# Test 4 Sample Problem Solutions, = , 7 5, = = 1.4. Moving the decimal two spots to the left gives

Size: px
Start display at page:

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

## Transcription

1 Test 4 Sample Problem Solutions Convert from a decimal to a fraction: 0.023, 27.58, For the first two we have = 23 58, = For the last, if we set x = , then 10x = Subtracting gives 9x = 7, so that x = 7 9. Convert from a fraction to a decimal: , 7 5, 1 6. For the first two we have = 0.47, 7 5 = = 1.4. For the last we do the division, obtaining 1 6 = Convert from a percent to a decimal: 37%, 162%, 0.7%. Moving the decimal two spots to the left gives 37% = 0.37, 162% = 1.62, 0.7% = Convert from a percent to a fraction: 11%, 23.4%, 100%. We convert from a percent to a decimal and then to a fraction: 11% = 0.11 = , 23.4% = =, 100% = Convert from a decimal to a percent: 0.28, 0.062, 3.2. Moving the decimal two spots to the right gives 0.28 = 28%, = 6.2%, 3.2 = 320%. Convert from a fraction to a percent: , 4 5, 2 3.

2 We convert from a fraction to a decimal and then to a percent: = 0.73 = 73%, 4 5 = 8 10 = 0.8 = 80%, 2 = = %. 3 Write these decimals in expanded form: 23.64, 0.028, = , = , = Arrange these decimals in order from smallest to largest: 0.37, 0.6, Writing them with the same number of decimal places gives 0.370, 0.600, and 0.073, at which point the order becomes clear: 0.073,0.370, Compute: ; ; ; , 9.61, , 5.75 A fruit basket contains five apples, eight oranges, and ten bananas. What fraction of the fruit is apples? What is the ratio of apples to bananas? What fraction of the fruit is not oranges? Apples to total is Apples to bananas is 5 10 = 1 2. Not-oranges to total is Solve for x: x 35 = 2 7 ; = 30 x. Cros multiplying gives 7x = 70 so that x = 10. For the second we have 45x = 3000 so x = = = A family uses 5 gallons of milk every 3 weeks. How many gallons will they need to purchase over a 2 month period? (Assume 30 days in a month.)

3 They use five gallons in 21 days and x gallons in 60 days. This gives the proportion 5 21 = x, which we solve by cross-multiplying, obtaining 60 21x = 300, so x = = On a map, 1/3 inch equals 15 miles. The distance between two towns on a map is inches. How many miles are actually between the two towns? Since 1/3 of an inch corresponds to 15 miles and to x miles, we have the equation inches corresponds 1/3 15 = 32 3 x. Cross-multiplying gives x 3 = 55 so that x = 165 miles. It takes 10,000 silkworms to make one pound of silk. How many silkworms are needed to make one ounce of silk? (There are 16 ounces in a pound.) We know that 10,000 worms make 16 ounces and x worms make one ounce. So we have the equation 10,000 = x, so x = 10,000/16 = 625 worms Find 23% of = 18.4 Find 400% of = 12 Find 1 % of Since 1/5 = 0.2, we have that 1/5% = 0.2% = So = 0.1 A dress costs \$75 but is on sale for 30% off. What is the new price?

4 Thirty percent of 75 is.3 75 = 22.5, so the new price is = 52.5, which is \$ A dress is on sale for \$50, after having been marked down by 10%. What was the original price? If you take 10% off the original price, the new sale price is 90% the original. Thus the question is, 50 is 90% of what? This leads to the equation.9 P = 50, so that P = \$ Model the following using colored chips. Do each of them in two ways: as a subtraction problem and as an addition problem where the second number is negative: 7 5; 5 7; 3 2; 3 5. For 7 5, we begin with seven chips and take five away, leaving two chips remaining. For 7+( 5) we begin with seven chips and add five chips. Since this gives us mixed chips, we remove them a / pair at a time, leaving two chips remaining. For 5 7 we begin with five chips and we want to take away seven chips. Since we re two chips short, we add two / pairs, allowing us now to remove the seven chips. When this is done, two chips remain. For 5+( 7) we begin with five chips and add seven chips. Removing / pairs leaves two chips. For 3 2 we begin with three chips and we want to take away two chips. So we add two / pairs and then remove the two chips, leaving five chips. For 3+( 2) we begin with three chips and add two chips, giving five chips. For 3 5 we begin with three chips and we want to take away five chips. So we add five / pairs and then take away five chips, leaving eight chips. For 3+( 5) we begin with three chips and add five chips, giving eight chips. Explain how to compute the following: ( 3) (2) ( 4).

5 We think of 3 as 1 3 and 4 as 1 4, making this product ( 1 3) 2 ( 1 4). Since this is just a sequence of several products, and multiplication is associative, we can ignore the parentheses. Also, since multiplication is commutative, we can move the 1 terms to the front. The product then becomes ( 1 1) (3 2 4) = This explains why we can multiply these numbers ignoring the negative signs to obtain 24, and then just count the negative signs (odd gives negative, even gives positive).

### 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),

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

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

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

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

### Grade 4 - Module 5: Fraction Equivalence, Ordering, and Operations

Grade 4 - Module 5: Fraction Equivalence, Ordering, and Operations Benchmark (standard or reference point by which something is measured) Common denominator (when two or more fractions have the same denominator)

### 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,

### GEARING UP EXAMPLES. 4 to 3 4:3

GEARING UP EXAMPLES B 2 Teeth A 8 Teeth DEFINITION - RATIO As gear A revolves times, it will cause gear B to revolve times. Hence, we say that gear ratio of A to B is to. In mathematics, a ratio is a comparison

### Math Review. for the Quantitative Reasoning Measure of the GRE revised General Test

Math Review for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important

### Revision Notes Adult Numeracy Level 2

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

### Prealgebra Textbook. Chapter 6 Odd Solutions

Prealgebra Textbook Second Edition Chapter 6 Odd Solutions Department of Mathematics College of the Redwoods 2012-2013 Copyright All parts of this prealgebra textbook are copyrighted c 2009 in the name

### 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

### 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

### 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

### Using Proportions to Solve Percent Problems I

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

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

### Unit 7 The Number System: Multiplying and Dividing Integers

Unit 7 The Number System: Multiplying and Dividing Integers Introduction In this unit, students will multiply and divide integers, and multiply positive and negative fractions by integers. Students will

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

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

### 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

### Using Patterns of Integer Exponents

8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. How can you develop and use the properties of integer exponents? The table below shows powers of

### a. 2 b. 54 c. 28 d. 66 e. 45 5. A blouse that sold for \$59 was reduced 30%. After 6 months it was raised 30%. What was the last price of the blouse?

Pre-Algebra Topics COMPASS Review - revised Summer 0 You will be allowed to use a calculator on the COMPASS test. Acceptable calculators are basic calculators, scientific calculators, and approved graphing

### 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,

### MEP Y9 Practice Book A

1 Base Arithmetic 1.1 Binary Numbers We normally work with numbers in base 10. In this section we consider numbers in base 2, often called binary numbers. In base 10 we use the digits 0, 1, 2, 3, 4, 5,

### How Far Away is That? Ratios, Proportions, Maps and Medicine

38 How Far Away is That? Ratios, Proportions, Maps and Medicine Maps A ratio is simply a fraction; it gives us a way of comparing two quantities. A proportion is an equation that has exactly one ratio

### 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)

### Sample Problems. Practice Problems

Lecture Notes Quadratic Word Problems page 1 Sample Problems 1. The sum of two numbers is 31, their di erence is 41. Find these numbers.. The product of two numbers is 640. Their di erence is 1. Find these

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

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

### 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

### Mathematics Common Core Sample Questions

New York State Testing Program Mathematics Common Core Sample Questions Grade6 The materials contained herein are intended for use by New York State teachers. Permission is hereby granted to teachers and

### Means, Medians, and Modes

8.1 Means, Medians, and Modes 8.1 OBJECTIVES 1. Calculate the mean 2. Interpret the mean 3. Find the median 4. Interpret the median 5. Find a mode A very useful concept is the average of a group of numbers.

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

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

### 5.4 Solving Percent Problems Using the Percent Equation

5. Solving Percent Problems Using the Percent Equation In this section we will develop and use a more algebraic equation approach to solving percent equations. Recall the percent proportion from the last

### Story Problems With Remainders

Mastery Drill 8 8 Story Problems With Remainders What we do with the remainder after working a division story problem depends on the story. Three hungry boys divided ten pieces of pizza equally among themselves.

### 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

### Five Ways to Solve Proportion Problems

Five Ways to Solve Proportion Problems Understanding ratios and using proportional thinking is the most important set of math concepts we teach in middle school. Ratios grow out of fractions and lead into

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

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

### Charlesworth School Year Group Maths Targets

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

### BASIC MATHEMATICS. WORKBOOK Volume 2

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

### 3.3 Addition and Subtraction of Rational Numbers

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

### Student Exploration: Unit Conversions

Name: Date: Student Exploration: Unit Conversions Vocabulary: base unit, cancel, conversion factor, dimensional analysis, metric system, prefix, scientific notation Prior Knowledge Questions (Do these

### Assessment For The California Mathematics Standards Grade 6

Introduction: Summary of Goals GRADE SIX By the end of grade six, students have mastered the four arithmetic operations with whole numbers, positive fractions, positive decimals, and positive and negative

### 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

### Fractional Part of a Set

Addition and Subtraction Basic Facts... Subtraction Basic Facts... Order in Addition...7 Adding Three Numbers...8 Inverses: Addition and Subtraction... Problem Solving: Two-Step Problems... 0 Multiplication

### Chapter 5. Decimals. Use the calculator.

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

### Number Sense and Operations

Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents

### Chapter 3 Review Math 1030

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

### Wigan LEA Numeracy Centre. Year 6 Mental Arithmetic Tests. Block 1

Wigan LEA Numeracy Centre Year 6 Mental Arithmetic Tests Block 1 6 Produced by Wigan Numeracy Centre July 2001 Year Six Mental Arithmetic Test 1 (5 seconds response time) 1. Write the number three hundred

### 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

### 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,

### 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

### MATH COMPUTATION. Part 1. TIME : 15 Minutes

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

### Overview for Families

unit: Ratios and Rates Mathematical strand: Number The following pages will help you to understand the mathematics that your child is currently studying as well as the type of problems (s)he will solve

### 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.

### 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

### Use order of operations to simplify. Show all steps in the space provided below each problem. INTEGER OPERATIONS

ORDER OF OPERATIONS In the following order: 1) Work inside the grouping smbols such as parenthesis and brackets. ) Evaluate the powers. 3) Do the multiplication and/or division in order from left to right.

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

### The Utah Basic Skills Competency Test Framework Mathematics Content and Sample Questions

The Utah Basic Skills Competency Test Framework Mathematics Content and Questions Utah law (53A-1-611) requires that all high school students pass The Utah Basic Skills Competency Test in order to receive

### 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

### Calculate Highest Common Factors(HCFs) & Least Common Multiples(LCMs) NA1

Calculate Highest Common Factors(HCFs) & Least Common Multiples(LCMs) NA1 What are the multiples of 5? The multiples are in the five times table What are the factors of 90? Each of these is a pair of factors.

### EXAMPLES OF ASSIGNING DEPTH-OF-KNOWLEDGE LEVELS ALIGNMENT ANALYSIS CCSSO TILSA ALIGNMENT STUDY May 21-24, 2001 version 2.0

EXAMPLES OF ASSIGNING DEPTH-OF-KNOWLEDGE LEVELS ALIGNMENT ANALYSIS CCSSO TILSA ALIGNMENT STUDY May 21-24, 2001 version 2.0 Level 1 Recall Recall of a fact, information or procedure Example 1:1 Grade 8

### Conversions. 12 in. 1 ft = 1.

Conversions There are so many units that you can use to express results that you need to become proficient at converting from one to another. Fortunately, there is an easy way to do this and it works every

### Customary Length, Weight, and Capacity

15 CHAPTER Lesson 15.1 Customary Length, Weight, and Capacity Measuring Length Measure each object to the nearest inch. 1. The crayon is about inches long. 2. 3. The toothbrush is about The rope is about

### Financial Mathematics

Financial Mathematics For the next few weeks we will study the mathematics of finance. Apart from basic arithmetic, financial mathematics is probably the most practical math you will learn. practical in

### Measurement. Customary Units of Measure

Chapter 7 Measurement There are two main systems for measuring distance, weight, and liquid capacity. The United States and parts of the former British Empire use customary, or standard, units of measure.

### Activity 1: Using base ten blocks to model operations on decimals

Rational Numbers 9: Decimal Form of Rational Numbers Objectives To use base ten blocks to model operations on decimal numbers To review the algorithms for addition, subtraction, multiplication and division

### 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) =

### TEKS TAKS 2010 STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM

7 th Grade Math TAKS-STAAR-STAAR-M Comparison Spacing has been deleted and graphics minimized to fit table. (1) Number, operation, and quantitative reasoning. The student represents and uses numbers in

### 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

### Converting Units of Measure Measurement

Converting Units of Measure Measurement Outcome (lesson objective) Given a unit of measurement, students will be able to convert it to other units of measurement and will be able to use it to solve contextual

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

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

### Quarterly Cumulative Test 2

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

### Computation Strategies for Basic Number Facts +, -, x,

Computation Strategies for Basic Number Facts +, -, x, Addition Subtraction Multiplication Division Proficiency with basic facts aids estimation and computation of multi-digit numbers. The enclosed strategies

### From the Webisode: Math Meets Fashion

lesson CCSS CONNECTIONS Percent Markups From the Webisode: Math Meets Fashion In this lesson, s solve a multi-step problem by identifying percent markups of a whole and calculating a final sale price.

### Summer Math Packet. For Students Entering Grade 5 \$3.98. Student s Name 63 9 = Review and Practice of Fairfield Math Objectives and CMT Objectives

Summer Math Packet 63 9 = Green Yellow Green Orange Orange Yellow \$3.98 1 Green A B C D Red 8 1 2 3 4 5 Student s Name June 2013 Review and Practice of Fairfield Math Objectives and CMT Objectives 1 Summer

### Fraction Problems. Figure 1: Five Rectangular Plots of Land

Fraction Problems 1. Anna says that the dark blocks pictured below can t represent 1 because there are 6 dark blocks and 6 is more than 1 but 1 is supposed to be less than 1. What must Anna learn about

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

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

### Ch.4 Fractions and Mixed Numbers

Ch. Fractions and Mixed Numbers. An Introduction to Fractions. Multiplying Fractions. Dividing Fractions. Adding and Subtracting Fractions. Multiplying and Dividing Mixed Numbers.6 Adding and Subtracting

### GCSE MATHEMATICS. 43602H Unit 2: Number and Algebra (Higher) Report on the Examination. Specification 4360 November 2014. Version: 1.

GCSE MATHEMATICS 43602H Unit 2: Number and Algebra (Higher) Report on the Examination Specification 4360 November 2014 Version: 1.0 Further copies of this Report are available from aqa.org.uk Copyright

### Multiplication and Division with Rational Numbers

Multiplication and Division with Rational Numbers Kitty Hawk, North Carolina, is famous for being the place where the first airplane flight took place. The brothers who flew these first flights grew up

### Arithmetic Review ORDER OF OPERATIONS WITH WHOLE NUMBERS

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

### 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

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

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

### Mathematics Navigator. Misconceptions and Errors

Mathematics Navigator Misconceptions and Errors Introduction In this Guide Misconceptions and errors are addressed as follows: Place Value... 1 Addition and Subtraction... 4 Multiplication and Division...

### Autumn 1 Maths Overview. Year groups Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 1 Number and place value. Counting. 2 Sequences and place value.

Autumn 1 Maths Overview. Year groups Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 1 Number and place Counting. 2 Sequences and place Number facts and counting. Money and time. Length, position and

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

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

### 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

### 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

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

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

by Teresa Evans Copyright 2010 Teresa Evans. All rights reserved. Permission is given for the making of copies for use in the home or classroom of the purchaser only. Looking for More Math Fun? Making

### Paper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 6 8

Ma KEY STAGE 3 Mathematics test TIER 6 8 Paper 1 Calculator not allowed First name Last name School 2009 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You

### Solving Proportions by Cross Multiplication Objective To introduce and use cross multiplication to solve proportions.

Solving Proportions by Cross Multiplication Objective To introduce and use cross multiplication to solve proportions. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop

### Unit 1 Equations, Inequalities, Functions

Unit 1 Equations, Inequalities, Functions Algebra 2, Pages 1-100 Overview: This unit models real-world situations by using one- and two-variable linear equations. This unit will further expand upon pervious

### 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

### Division of whole numbers is defined in terms of multiplication using the idea of a missing factor.

32 CHAPTER 1. PLACE VALUE AND MODELS FOR ARITHMETIC 1.6 Division Division of whole numbers is defined in terms of multiplication using the idea of a missing factor. Definition 6.1. Division is defined

### Assessment For The California Mathematics Standards Grade 3

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

### 2. Cost-Volume-Profit Analysis

Cost-Volume-Profit Analysis Page 1 2. Cost-Volume-Profit Analysis Now that we have discussed a company s cost function, learned how to identify its fixed and variable costs. We will now discuss a manner

### Chapter 4. Applying Linear Functions

Chapter 4 Applying Linear Functions Many situations in real life can be represented mathematically. You can write equations, create tables, or even construct graphs that display real-life data. Part of

### Algebra Word Problems

WORKPLACE LINK: Nancy works at a clothing store. A customer wants to know the original price of a pair of slacks that are now on sale for 40% off. The sale price is \$6.50. Nancy knows that 40% of the original

### 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

### Math Refresher. Book #2. Workers Opportunities Resources Knowledge

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