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

Size: px
Start display at page:

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

Transcription

1 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. One way is to express each mixed number as an improper fraction and then add or subtract the fractions. Ex : Add If possible, express your answer as a mixed number. 5 First, we write each mixed number as an improper fraction So, 5 The LCD of the fractions is Changing each fraction to an equivalent fraction with 5 as the denominator, we have Therefore, Now, express 6 5 as a mixed number Ex : Subtract 5 If possible, express your answer as a mixed number. First we write each mixed number as an improper fraction So, The LCD of the fractions is. Revised 0/0

2 Changing 9 to an equivalent fraction with as the denominator, we have (The denominator is already.) Therefore, Reduce to the lowest terms and then change to a mixed number Ex : Subtract If possible, express your answer as a mixed number. First we write the whole number and the mixed number as improper fractions. 5 So, 5 The LCD of the fractions is. Changing to an equivalent fraction with as the denominator, we have (The denominator is already.) Therefore, Note: It is a common mistake to say that 5. Be careful! The correct answer is 6. Revised 0/0

3 Ex : Perform the indicated operations. 5 (Remember the Order of Operations: Add and subtract from left to right.) 0 5 First we write the whole number and the mixed numbers as improper fractions So, The LCD of the fractions is Changing each fraction to an equivalent fraction with 0 as the denominator, we have Therefore, Reduce 5 0 to lowest terms and then change to a mixed number Note: The above method of adding and subtracting mixed numbers becomes cumbersome and time consuming when the whole number parts of the mixed numbers are large numbers. For such problems, it is strongly recommended that you use the following method. Revised 0/0

4 Another way to add mixed numbers Step : Step : Add the fractional parts of the mixed numbers separately. Reduce the fraction obtained in step to lowest terms. If it is an improper fraction, change it to a mixed number. Note: If the fraction obtained in step is an improper fraction, you may first change it to a mixed number and then reduce the fractional part of the mixed number to lowest terms. Step : Add the whole number parts of the given mixed numbers. Step : Add the sum from step to the fraction or the mixed number obtained in step. Write your answer as a mixed number. Ex 5: Add and simplify Step : Add the fractions 5 and The LCD of the fractions is Step : 8 is already in lowest terms and cannot be expressed as a mixed number. Step : Add the whole numbers. 5 5 Step : Add 5 to (Remember, whenever we add a mixed number and 8 8 a proper fraction, we omit the + and write the sum as a mixed number.) Revised 0/0

5 Ex 6: Add and simplify. 9 Step : Add the fractions and. The LCD of the fractions is. 0 Step : Reduce 0 to lowest terms and then change to a mixed number Step : Add the whole numbers Step : Add 66 to. 66 6, so Ex : Add and simplify: First, we reduce the fractional part of each mixed number to lowest terms Therefore, Steps & : Add the fractional parts and reduce. Step : Add the whole numbers Step : Add the results of Step and Step Revised 0/0 5

6 Another way to subtract mixed numbers Step : Write the fractional part of each mixed number as an equivalent fraction, using the LCD as the new denominator. Step : Look at the two numerators obtained in Step. If the first numerator is greater than the second, then (A) (B) (C) Subtract the fractional parts separately. Reduce to lowest terms. Subtract the whole number parts of the given mixed numbers. The final answer is the mixed number obtained by adding the whole number in (B) and the fraction in (A). If the first numerator in Step is smaller than the second, we omit Step and go to Step. Step : Borrow from the whole number part of the first mixed number. Decrease the whole number part by. Add this to the fractional part of the first mixed number and write it as an improper fraction. Then (A) (B) (C) Subtract the fractional parts separately. Reduce to lowest terms. Subtract the whole number parts. The final answer is the mixed number obtained by adding the whole number in (B) and the fraction in (A). Ex 8: Subtract and simplify Step : The LCD of the fractional parts is Since the first numerator, 5, is greater than the second numerator,, we complete Step. Step : (A) Subtract the fractional parts and reduce to lowest terms: Revised 0/0 6

7 (B) Subtract the whole number parts: 0 (C) Ex 9: Subtract and simplify. Add the results obtained in (B) and (A): Step : The LCD of the fractional parts is Step : Since the first numerator 9, is smaller than the second numerator,, and we cannot subtract from 9, we go to Step. Step : Borrow from and decrease by. So, (Write as ) (Add 9 ) Thus, 8 Therefore, (A) Subtract the fractional parts: 9 (B) Subtract the whole number parts: 6 6 (C) Add the results obtained in (B) and (A): Revised 0/0

8 Ex 0: Subtract and simplify In this problem, we are subtracting a whole number from a mixed number. Since the 0 whole number,, does not have a fractional part, we can say:. 9 Therefore, A) Subtract the fractional parts: (B) Subtract the whole number parts: 56 (C) Add the results obtained in (B) and (A): Concept: To subtract a whole number from a mixed number, we subtract the whole number parts. Then, add this difference to the fractional part of the first mixed number to obtain the final answer. Ex : Subtract and simplify In this problem, we are subtracting a mixed number from a whole number. Since the 0 whole number, 56, does not have a fractional part, we can say: 56 = 56. We borrow 9 from 56 and decrease 56 by. Write as an improper fraction with its denominator = 9, 5 which is the same as the denominator of the fractional part of. 9 So, Therefore, (A) Subtract the fractional parts: (B) Subtract the whole number parts: 55 Revised 0/0 8

9 (C) Add the results obtained in (B) and (A) + 9 = Concept: To subtract a mixed number from a whole number, we write the whole number as a mixed number by borrowing from the whole number, decreasing the whole number by and writing as an improper fraction with denominator the same as the denominator of the fractional part in the given mixed number. Then (A) (B) (C) Subtract the fractional parts. Subtract the whole number parts. Add the results obtained in (B) and (A). Note: It is very common for students to get mixed up between Ex 0 and Ex. Be very very careful! Notice that but, The correct answer for 5 56 is. 9 9 Exercises: Perform the indicated operations by first changing mixed numbers to improper fractions. Simplify your answers and whenever possible, express your answers as mixed numbers Revised 0/0 9

10 Add and simplify without changing mixed numbers to improper fractions. Whenever possible, express your answer as a mixed number Subtract and simplify without changing mixed numbers to improper fractions. Whenever possible, express your answer as a mixed number Solutions to odd numbered problems and answers to even numbered problems. 9 5 The LCD is Revised 0/0 0

11 . 5 Reduce The LCD is The LCD is The LCD is The LCD is Revised 0/0

12 The LCD is Since 5 96, we have The LCD is Reducing fractions: and 5 6 0, we have The LCD is Revised 0/0

13 Reducing fractions: 9 and 8, we have The LCD is Since 65 =, we have Revised 0/0

14 Part II: Multiplication and Division of Mixed Numbers To multiply or divide mixed numbers, we use the following two steps. Step : Step : Express each mixed number as an improper fraction. Multiply or divide, using the procedures for multiplying and dividing fractions. Ex : Multiply and simplify. If possible, express your answer as a mixed number. 5 First, we write each of the mixed numbers as an improper fraction Ex : Multiply and simplify. If possible, express your answer as a mixed number. 8 First, we write the whole number and the mixed number as improper fractions (Divide 8 and 6 by ) Ex : Multiply and simplify. If possible, express your answers as a mixed number. 5 5 First, we write each mixed number and the whole number as an 5 improper fraction = (Divide 5 and 5 by 5. Divide 8 and by 6) Revised 0/0

15 Ex : Divide and simplify. If possible, express your answer as a mixed number. 5 8 First, we write each mixed number as an improper fraction. 5 Changing division to multiplication by the reciprocal, we have Ex 5: Divide and simplify. If possible, express your answer as a mixed number. 5 5 First, we write the whole number and the mixed number as improper 5 5 fractions. 5 Changing division to multiplication by the reciprocal, we have = (Divide 5 and by ) Ex 6: Divide and simplify. If possible, express your answer as a mixed number. 6 9 First, we write the whole number and the mixed number as improper fractions Changing division to multiplication by the reciprocal, we have (Divide 6 and 9 by 9) Revised 0/0 5

16 Ex : Divide and simplify. If possible, express your answer as a mixed number. 5 5 Since a fraction means to divide, rewrite as a division problem Change to improper fractions Rewrite as a multiplication problem (Divide 6 and 6 by. Divide 5 and 5 by 5) 9 9 Exercises: Multiply the following. Simplify your answers and whenever possible, express your answers as a mixed numbers Revised 0/0 6

17 Divide the following. Simplify your answers and whenever possible, express your answers as a mixed numbers Solutions to odd numbered problems and answers to even numbered problems Revised 0/0

18 Revised 0/0 8

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

Self-Directed Course: Transitional Math Module 2: Fractions

Self-Directed Course: Transitional Math Module 2: Fractions Lesson #1: Comparing Fractions Comparing fractions means finding out which fraction is larger or smaller than the other. To compare fractions, use the following inequality and equal signs: - greater than

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

FRACTION REVIEW. 3 and. Any fraction can be changed into an equivalent fraction by multiplying both the numerator and denominator by the same number

FRACTION REVIEW. 3 and. Any fraction can be changed into an equivalent fraction by multiplying both the numerator and denominator by the same number FRACTION REVIEW A. INTRODUCTION. What is a fraction? A fraction consists of a numerator (part) on top of a denominator (total) separated by a horizontal line. For example, the fraction of the circle which

More information

MULTIPLICATION OF FRACTIONS AND MIXED NUMBERS. 1 of 6 objects, you make 2 (the denominator)

MULTIPLICATION OF FRACTIONS AND MIXED NUMBERS. 1 of 6 objects, you make 2 (the denominator) Tallahassee Community College 0 MULTIPLICATION OF FRACTIONS AND MIXED NUMBERS You know that of is. When you get of objects, you make (the denominator) equal groups of the objects and you take (the numerator)

More information

Section R.2. Fractions

Section R.2. Fractions Section R.2 Fractions Learning objectives Fraction properties of 0 and 1 Writing equivalent fractions Writing fractions in simplest form Multiplying and dividing fractions Adding and subtracting fractions

More information

Improper Fractions and Mixed Numbers

Improper Fractions and Mixed Numbers This assignment includes practice problems covering a variety of mathematical concepts. Do NOT use a calculator in this assignment. The assignment will be collected on the first full day of class. All

More information

Module 2: Working with Fractions and Mixed Numbers. 2.1 Review of Fractions. 1. Understand Fractions on a Number Line

Module 2: Working with Fractions and Mixed Numbers. 2.1 Review of Fractions. 1. Understand Fractions on a Number Line Module : Working with Fractions and Mixed Numbers.1 Review of Fractions 1. Understand Fractions on a Number Line Fractions are used to represent quantities between the whole numbers on a number line. A

More information

A fraction is a noninteger quantity expressed in terms of a numerator and a denominator.

A fraction is a noninteger quantity expressed in terms of a numerator and a denominator. 1 Fractions Adding & Subtracting A fraction is a noninteger quantity expressed in terms of a numerator and a denominator. 1. FRACTION DEFINITIONS 1) Proper fraction: numerator is less than the denominator.

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

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

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

HFCC Math Lab Intermediate Algebra - 7 FINDING THE LOWEST COMMON DENOMINATOR (LCD)

HFCC Math Lab Intermediate Algebra - 7 FINDING THE LOWEST COMMON DENOMINATOR (LCD) HFCC Math Lab Intermediate Algebra - 7 FINDING THE LOWEST COMMON DENOMINATOR (LCD) Adding or subtracting two rational expressions require the rational expressions to have the same denominator. Example

More information

made up of 2 parts, a Saying a 3 To say or write a 7 - seven eighths 8

made up of 2 parts, a Saying a 3 To say or write a 7 - seven eighths 8 Day 1 Fractions Obj: To learn how to write fractions, define,and classify fractions Def Fraction Numerator Denominator Fraction part of a whole; made up of 2 parts, a numerator and denominator. The denominator

More information

Chapter 4 Fractions and Mixed Numbers

Chapter 4 Fractions and Mixed Numbers Chapter 4 Fractions and Mixed Numbers 4.1 Introduction to Fractions and Mixed Numbers Parts of a Fraction Whole numbers are used to count whole things. To refer to a part of a whole, fractions are used.

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

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 Basic review Writing fractions in simplest form Comparing fractions Converting between Improper fractions and whole/mixed numbers Operations

More information

Algebra 1A and 1B Summer Packet

Algebra 1A and 1B Summer Packet 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

More information

Simplification Problems to Prepare for Calculus

Simplification Problems to Prepare for Calculus Simplification Problems to Prepare for Calculus In calculus, you will encounter some long epressions that will require strong factoring skills. This section is designed to help you develop those skills.

More information

Fractions, Ratios, and Proportions Work Sheets. Contents

Fractions, Ratios, and Proportions Work Sheets. Contents Fractions, Ratios, and Proportions Work Sheets The work sheets are grouped according to math skill. Each skill is then arranged in a sequence of work sheets that build from simple to complex. Choose the

More information

Objectives: In this fractions unit, we will

Objectives: In this fractions unit, we will Objectives: In this fractions unit, we will subtract and add fractions with unlike denominators (pp. 101 102) multiply fractions(pp.109 110) Divide fractions (pp. 113 114) Review: Which is greater, 1/3

More information

Introduction to Fractions

Introduction to Fractions Introduction to Fractions Fractions represent parts of a whole. The top part of a fraction is called the numerator, while the bottom part of a fraction is called the denominator. The denominator states

More information

Adding and Subtracting Mixed Numbers and Improper Fractions

Adding and Subtracting Mixed Numbers and Improper Fractions Just like our counting numbers (1, 2, 3, ), fractions can also be added and subtracted. When counting improper fractions and mixed numbers, we are counting the number wholes and parts. Note: The rules

More information

ARITHMETIC. Overview. Testing Tips

ARITHMETIC. Overview. Testing Tips ARITHMETIC Overview The Arithmetic section of ACCUPLACER contains 17 multiple choice questions that measure your ability to complete basic arithmetic operations and to solve problems that test fundamental

More information

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

HFCC Math Lab Intermediate Algebra - 17 DIVIDING RADICALS AND RATIONALIZING THE DENOMINATOR

HFCC Math Lab Intermediate Algebra - 17 DIVIDING RADICALS AND RATIONALIZING THE DENOMINATOR HFCC Math Lab Intermediate Algebra - 17 DIVIDING RADICALS AND RATIONALIZING THE DENOMINATOR Dividing Radicals: To divide radical expression we use Step 1: Simplify each radical Step 2: Apply the Quotient

More information

Word Problems. Simplifying Word Problems

Word Problems. Simplifying Word Problems Word Problems This sheet is designed as a review aid. If you have not previously studied this concept, or if after reviewing the contents you still don t pass, you should enroll in the appropriate math

More information

Numerical and Algebraic Fractions

Numerical and Algebraic Fractions Numerical and Algebraic Fractions Aquinas Maths Department Preparation for AS Maths This unit covers numerical and algebraic fractions. In A level, solutions often involve fractions and one of the Core

More information

Decimal and Fraction Review Sheet

Decimal and Fraction Review Sheet Decimal and Fraction Review Sheet Decimals -Addition To add 2 decimals, such as 3.25946 and 3.514253 we write them one over the other with the decimal point lined up like this 3.25946 +3.514253 If one

More information

1.4. Arithmetic of Algebraic Fractions. Introduction. Prerequisites. Learning Outcomes

1.4. Arithmetic of Algebraic Fractions. Introduction. Prerequisites. Learning Outcomes Arithmetic of Algebraic Fractions 1.4 Introduction Just as one whole number divided by another is called a numerical fraction, so one algebraic expression divided by another is known as an algebraic fraction.

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

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

Math Help and Additional Practice Websites

Math Help and Additional Practice Websites Name: Math Help and Additional Practice Websites http://www.coolmath.com www.aplusmath.com/ http://www.mathplayground.com/games.html http://www.ixl.com/math/grade-7 http://www.softschools.com/grades/6th_and_7th.jsp

More information

Changing a Mixed Number to an Improper Fraction

Changing a Mixed Number to an Improper Fraction Example: Write 48 4 48 4 = 48 8 4 8 = 8 8 = 2 8 2 = 4 in lowest terms. Find a number that divides evenly into both the numerator and denominator of the fraction. For the fraction on the left, there are

More information

Sometimes it is easier to leave a number written as an exponent. For example, it is much easier to write

Sometimes it is easier to leave a number written as an exponent. For example, it is much easier to write 4.0 Exponent Property Review First let s start with a review of what exponents are. Recall that 3 means taking four 3 s and multiplying them together. So we know that 3 3 3 3 381. You might also recall

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

LESSON SUMMARY. Manipulation of Real Numbers

LESSON SUMMARY. Manipulation of Real Numbers LESSON SUMMARY CXC CSEC MATHEMATICS UNIT TWO: COMPUTATION Lesson 2 Manipulation of Real Numbers Textbook: Mathematics, A Complete Course by Raymond Toolsie, Volume 1. (Some helpful exercises and page numbers

More information

1.6 The Order of Operations

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

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

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

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

NAME TEST DATE FRACTION STUDY GUIDE/EXTRA PRACTICE PART 1: PRIME OR COMPOSITE?

NAME TEST DATE FRACTION STUDY GUIDE/EXTRA PRACTICE PART 1: PRIME OR COMPOSITE? NAME TEST DATE FRACTION STUDY GUIDE/EXTRA PRACTICE PART 1: PRIME OR COMPOSITE? A prime number is a number that has exactly 2 factors, one and itself. Examples: 2, 3, 5, 11, 31 2 is the only even number

More information

Fractions. Introduction... 2

Fractions. Introduction... 2 Introduction... 2 Unit 1: FACTORS AND MULTIPLES Lesson 1: Factors, Prime, and Composite Numbers... 2 Lesson 2: Factors Word Problems... 2 Lesson 3: Grea Common Factor... 3 Lesson 4: Multiples and Least

More information

Fractions. Cavendish Community Primary School

Fractions. Cavendish Community Primary School Fractions Children in the Foundation Stage should be introduced to the concept of halves and quarters through play and practical activities in preparation for calculation at Key Stage One. Y Understand

More information

FRACTIONS MODULE Part I

FRACTIONS MODULE Part I FRACTIONS MODULE Part I I. Basics of Fractions II. Rewriting Fractions in the Lowest Terms III. Change an Improper Fraction into a Mixed Number IV. Change a Mixed Number into an Improper Fraction BMR.Fractions

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

2) Based on the information in the table which choice BEST shows the answer to 1 906? 906 899 904 909

2) Based on the information in the table which choice BEST shows the answer to 1 906? 906 899 904 909 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ) Multiplying a number by results in what type of. even. 0. even.,0. odd..,0. even ) Based on the information in the table which choice BEST shows the answer to 0? 0 0 0 )

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

2.6 Adding and Subtracting Fractions and Mixed Numbers with Unlike Denominators

2.6 Adding and Subtracting Fractions and Mixed Numbers with Unlike Denominators 2.6 Adding and Subtracting Fractions and Mixed Numbers with Unlike Denominators Learning Objective(s) 1 Find the least common multiple (LCM) of two or more numbers. 2 Find the Least Common Denominator

More information

Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers. with Integers Divide Integers

Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers. with Integers Divide Integers Page1 Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers Lesson Topic I Can 1 Ordering & Adding Create a number line to order integers Integers Identify integers Add integers 2 Subtracting

More information

Accuplacer Arithmetic Study Guide

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

More information

Math 016. Materials With Exercises

Math 016. Materials With Exercises Math 06 Materials With Exercises June 00, nd version TABLE OF CONTENTS Lesson Natural numbers; Operations on natural numbers: Multiplication by powers of 0; Opposite operations; Commutative Property of

More information

HOW TO ADD AND SUBTRACT MIXED NUMBERS

HOW TO ADD AND SUBTRACT MIXED NUMBERS WHAT'S THAT MEAN...? HOW TO ADD AND SUBTRACT MIXED NUMBERS 8 2/3 1 1/4 5 TWO METHODS THAT WORK!! 1 Method 1: Use Improper Fractions What size parts are the circles cut into? How many yellow parts are on

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

Factor Diamond Practice Problems

Factor Diamond Practice Problems Factor Diamond Practice Problems 1. x 2 + 5x + 6 2. x 2 +7x + 12 3. x 2 + 9x + 8 4. x 2 + 9x +14 5. 2x 2 7x 4 6. 3x 2 x 4 7. 5x 2 + x -18 8. 2y 2 x 1 9. 6-13x + 6x 2 10. 15 + x -2x 2 Factor Diamond Practice

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

NUMBER SENSE MAGIC BY LEO A. RAMIREZ, SR.

NUMBER SENSE MAGIC BY LEO A. RAMIREZ, SR. NUMBER SENSE MAGIC BY LEO A. RAMIREZ, SR. Multiplying two numbers close to 100 (Both numbers are less than 100) Step # 1 : Step # : Example A : Find the difference of each number and 100. Multiply the

More information

Order of Operations - PEMDAS. Rules for Multiplying or Dividing Positive/Negative Numbers

Order of Operations - PEMDAS. Rules for Multiplying or Dividing Positive/Negative Numbers Order of Operations - PEMDAS *When evaluating an expression, follow this order to complete the simplification: Parenthesis ( ) EX. (5-2)+3=6 (5 minus 2 must be done before adding 3 because it is in parenthesis.)

More information

Welcome to Basic Math Skills!

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

More information

FRACTIONS 1 MANIPULATING FRACTIONS. the denominator represents the kind of pieces the whole has been divided into

FRACTIONS 1 MANIPULATING FRACTIONS. the denominator represents the kind of pieces the whole has been divided into CONNECT: Fractions FRACTIONS 1 MANIPULATING FRACTIONS Firstly, let s think about what a fraction is. 1. One way to look at a fraction is as part of a whole. Fractions consist of a numerator and a denominator:

More information

Introduction to Fractions, Equivalent and Simplifying (1-2 days)

Introduction to Fractions, Equivalent and Simplifying (1-2 days) Introduction to Fractions, Equivalent and Simplifying (1-2 days) 1. Fraction 2. Numerator 3. Denominator 4. Equivalent 5. Simplest form Real World Examples: 1. Fractions in general, why and where we use

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

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

Session 22 Fraction Multiplication. Pat used three-fourths of a bag of flour that was two-thirds full. How much of a full bag of flour did Pat use.

Session 22 Fraction Multiplication. Pat used three-fourths of a bag of flour that was two-thirds full. How much of a full bag of flour did Pat use. Session 22 Fraction Multiplication Solve the following problem. Pat used three-fourths of a bag of flour that was two-thirds full. How much of a full bag of flour did Pat use. Here, we solve this problem

More information

Simplifying Radical Expressions

Simplifying Radical Expressions In order to simplifying radical expression, it s important to understand a few essential properties. Product Property of Like Bases a a = a Multiplication of like bases is equal to the base raised to the

More information

Adding Fractions. Adapted from MathisFun.com

Adding Fractions. Adapted from MathisFun.com Adding Fractions Adapted from MathisFun.com There are 3 Simple Steps to add fractions: Step 1: Make sure the bottom numbers (the denominators) are the same Step 2: Add the top numbers (the numerators).

More information

Rules for Exponents and the Reasons for Them

Rules for Exponents and the Reasons for Them Print this page Chapter 6 Rules for Exponents and the Reasons for Them 6.1 INTEGER POWERS AND THE EXPONENT RULES Repeated addition can be expressed as a product. For example, Similarly, repeated multiplication

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

OpenStax-CNX module: m Adding Fractions. Scott Starks = 2 5 (2) We do the same with the denominator of the second fraction

OpenStax-CNX module: m Adding Fractions. Scott Starks = 2 5 (2) We do the same with the denominator of the second fraction OpenStax-CNX module: m38554 Adding Fractions Scott Starks This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 3.0 Abstract This module is part of a collection

More information

Chapter 7 - Roots, Radicals, and Complex Numbers

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

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

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

Using a Scientific Calculator

Using a Scientific Calculator 1 Using a Scientific Calculator In this course, we will be using a scientific calculator to do all of our computations. So, in this section, we want to get use to some of the features of a scientific calculator.

More information

3. Power of a Product: Separate letters, distribute to the exponents and the bases

3. Power of a Product: Separate letters, distribute to the exponents and the bases Chapter 5 : Polynomials and Polynomial Functions 5.1 Properties of Exponents Rules: 1. Product of Powers: Add the exponents, base stays the same 2. Power of Power: Multiply exponents, bases stay the same

More information

Key. Introduction. What is a Fraction. Better Math Numeracy Basics Fractions. On screen content. Narration voice-over

Key. Introduction. What is a Fraction. Better Math Numeracy Basics Fractions. On screen content. Narration voice-over Key On screen content Narration voice-over Activity Under the Activities heading of the online program Introduction This topic will cover how to: identify and distinguish between proper fractions, improper

More information

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 8 Powers and Exponents

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 8 Powers and Exponents Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Please watch Section 8 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm

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

Round decimals to the nearest whole number

Round decimals to the nearest whole number Round decimals to the nearest whole number Learning Objective Simplifying Fractions Simplified Fractions To simplify a fraction, we find an equivalent fraction which uses the smallest numbers possible.

More information

NOTE: Gateway problems 1 & 2 on adding and subtracting fractions canboth be done using the same set of steps.

NOTE: Gateway problems 1 & 2 on adding and subtracting fractions canboth be done using the same set of steps. Sample Gateway Problems:.. Working with Fractions and the Order of Operations Without Using a Calculator NOTE: Gateway problems 1 & 2 on adding and subtracting fractions canboth be done using the same

More information

Unit purpose and aim. Externally assessed by OCR. Fractions, decimals and percentages Level: 1 Credit value: 3 Guided learning hours: 30

Unit purpose and aim. Externally assessed by OCR. Fractions, decimals and percentages Level: 1 Credit value: 3 Guided learning hours: 30 Externally assessed by OCR Unit Title: Fractions, decimals Level: Credit value: 3 Guided learning hours: 30 Unit reference number: D/504/6034 Unit purpose and aim On completion of this unit the learner

More information

Guide to SRW Section 1.7: Solving inequalities

Guide to SRW Section 1.7: Solving inequalities Guide to SRW Section 1.7: Solving inequalities When you solve the equation x 2 = 9, the answer is written as two very simple equations: x = 3 (or) x = 3 The diagram of the solution is -6-5 -4-3 -2-1 0

More information

Chapter 5. Rational Expressions

Chapter 5. Rational Expressions 5.. Simplify Rational Expressions KYOTE Standards: CR ; CA 7 Chapter 5. Rational Expressions Definition. A rational expression is the quotient P Q of two polynomials P and Q in one or more variables, where

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

Solving a System of Equations by Elimination

Solving a System of Equations by Elimination Section 5 3: Solving a System of Equations by Elimination The Addition Property of Equality states that You can add the same number to both sides of an equation and still have an equivalent equation. If

More information

Calculator Worksheet--page 1

Calculator Worksheet--page 1 Calculator Worksheet--page 1 Name On this worksheet, I will be referencing keys that are on the TI30Xa. If you re using a different calculator, similar keys should be there; you just need to fi them! Positive/Negative

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

1.3 Order of Operations

1.3 Order of Operations 1.3 Order of Operations As it turns out, there are more than just 4 basic operations. There are five. The fifth basic operation is that of repeated multiplication. We call these exponents. There is a bit

More information

Summer Math Packet. Number Sense & Math Skills For Students Entering Pre-Algebra. No Calculators!!

Summer Math Packet. Number Sense & Math Skills For Students Entering Pre-Algebra. No Calculators!! Summer Math Packet Number Sense & Math Skills For Students Entering Pre-Algebra No Calculators!! Within the first few days of your Pre-Algebra course you will be assessed on the prerequisite skills outlined

More information

HOSPITALITY Math Assessment Preparation Guide. Introduction Operations with Whole Numbers Operations with Integers 9

HOSPITALITY Math Assessment Preparation Guide. Introduction Operations with Whole Numbers Operations with Integers 9 HOSPITALITY Math Assessment Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre at George

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

Estimating Products (pages 256 258)

Estimating Products (pages 256 258) A Estimating Products (pages 8) You can use compatible numbers to estimate products when multiplying fractions. Compatible numbers are easy to divide mentally. A Estimate. means of.? For, the nearest multiple

More information

Exponents, Factors, and Fractions. Chapter 3

Exponents, Factors, and Fractions. Chapter 3 Exponents, Factors, and Fractions Chapter 3 Exponents and Order of Operations Lesson 3-1 Terms An exponent tells you how many times a number is used as a factor A base is the number that is multiplied

More information

Maths for Nurses: Fractions and Decimals

Maths for Nurses: Fractions and Decimals Maths for Nurses: Fractions and Decimals This booklet will provide an overview of the basic numeracy skills for Nursing students. If you have any problems in answering the questions within the booklet

More information

Fractions. If the top and bottom numbers of a fraction are the same then you have a whole one.

Fractions. If the top and bottom numbers of a fraction are the same then you have a whole one. What do fractions mean? Fractions Academic Skills Advice Look at the bottom of the fraction first this tells you how many pieces the shape (or number) has been cut into. Then look at the top of the fraction

More information

MTH 086 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 20, 2006

MTH 086 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 20, 2006 MTH 06 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 0, 006 Math 06, Introductory Algebra, covers the mathematical content listed below. In order

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

1.3 Algebraic Expressions

1.3 Algebraic Expressions 1.3 Algebraic Expressions A polynomial is an expression of the form: a n x n + a n 1 x n 1 +... + a 2 x 2 + a 1 x + a 0 The numbers a 1, a 2,..., a n are called coefficients. Each of the separate parts,

More information

COMPASS Numerical Skills/Pre-Algebra Preparation Guide. Introduction Operations with Integers Absolute Value of Numbers 13

COMPASS Numerical Skills/Pre-Algebra Preparation Guide. Introduction Operations with Integers Absolute Value of Numbers 13 COMPASS Numerical Skills/Pre-Algebra Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre

More information

Saxon Math Home School Edition. September 2008

Saxon Math Home School Edition. September 2008 Saxon Math Home School Edition September 2008 Saxon Math Home School Edition Lesson 4: Comparing Whole Lesson 5: Naming Whole Through Hundreds, Dollars and Cent Lesson 7: Writing and Comparing Through

More information