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

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

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

Transcription

1 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.) Exponents 3 2 EX. 3 2 (4)=36 (3 2 must be done before multiplying by 4 because exponents come before multiplying.) Multiplication x,. EX. 3x2-5=1 (3 times 2 must be done before subtracting 5 because multiplying comes before subtraction.) Division - EX. 4/2-1=1 (4 divided by 2 must be done before subtracting 1 because division comes before subtraction.) Addition + EX =0 (5 plus 2 must be done before subtracting 3 because addition comes before subtraction.) Subtraction - is done last Rules for Multiplying or Dividing Positive/Negative Numbers *When multiplying or dividing, if the signs of the integers (numbers) are the same, the answer will ALWAYS be positive. +, (+3)=+24 (Positive 8 times positive 3 equals positive 24) -, - -5 x -6=30 (Negative 5 times negative 6 equals positive 30) +6/+2=+3 (Positive 6 divided by positive 2 equals positive 3) -8/-4=+2 (Negative 8 divided by negative 4 equals positive 2) *When multiplying or dividing, if the signs of the integers (numbers) are different, the answer will ALWAYS be negative. +,- -3(3)=-9 (Negative 3 times positive 3 equals negative 9) -,+ - 4 x (-2)=-8 (Positive 4 times negative 2 equals negative 8) -12/+4=-3 (Negative 12 divided by positive 4 equals negative 3) +9/-3=-3 (Positive 9 divided by negative 3 equals negative 3)

2 Rules for Adding/Subtracting Positive/Negative Numbers *If the signs of the integers (numbers) are the same, then add the numbers and keep the same sign. 3+4=+7 (A positive plus a positive gives us a larger positive) -7-2=-9 (A negative and another negative gives us a larger negative) *If the signs of the integers (numbers) are different, then subtract the numbers and keep the sign of the larger number. +8-3=+5 (Subtract 8 minus 3 to get 5, then keep the sign of the larger number (8), which is positive) -7+5=-2 (Subtract 7 minus 5 to get 2, then keep the sign of the larger number (7), which is negative)

3 ADDING AND SUBTRACTING FRACTIONS * In order to add or subtract fractions, you must first find the LCD (Lowest Common Denominator). Top number is always the numerator, bottom always the denominator. Example (6 and 2 are numerators) (both 7 s are denominators) * When adding or subtracting fractions with given common denominators, just add or subtract the numerators (top numbers). The denominators will not change final answer 6 2 = = 4 final answer * If you are asked to add or subtract fractions which do not have a given common denominator, we must use multiples of each denominator to find the LCD (Lowest Common Denominator) multiples of 4: 4, 8, 12, 16 multiples of 5: 5, 10, 15, 20 multiples of 8: 8, 16, 24 multiples of 15: 15, 30, 45 Which is the lowest common number in both lines? ~ 8 is the lowest common denominator for 4 and 8. ~ 15 is the lowest common denominator for 5 and 15. * In order to create common denominators, one or more numbers might need to be multiplied. Whatever is multiplied for the denominator must be multiplied to the numerator. For example: becomes becomes *Now, just add or subtract the numerators final answer final answer = =

4 MULTIPLYING FRACTIONS * When multiplying fractions, simply multiply numerator times numerator and denominator times denominator. Example x = = * Now see if the fraction in your answer can be reduced final answer final answer DIVIDING FRACTIONS * When dividing fractions, you must first change the division sign to multiplication. Then you must flip the dividend (2nd number in the problem) upside down. For example: * Now, just multiply becomes 4 x 3 1 x x 3 = = * Now see if the fraction in your answer can be reduced final answer 4 final answer 5 15

5 ADDING AND SUBTRACTING DECIMALS * When adding or subtracting decimals, decimals points must line up. Then add or subtract and drop the decimal straight down. Example MULTIPLYING DECIMALS * When multiplying decimals, first multiply the numbers as if the decimals don t exist. Example x.2 x * Next, count up the amount of numbers that are to the right of any decimal points..3 2 numbers to numbers to x.2 the right of the decimal x.23 to the right of the decimal 6 (3 and 2) 162 (4, 3, and 2) * Place your decimal at the end of the answer x.2 x * Now, move the decimal to the left..3 (2 times) 5.4 (3 times) x.2 x final answer final answer 1.242

6 DIVIDING DECIMALS Example * When dividing numbers with decimals, place your divisor (outside number/# dividing by) and dividend (inside number/# being divided) in the correct places * Next, the decimal in the divisor (outside number) must be moved until it is all the way to the right of all the numbers of the divisor Once Once Twice * Count how many numbers you had to move the divisor (outside number) to the right Once Once Twice * Now move the decimal in the dividend (inside number) to the right the same amount of times that you moved the divisor (outside number) Once Once Twice * Divide regularly * The decimal point in the dividend (inside number goes straight up. Final answer Final answer Final answer 12

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

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

Now that we have a handle on the integers, we will turn our attention to other types of numbers.

Now that we have a handle on the integers, we will turn our attention to other types of numbers. 1.2 Rational Numbers Now that we have a handle on the integers, we will turn our attention to other types of numbers. We start with the following definitions. Definition: Rational Number- any number that

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

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

equals equals equals equals

equals equals equals equals Addition of Integers Rules Same Sign ---------------- Add --------------- Keep the Sign Different Signs -------- Subtract ------- Take the sign of the integer with the larger absolute value plus plus plus

More information

Addition with regrouping (carrying)

Addition with regrouping (carrying) Addition with regrouping (carrying) tens 10's ones 1's Put the tens guy up in the tens column... Put the ones guy in the ones answer spot Subtraction with regrouping (borrowing) Place Value Chart Place

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

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

Appendix A: 20 Items and Their Associated 80 Solution Strategies, Proportion Correct Scores, Proportion of Students Selecting the Solution Strategies

Appendix A: 20 Items and Their Associated 80 Solution Strategies, Proportion Correct Scores, Proportion of Students Selecting the Solution Strategies Appendix A: 20 Items and Their Associated 80 Solution Strategies, Correct Scores, of Students Selecting the Solution Strategies Table A1. Math Test Items with Associated Strategies and Summaries of Student

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

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

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

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

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

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

Operations on Decimals

Operations on Decimals Operations on Decimals Addition and subtraction of decimals To add decimals, write the numbers so that the decimal points are on a vertical line. Add as you would with whole numbers. Then write the decimal

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

Sect Exponents: Multiplying and Dividing Common Bases

Sect Exponents: Multiplying and Dividing Common Bases 40 Sect 5.1 - Exponents: Multiplying and Dividing Common Bases Concept #1 Review of Exponential Notation In the exponential expression 4 5, 4 is called the base and 5 is called the exponent. This says

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

ADDITION. Children should extend the carrying method to numbers with at least four digits.

ADDITION. Children should extend the carrying method to numbers with at least four digits. Y5 AND Y6 ADDITION Children should extend the carrying method to numbers with at least four digits. 587 3587 + 475 + 675 1062 4262 1 1 1 1 1 Using similar methods, children will: add several numbers with

More information

How To Math Properties

How To Math Properties CLOSURE a + b is a real number; when you add 2 real numbers, the result is also a real number. and 5 are both real numbers, + 5 8 and the sum, 8, is also a real number. a b is a real number; when you subtract

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

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

Decimals Adding and Subtracting

Decimals Adding and Subtracting 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

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

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

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

Solution Guide Chapter 14 Mixing Fractions, Decimals, and Percents Together

Solution Guide Chapter 14 Mixing Fractions, Decimals, and Percents Together Solution Guide Chapter 4 Mixing Fractions, Decimals, and Percents Together Doing the Math from p. 80 2. 0.72 9 =? 0.08 To change it to decimal, we can tip it over and divide: 9 0.72 To make 0.72 into a

More information

Basic Math Principles

Basic Math Principles Chapter Basic Math Principles In this chapter, we will learn the following to World Class CAD standards: Create a Fraction Convert a Fraction to Lowest Terms Adding Fractions with a Common Denominator

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

eday Lessons Mathematics Grade 8 Student Name:

eday Lessons Mathematics Grade 8 Student Name: eday Lessons Mathematics Grade 8 Student Name: Common Core State Standards- Expressions and Equations Work with radicals and integer exponents. 3. Use numbers expressed in the form of a single digit times

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

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

Bell Ringer. Solve each equation. Show you work. Check the solution. 8 = -7 + m = m 15 = m = 7 + m 8 = = 8

Bell Ringer. Solve each equation. Show you work. Check the solution. 8 = -7 + m = m 15 = m = 7 + m 8 = = 8 Bell Ringer Solve each equation. Show you work. the solution. 1. 8 = 7 + m 8 = -7 + m 8 + 7 = -7 + 7 + m 15 = m 8 = -7 + m 8 = -7 + 15 8 = 8 Answers to Homework Worksheet 2-1 Today s Objectives Solving

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

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

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

6th Grade Vocabulary Words

6th Grade Vocabulary Words 1. sum the answer when you add Ex: 3 + 9 = 12 12 is the sum 2. difference the answer when you subtract Ex: 17-9 = 8 difference 8 is the 3. the answer when you multiply Ex: 7 x 8 = 56 56 is the 4. quotient

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

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

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 9 Order of Operations

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 9 Order of Operations Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Please watch Section 9 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm

More information

Solution: There are TWO square roots of 196, a positive number and a negative number. So, since and 14 2

Solution: There are TWO square roots of 196, a positive number and a negative number. So, since and 14 2 5.7 Introduction to Square Roots The Square of a Number The number x is called the square of the number x. EX) 9 9 9 81, the number 81 is the square of the number 9. 4 4 4 16, the number 16 is the square

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

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

DECIMAL REVIEW. 2. Change to a fraction Notice that =.791 The zero in front of the decimal place is not needed.

DECIMAL REVIEW. 2. Change to a fraction Notice that =.791 The zero in front of the decimal place is not needed. DECIMAL REVIEW A. INTRODUCTION TO THE DECIMAL SYSTEM The Decimal System is another way of expressing a part of a whole number. A decimal is simply a fraction with a denominator of 10, 100, 1 000 or 10

More information

Learning new things and building basic skills

Learning new things and building basic skills Math Review TABE Answer Key 2 Learning new things and building basic skills may be challenging for you, but they also can be very exciting. When you follow the guidelines for learning basic skills, you

More information

Scientific Notation Notes

Scientific Notation Notes Scientific Notation Notes Scientific notation is a short way to write very large or very small numbers. It is written as the product of a number between 1 and 10 and a power of 10. TO CONVERT A NUMBER

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

Exponents. Laws of Exponents. SWBAT understand the laws of zero, negative, multiplying, dividing, and power to power exponents. September 26, 2012

Exponents. Laws of Exponents. SWBAT understand the laws of zero, negative, multiplying, dividing, and power to power exponents. September 26, 2012 SWBAT understand the laws of zero, negative, multiplying, dividing, and power to power exponents. Nov 4 10:28 AM Exponents An exponent tells how many times a number, the base, is used as a factor. A power

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

1.2 Linear Equations and Rational Equations

1.2 Linear Equations and Rational Equations Linear Equations and Rational Equations Section Notes Page In this section, you will learn how to solve various linear and rational equations A linear equation will have an variable raised to a power of

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

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

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

Section P.9 Notes Page 1 P.9 Linear Inequalities and Absolute Value Inequalities

Section P.9 Notes Page 1 P.9 Linear Inequalities and Absolute Value Inequalities Section P.9 Notes Page P.9 Linear Inequalities and Absolute Value Inequalities Sometimes the answer to certain math problems is not just a single answer. Sometimes a range of answers might be the answer.

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

2. Perform the division as if the numbers were whole numbers. You may need to add zeros to the back of the dividend to complete the division

2. Perform the division as if the numbers were whole numbers. You may need to add zeros to the back of the dividend to complete the division Math Section 5. Dividing Decimals 5. Dividing Decimals Review from Section.: Quotients, Dividends, and Divisors. In the expression,, the number is called the dividend, is called the divisor, and is called

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

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

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

Decimals and other fractions

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

More information

47 Numerator Denominator

47 Numerator Denominator JH WEEKLIES ISSUE #22 2012-2013 Mathematics Fractions Mathematicians often have to deal with numbers that are not whole numbers (1, 2, 3 etc.). The preferred way to represent these partial numbers (rational

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

6.3 SIMPLIFYING EXPRESSIONS USING THE ORDER OF OPERATIONS

6.3 SIMPLIFYING EXPRESSIONS USING THE ORDER OF OPERATIONS 6.3 SIMPLIFYING EXPRESSIONS USING THE ORDER OF OPERATIONS Brian has decided to open a savings account, where he will earn 4% interest, compounded semi-annually. He will deposit $500 to open the account.

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

Exponents, Polynomials and Functions. Copyright Cengage Learning. All rights reserved.

Exponents, Polynomials and Functions. Copyright Cengage Learning. All rights reserved. Exponents, Polynomials and Functions 3 Copyright Cengage Learning. All rights reserved. 3.1 Rules for Exponents Copyright Cengage Learning. All rights reserved. Rules for Exponents The basic concept of

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

TI-83 Plus Graphing Calculator Keystroke Guide

TI-83 Plus Graphing Calculator Keystroke Guide TI-83 Plus Graphing Calculator Keystroke Guide In your textbook you will notice that on some pages a key-shaped icon appears next to a brief description of a feature on your graphing calculator. In this

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

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

Sect 3.2 - Least Common Multiple

Sect 3.2 - Least Common Multiple Let's start with an example: Sect 3.2 - Least Common Multiple Ex. 1 Suppose a family has two different pies. If they have 2 3 of one type of pie and 3 of another pie, is it possible to combine the pies

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

Date: Section P.2: Exponents and Radicals. Properties of Exponents: Example #1: Simplify. a.) 3 4. b.) 2. c.) 3 4. d.) Example #2: Simplify. b.) a.

Date: Section P.2: Exponents and Radicals. Properties of Exponents: Example #1: Simplify. a.) 3 4. b.) 2. c.) 3 4. d.) Example #2: Simplify. b.) a. Properties of Exponents: Section P.2: Exponents and Radicals Date: Example #1: Simplify. a.) 3 4 b.) 2 c.) 34 d.) Example #2: Simplify. a.) b.) c.) d.) 1 Square Root: Principal n th Root: Example #3: Simplify.

More information

Associative Property The property that states that the way addends are grouped or factors are grouped does not change the sum or the product.

Associative Property The property that states that the way addends are grouped or factors are grouped does not change the sum or the product. addend A number that is added to another in an addition problem. 2 + 3 = 5 The addends are 2 and 3. area The number of square units needed to cover a surface. area = 9 square units array An arrangement

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

PAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE

PAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE PAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE 1 Property of Paychex, Inc. Basic Business Math Table of Contents Overview...3 Objectives...3 Calculator...4 Basic Calculations...6 Order of Operation...9

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

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

Chapter 15 Radical Expressions and Equations Notes

Chapter 15 Radical Expressions and Equations Notes Chapter 15 Radical Expressions and Equations Notes 15.1 Introduction to Radical Expressions The symbol is called the square root and is defined as follows: a = c only if c = a Sample Problem: Simplify

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

Section 1.2 Exponents and the Order of Operations

Section 1.2 Exponents and the Order of Operations 4. ( (4 + 1) ( + ) ) = ( 5 ( 8 )) = (5 5) = ( -51 ) = -15 Technical Writing 44. Explain different methods for grouping expressions and why it s important to have them. The student s answer should discuss

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

Placement Test Review Materials for

Placement Test Review Materials for Placement Test Review Materials for 1 To The Student This workbook will provide a review of some of the skills tested on the COMPASS placement test. Skills covered in this workbook will be used on the

More information

Simply Math. Everyday Math Skills NWT Literacy Council

Simply Math. Everyday Math Skills NWT Literacy Council Simply Math Everyday Math Skills 2009 NWT Literacy Council Acknowledgement The NWT Literacy Council gratefully acknowledges the financial assistance for this project from the Department of Education, Culture

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

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

EVALUATING ACADEMIC READINESS FOR APPRENTICESHIP TRAINING Revised For ACCESS TO APPRENTICESHIP

EVALUATING ACADEMIC READINESS FOR APPRENTICESHIP TRAINING Revised For ACCESS TO APPRENTICESHIP EVALUATING ACADEMIC READINESS FOR APPRENTICESHIP TRAINING For ACCESS TO APPRENTICESHIP MATHEMATICS SKILL OPERATIONS WITH INTEGERS AN ACADEMIC SKILLS MANUAL for The Precision Machining And Tooling Trades

More information

STUDY GUIDE FOR SOME BASIC INTERMEDIATE ALGEBRA SKILLS

STUDY GUIDE FOR SOME BASIC INTERMEDIATE ALGEBRA SKILLS STUDY GUIDE FOR SOME BASIC INTERMEDIATE ALGEBRA SKILLS The intermediate algebra skills illustrated here will be used extensively and regularly throughout the semester Thus, mastering these skills is an

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

Total Gadha s Complete Book of NUMBER SYSTEM

Total Gadha s Complete Book of NUMBER SYSTEM Total Gadha s Complete Book of NUMBER SYSTEM TYPES OF NUMBERS Natural Numbers The group of numbers starting from 1 and including 1, 2, 3, 4, 5, and so on, are known as natural numbers. Zero, negative numbers,

More information

The notation above read as the nth root of the mth power of a, is a

The notation above read as the nth root of the mth power of a, is a Let s Reduce Radicals to Bare Bones! (Simplifying Radical Expressions) By Ana Marie R. Nobleza The notation above read as the nth root of the mth power of a, is a radical expression or simply radical.

More information

Scientific Notation and Powers of Ten Calculations

Scientific Notation and Powers of Ten Calculations Appendix A Scientific Notation and Powers of Ten Calculations A.1 Scientific Notation Often the quantities used in chemistry problems will be very large or very small numbers. It is much more convenient

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

Repeating Decimals. where the bar over the six block set of digits indicates that that block repeats indefinitely.

Repeating Decimals. where the bar over the six block set of digits indicates that that block repeats indefinitely. Warm up problems. Repeating Decimals a. Find the decimal expressions for the fractions What interesting things do you notice? b. Repeat the problem for the fractions What is interesting about these answers?

More information

Calculation of Exponential Numbers

Calculation of Exponential Numbers Calculation of Exponential Numbers Written by: Communication Skills Corporation Edited by: The Science Learning Center Staff Calculation of Exponential Numbers is a written learning module which includes

More information

Direct Translation is the process of translating English words and phrases into numbers, mathematical symbols, expressions, and equations.

Direct Translation is the process of translating English words and phrases into numbers, mathematical symbols, expressions, and equations. Section 1 Mathematics has a language all its own. In order to be able to solve many types of word problems, we need to be able to translate the English Language into Math Language. is the process of translating

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

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

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