Equations When asked to solve an exponential equation such as x + 6 = or x = 18, the first thing we need to do is to decide which way is

More information

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

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

More information

2.3. Finding polynomial functions. An Introduction:

2.3. Finding polynomial functions. An Introduction: 2.3. Finding polynomial functions. An Introduction: As is usually the case when learning a new concept in mathematics, the new concept is the reverse of the previous one. Remember how you first learned

More information

Negative Integer Exponents

Negative Integer Exponents 7.7 Negative Integer Exponents 7.7 OBJECTIVES. Define the zero exponent 2. Use the definition of a negative exponent to simplify an expression 3. Use the properties of exponents to simplify expressions

More information

Using the Properties in Computation. a) 347 35 65 b) 3 435 c) 6 28 4 28

Using the Properties in Computation. a) 347 35 65 b) 3 435 c) 6 28 4 28 (1-) Chapter 1 Real Numbers and Their Properties In this section 1.8 USING THE PROPERTIES TO SIMPLIFY EXPRESSIONS The properties of the real numbers can be helpful when we are doing computations. In this

More information

Clifton High School Mathematics Summer Workbook Algebra 1

Clifton High School Mathematics Summer Workbook Algebra 1 1 Clifton High School Mathematics Summer Workbook Algebra 1 Completion of this summer work is required on the first day of the school year. Date Received: Date Completed: Student Signature: Parent Signature:

More information

ACCUPLACER MATH TEST REVIEW

ACCUPLACER MATH TEST REVIEW ACCUPLACER MATH TEST REVIEW ARITHMETIC ELEMENTARY ALGEBRA COLLEGE ALGEBRA The following pages are a comprehensive tool used to maneuver the ACCUPLACER UAS Math portion. This tests your mathematical capabilities

More information

Radicals - Multiply and Divide Radicals

Radicals - Multiply and Divide Radicals 8. Radicals - Multiply and Divide Radicals Objective: Multiply and divide radicals using the product and quotient rules of radicals. Multiplying radicals is very simple if the index on all the radicals

More information

An equation containing one variable raised to the power of one (1) is called a linear equation in one variable.

An equation containing one variable raised to the power of one (1) is called a linear equation in one variable. DETAILED SOLUTIONS AND CONCEPTS - LINEAR EQUATIONS IN ONE VARIABLE Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you!

More information

Accentuate the Negative: Homework Examples from ACE

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),

More information

RAVEN S GUIDE TO BRITISH COLUMBIA LINKED DIRECTLY TO NEW CURRICULUM REQUIREMENTS FROM THE WESTERN PROTOCOLS FOR 2008 AND BEYOND

RAVEN S GUIDE TO BRITISH COLUMBIA LINKED DIRECTLY TO NEW CURRICULUM REQUIREMENTS FROM THE WESTERN PROTOCOLS FOR 2008 AND BEYOND RAVEN S GUIDE TO BRITISH COLUMBIA MATHEMATICS GRADE 6 LINKED DIRECTLY TO NEW CURRICULUM REQUIREMENTS FROM THE WESTERN PROTOCOLS FOR 2008 AND BEYOND STUDENT GUIDE AND RESOURCE BOOK Key to Student Success

More information

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

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

More information

Simplifying Exponential Expressions

Simplifying Exponential Expressions Simplifying Eponential Epressions Eponential Notation Base Eponent Base raised to an eponent Eample: What is the base and eponent of the following epression? 7 is the base 7 is the eponent Goal To write

More information

Rules of Exponents. Math at Work: Motorcycle Customization OUTLINE CHAPTER

Rules of Exponents. Math at Work: Motorcycle Customization OUTLINE CHAPTER Rules of Exponents CHAPTER 5 Math at Work: Motorcycle Customization OUTLINE Study Strategies: Taking Math Tests 5. Basic Rules of Exponents Part A: The Product Rule and Power Rules Part B: Combining the

More information

This is a square root. The number under the radical is 9. (An asterisk * means multiply.)

This is a square root. The number under the radical is 9. (An asterisk * means multiply.) Page of Review of Radical Expressions and Equations Skills involving radicals can be divided into the following groups: Evaluate square roots or higher order roots. Simplify radical expressions. Rationalize

More information

LESSON 4 Missing Numbers in Multiplication Missing Numbers in Division LESSON 5 Order of Operations, Part 1 LESSON 6 Fractional Parts LESSON 7 Lines,

LESSON 4 Missing Numbers in Multiplication Missing Numbers in Division LESSON 5 Order of Operations, Part 1 LESSON 6 Fractional Parts LESSON 7 Lines, Saxon Math 7/6 Class Description: Saxon mathematics is based on the principle of developing math skills incrementally and reviewing past skills daily. It also incorporates regular and cumulative assessments.

More information

MTN Learn. Mathematics. Grade 10. radio support notes

MTN Learn. Mathematics. Grade 10. radio support notes MTN Learn Mathematics Grade 10 radio support notes Contents INTRODUCTION... GETTING THE MOST FROM MINDSET LEARN XTRA RADIO REVISION... 3 BROADAST SCHEDULE... 4 ALGEBRAIC EXPRESSIONS... 5 EXPONENTS... 9

More information

Addition with Unlike Denominators

Addition with Unlike Denominators Lesson. Addition with Unlike Denominators Karen is stringing a necklace with beads. She puts green beads on _ of the string and purple beads on of the string. How much of the string does Karen cover with

More information

Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III

Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III Name Date Adding and Subtracting Polynomials Algebra Standard 10.0 A polynomial is a sum of one ore more monomials. Polynomial

More information

Multiplying and Dividing Fractions

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

More information

MyMathLab ecourse for Developmental Mathematics

MyMathLab ecourse for Developmental Mathematics MyMathLab ecourse for Developmental Mathematics, North Shore Community College, University of New Orleans, Orange Coast College, Normandale Community College Table of Contents Module 1: Whole Numbers and

More information

FRACTIONS COMMON MISTAKES

FRACTIONS COMMON MISTAKES FRACTIONS COMMON MISTAKES 0/0/009 Fractions Changing Fractions to Decimals How to Change Fractions to Decimals To change fractions to decimals, you need to divide the numerator (top number) by the denominator

More information

2.2 Scientific Notation: Writing Large and Small Numbers

2.2 Scientific Notation: Writing Large and Small Numbers 2.2 Scientific Notation: Writing Large and Small Numbers A number written in scientific notation has two parts. A decimal part: a number that is between 1 and 10. An exponential part: 10 raised to an exponent,

More information

Equations and Inequalities

Equations and Inequalities Rational Equations Overview of Objectives, students should be able to: 1. Solve rational equations with variables in the denominators.. Recognize identities, conditional equations, and inconsistent equations.

More information

Quick Reference ebook

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

More information

Numerator Denominator

Numerator Denominator Fractions A fraction is any part of a group, number or whole. Fractions are always written as Numerator Denominator A unitary fraction is one where the numerator is always 1 e.g 1 1 1 1 1...etc... 2 3

More information

Training Manual. Pre-Employment Math. Version 1.1

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

More information

Roots and Powers. Written by: Bette Kreuz Edited by: Science Learning Center Staff

Roots and Powers. Written by: Bette Kreuz Edited by: Science Learning Center Staff Roots and Powers Written by: Bette Kreuz Edited by: Science Learning Center Staff The objectives for this module are to: 1. Raise exponential numbers to a power. 2. Extract the root of an exponential number.

More information

Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any.

Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any. Algebra 2 - Chapter Prerequisites Vocabulary Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any. P1 p. 1 1. counting(natural) numbers - {1,2,3,4,...}

More information

Properties of Real Numbers

Properties of Real Numbers 16 Chapter P Prerequisites P.2 Properties of Real Numbers What you should learn: Identify and use the basic properties of real numbers Develop and use additional properties of real numbers Why you should

More information

23. RATIONAL EXPONENTS

23. RATIONAL EXPONENTS 23. RATIONAL EXPONENTS renaming radicals rational numbers writing radicals with rational exponents When serious work needs to be done with radicals, they are usually changed to a name that uses exponents,

More information

FRACTION WORKSHOP. Example: Equivalent Fractions fractions that have the same numerical value even if they appear to be different.

FRACTION WORKSHOP. Example: Equivalent Fractions fractions that have the same numerical value even if they appear to be different. FRACTION WORKSHOP Parts of a Fraction: Numerator the top of the fraction. Denominator the bottom of the fraction. In the fraction the numerator is 3 and the denominator is 8. Equivalent Fractions: Equivalent

More information

Simplifying Square-Root Radicals Containing Perfect Square Factors

Simplifying Square-Root Radicals Containing Perfect Square Factors DETAILED SOLUTIONS AND CONCEPTS - OPERATIONS ON IRRATIONAL NUMBERS Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you!

More information

Section 1.1 Linear Equations: Slope and Equations of Lines

Section 1.1 Linear Equations: Slope and Equations of Lines Section. Linear Equations: Slope and Equations of Lines Slope The measure of the steepness of a line is called the slope of the line. It is the amount of change in y, the rise, divided by the amount of

More information

REVIEW SHEETS BASIC MATHEMATICS MATH 010

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

More information

Welcome to Math 19500 Video Lessons. Stanley Ocken. Department of Mathematics The City College of New York Fall 2013

Welcome to Math 19500 Video Lessons. Stanley Ocken. Department of Mathematics The City College of New York Fall 2013 Welcome to Math 19500 Video Lessons Prof. Department of Mathematics The City College of New York Fall 2013 An important feature of the following Beamer slide presentations is that you, the reader, move

More information

Connect Four Math Games

Connect Four Math Games Connect Four Math Games Connect Four Addition Game (A) place two paper clips on two numbers on the Addend Strip whose sum is that desired square. Once they have chosen the two numbers, they can capture

More information

New York State Mathematics Content Strands, Grade 6, Correlated to Glencoe MathScape, Course 1 and Quick Review Math Handbook Book 1

New York State Mathematics Content Strands, Grade 6, Correlated to Glencoe MathScape, Course 1 and Quick Review Math Handbook Book 1 New York State Mathematics Content Strands, Grade 6, Correlated to Glencoe MathScape, Course 1 and The lessons that address each Performance Indicator are listed, and those in which the Performance Indicator

More information

8-6 Radical Expressions and Rational Exponents. Warm Up Lesson Presentation Lesson Quiz

8-6 Radical Expressions and Rational Exponents. Warm Up Lesson Presentation Lesson Quiz 8-6 Radical Expressions and Rational Exponents Warm Up Lesson Presentation Lesson Quiz Holt Algebra ALgebra2 2 Warm Up Simplify each expression. 1. 7 3 7 2 16,807 2. 11 8 11 6 121 3. (3 2 ) 3 729 4. 5.

More information

5.1 Radical Notation and Rational Exponents

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

More information

Negative Exponents and Scientific Notation

Negative Exponents and Scientific Notation 3.2 Negative Exponents and Scientific Notation 3.2 OBJECTIVES. Evaluate expressions involving zero or a negative exponent 2. Simplify expressions involving zero or a negative exponent 3. Write a decimal

More information

MATH 90 CHAPTER 1 Name:.

MATH 90 CHAPTER 1 Name:. MATH 90 CHAPTER 1 Name:. 1.1 Introduction to Algebra Need To Know What are Algebraic Expressions? Translating Expressions Equations What is Algebra? They say the only thing that stays the same is change.

More information

2.3 Solving Equations Containing Fractions and Decimals

2.3 Solving Equations Containing Fractions and Decimals 2. Solving Equations Containing Fractions and Decimals Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Solve equations containing fractions

More information

EXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS

EXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS To the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requires

More information

No Solution Equations Let s look at the following equation: 2 +3=2 +7

No Solution Equations Let s look at the following equation: 2 +3=2 +7 5.4 Solving Equations with Infinite or No Solutions So far we have looked at equations where there is exactly one solution. It is possible to have more than solution in other types of equations that are

More information

Vocabulary Words and Definitions for Algebra

Vocabulary Words and Definitions for Algebra Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms

More information

Introduction to Fractions

Introduction to Fractions Section 0.6 Contents: Vocabulary of Fractions A Fraction as division Undefined Values First Rules of Fractions Equivalent Fractions Building Up Fractions VOCABULARY OF FRACTIONS Simplifying Fractions Multiplying

More information

1.3 Polynomials and Factoring

1.3 Polynomials and Factoring 1.3 Polynomials and Factoring Polynomials Constant: a number, such as 5 or 27 Variable: a letter or symbol that represents a value. Term: a constant, variable, or the product or a constant and variable.

More information

Multiplying Fractions

Multiplying Fractions . Multiplying Fractions. OBJECTIVES 1. Multiply two fractions. Multiply two mixed numbers. Simplify before multiplying fractions 4. Estimate products by rounding Multiplication is the easiest of the four

More information

Fractions to decimals

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

More information

Number: Multiplication and Division

Number: Multiplication and Division MULTIPLICATION & DIVISION FACTS count in steps of 2, 3, and 5 count from 0 in multiples of 4, 8, 50 count in multiples of 6, count forwards or backwards from 0, and in tens from any and 100 7, 9, 25 and

More information

Paramedic Program Pre-Admission Mathematics Test Study Guide

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

More information

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

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

More information

north seattle community college

north seattle community college INTRODUCTION TO FRACTIONS If we divide a whole number into equal parts we get a fraction: For example, this circle is divided into quarters. Three quarters, or, of the circle is shaded. DEFINITIONS: The

More information

26 Integers: Multiplication, Division, and Order

26 Integers: Multiplication, Division, and Order 26 Integers: Multiplication, Division, and Order Integer multiplication and division are extensions of whole number multiplication and division. In multiplying and dividing integers, the one new issue

More information

FRACTIONS OPERATIONS

FRACTIONS OPERATIONS FRACTIONS OPERATIONS Summary 1. Elements of a fraction... 1. Equivalent fractions... 1. Simplification of a fraction... 4. Rules for adding and subtracting fractions... 5. Multiplication rule for two fractions...

More information

Maths Workshop for Parents 2. Fractions and Algebra

Maths Workshop for Parents 2. Fractions and Algebra Maths Workshop for Parents 2 Fractions and Algebra What is a fraction? A fraction is a part of a whole. There are two numbers to every fraction: 2 7 Numerator Denominator 2 7 This is a proper (or common)

More information

Students will benefit from pencils with erasers, if possible since revisions are part of learning.

Students will benefit from pencils with erasers, if possible since revisions are part of learning. Suggestions and/or Directions for Implementing Extended Concept (2) Activities Students will benefit from pencils with erasers, if possible since revisions are part of learning. Students should be allowed

More information

MATH 10034 Fundamental Mathematics IV

MATH 10034 Fundamental Mathematics IV MATH 0034 Fundamental Mathematics IV http://www.math.kent.edu/ebooks/0034/funmath4.pdf Department of Mathematical Sciences Kent State University January 2, 2009 ii Contents To the Instructor v Polynomials.

More information

Prentice Hall: Middle School Math, Course 1 2002 Correlated to: New York Mathematics Learning Standards (Intermediate)

Prentice Hall: Middle School Math, Course 1 2002 Correlated to: New York Mathematics Learning Standards (Intermediate) New York Mathematics Learning Standards (Intermediate) Mathematical Reasoning Key Idea: Students use MATHEMATICAL REASONING to analyze mathematical situations, make conjectures, gather evidence, and construct

More information

Algebra Unit 6 Syllabus revised 2/27/13 Exponents and Polynomials

Algebra Unit 6 Syllabus revised 2/27/13 Exponents and Polynomials Algebra Unit 6 Syllabus revised /7/13 1 Objective: Multiply monomials. Simplify expressions involving powers of monomials. Pre-assessment: Exponents, Fractions, and Polynomial Expressions Lesson: Pages

More information

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

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 Decimals 1 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 Some Older Number Systems 3 Can

More information

SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS

SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS (Section 0.6: Polynomial, Rational, and Algebraic Expressions) 0.6.1 SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS LEARNING OBJECTIVES Be able to identify polynomial, rational, and algebraic

More information

Lyman Memorial High School. Pre-Calculus Prerequisite Packet. Name:

Lyman Memorial High School. Pre-Calculus Prerequisite Packet. Name: Lyman Memorial High School Pre-Calculus Prerequisite Packet Name: Dear Pre-Calculus Students, Within this packet you will find mathematical concepts and skills covered in Algebra I, II and Geometry. These

More information