4 Percentages Chapter notes


 Logan Montgomery
 2 years ago
 Views:
Transcription
1 4 Percentages Chapter notes GCSE Specification concepts and skills Find a percentage of a quantity (N o): 4. Use percentages to solve problems (N m): 4., 4.2, 4., 4.4 Use percentages in reallife situations: VAT, value of profit or loss, simple interest, income tax calculations, find prices after a percentage increase or decrease, compound interest, depreciation, percentage profit and loss (N m): 4., 4.2, 4., 4.4 Use decimals to find quantities (N o): 4.2 Understand the multiplicative nature of percentages as operators (N o): 4.2 Use a multiplier to increase or decrease by a percentage in any scenario where percentages are used (N o): 4.2 Calculate and represent repeated proportional change using a multiplier raised to a power (N m, N o): 4. Express a given number as a percentage of another number (N o): 4.4 Support materials Support sheet 4. You can convert between fractions, percentages and decimals and order them Prior key knowledge, skills and concepts Students should already be able to: convert a fraction into a decimal find equivalent fractions find a fraction of a quantity multiply and divide fractions and integers write one quantity as a fraction of another quantity. Main teaching and learning Resources Calculators Resource sheet 4. [4.] Elicit from pupils which method(s) they have used previously to work out the percentage of a quantity and make a judgement about which method(s) to support when using worked examples in class. Complete Example with them using the chosen method(s). Remind the students of possible contexts in which percentages occur, for example in pay rises, income tax, VAT, hire purchase deposits and discounts. Ensure they are confident in using their calculator to work out percentages. Complete Example 2. [4.2] Discuss with students how to tackle problems where there is a need to add or subtract a percentage of a quantity and, if appropriate, explain the advantage of using decimal multipliers to solve such problems. Model the solution of problems like this using Examples and 4. [4.] [H] Remind students of the difference between simple interest and compound interest. [H] Use Example to demonstrate how to work out compound interest. You could compare the interest gained in this example with the simple interest you would get with the same amount of capital over the same time period. [H] Use Example 6 to show pupils how a similar process works for questions involving depreciation. Discuss other contexts in which a compound percentage reduction might occur, e.g. decrease in population. [4.4] Remind students how to work out one quantity as a percentage of another and discuss possible contexts where this would be used, e.g. marks in a test, nutrition information on food labels, percentage profit or loss. Use Examples 8 and 9 to model possible examination questions. 0
2 4 Percentages Chapter notes Exam tips Be careful not to read of as off. Check whether you just have to work out a percentage or whether the question requires you to then add or subtract your answer from a quantity. Be careful with decimal places when converting decimals to percentages. For example, 0.8 is equivalent to 80% and 0.08 is equivalent to 8%. Take care when changing a fraction into a percentage when the denominator is neither a factor nor a multiple of 0. Remember the link between working out the fraction as a decimal and converting it to a percentage. Do lots of practise with calculator methods. Mistakes in calculator use are a common cause of dropped marks. Do not try to use a buildup method for percentages when you are allowed a calculator. Although this is a valid method, it is easy to make errors in the arithmetic. You should use an appropriate method depending on the type of question. Remember to use the multiplier 0.8, not 0., to decrease a quantity by %. [H] When working out percentage profit or loss (or increase or decrease), remember not to use the final amount in this calculation. You should use the original amount. [H] Make sure you understand the difference between simple interest and compound interest. Always check your answers to help eliminate errors. Enrichment Students could investigate the tax system and work out how much tax is paid by employees earning pa, pa and pa. Uptodate tax rates can be found at Students could research the interest rates being offered by banks and building societies. Choose an amount to invest and, for each rate, work out how much interest they would get after one year. More able students could be given a reverse percentage problem (e.g. If the sale price of a shirt is 2 after a % discount, what is the normal price?). What is 60 as a percentage of 40? (0%) Discuss situations that could lead to percentages greater than 0%. Plenary Ask students to write 48% as a fraction and as a decimal and explain their answers. Display a variety of questions, e.g. % of 60, 2% of 6, and for each one ask whether it is best tackled by a mental method or by using a calculator. Discuss how to find VAT using a mental method and using a calculator method. Display pictures of several items for sale, each with a price. Ask students to work out the price of each after a % reduction or after VAT at % is added. Ask students to work out simple questions involving percentage profit and loss. Peter bought a bicycle for 60 and then sold it to a friend for 7. Work out his percentage profit. (2%) Ask students how they would use a calculator to work out the result of increasing an amount by three successive increases of 4%, by two successive decreases of %, etc. Students could play or make up their own dominoes game like the one described in Resource sheet 4..
3 4 Percentages Support material Questions in this exercise are targeted at the grades indicated. 4. You can convert between fractions, percentages and decimals and order them (N l) Key Points You can put a list with fractions, decimals and percentages in order of size by changing them to the same type of number. Example Write as a decimal: a 6% b % a 6% = 6 0 b % = = = 0.0 Write the percentage as a fraction. So 6% = 0.6 So % = 0.0 Exercise A G Write the following percentages as fractions in their simplest form. a 40% b 7% c % d 90% e % f 80% g 84% h 7% G 2 64% of the spectators at a football match were male. Write down the fraction of the spectators that were male. Give your fraction in its simplest form. Example 2 Write as a percentage: Method Without using a calculator: = 6 Write as an equivalent fraction with denominator 6 = tenths written as a decimal is 0.6 So = 60% 0.6 is equivalent to 60% Method 2 Using a calculator: = Use a calculator to divide the numerator by the denominator. = 0.6 Remember 0.60 and 0.6 are equivalent decimals. So = 0.6 2
4 4 Percentages Support material Exercise B G Write the following fractions as decimals: a b 8 0 c 7 0 d 6 00 G 2 Write the following fractions as decimals. Do not use a calculator. a 4 b c 0 d 2 2 G Write the following fractions as decimals. You may use a calculator. a 7 Example b c 7 8 d 6 Write the following numbers in order of size. Start with the smallest number. 0.4 % 8 8 = 0.7 Change 8 into a decimal is already a decimal. % = 0. Change % into a decimal Write the decimals in order of size. % Write each number in its original form. Exercise C G a Write 2% as a decimal. b Write as a decimal. 4 c Which is bigger, 2% or? 4 G 2 a Write 74% as a decimal. b Write 7 as a decimal. 7 c Which is bigger, 74% or? G Write each of the following lists in order of size, starting with the smallest number. a 2 48% 0.4 b 0.7 F 4 Write each of the following lists in order of size, starting with the smallest number. a 0.2 b 2 % 68% 0.6 % %
5 4 Percentages Skills worksheet Questions in this worksheet are targeted at the grades indicated. F Safiyah got 7 out of in a spelling test. What is 7 out of as a percentage? Remember: Write one amount as a percentage of another, form a fraction, then multiply by 0. F 2 In a maths test, Laura scored 4 out of 60 and in a science test she scored 2 out of 0. In which test did she do best? Hint: Write both scores as percentages. E There are 260 students in Year 7. On Friday % of these students were absent. How many students were absent on Friday? D 4 Last year a garage sold 270 cars. % of these were new cars. Work out how many new cars the garage sold last year. D Tamsin bought a flat costing 000. When she sold the flat she made a profit of 7%. Work out how much profit Tamsin made. D 6 Work out the sale price of each item, below. Remember: Write one amount as a percentage of another, form a fraction, then multiply by D 7 Adam s monthly salary is 860. His salary is increased by 4%. Work out Adam s new monthly salary. Remember: To increase a quantity, the multiplier will be greater than. For example, to add on 0% to a quantity, use. as the multiplier. 4
6 4 Percentages Skills worksheet D 8 A stereo costs 64 plus VAT at %. Calculate the total cost of the stereo. D 9 A train ticket costs 4. The price is increased by 6.%. Work out the new price of the train ticket. D A football stadium has a capacity of At a match one weekend, 8900 people were present. Work out the percentage of the stadium that was occupied. C In a sale, prices are reduced by 2%. A TV set normally costs 42. Calculate its price in the sale. Remember: To decrease a quantity, the multiplier will be less than. For example, to subtract 40% from a quantity, use 0.6 as the multiplier. Questions 2, and 4 are Higher tier only. C 2 In a sale, the price of an MP player is reduced from 68 to.04. Work out the percentage reduction in the price of the MP player. reduction Remember: Percentage reduction = original amount 0. C 000 is invested in a bank for 2 years. Compound interest is paid at a rate of 4% per annum. How much money is in the bank after 2 years? C 4 Alan bought a car for 600. Each year the total cost of the car depreciated by %. Work out the value of the car 2 years after he bought it.
7 4 Percentages Chapter test Questions in this test are targeted at the grades indicated. F Write the following percentages as decimals. a 7% b 8% c 90% () F 2 Write 8% as a fraction in its simplest form. () G a What is 7% of 0? (2) E b What is % of 4.80? (2) E AO2 *4 In a test, Wendy scored 24 out of 60, Jenni scored 4% and Kavish scored of the marks. 2 Which of the three scored the highest in this test? You must show all your working. (4) D Carl works for hours each week in a shop. From the beginning of March, Carl s hours were reduced by %. Work out how many hours Carl works each week in March. Give your answer to the nearest hour. () D AO2/ *6 Three shops were selling the same type of washing machine. Sam s Store Was 0 Now 0% off Eli s Emporium 0 deposit plus 7 monthly payments of 2.40 Monty s Machines 8 plus % VAT Helen wants to buy the cheapest washing machine. From which shop should she buy the washing machine? You must show how you decided on your answer. (6) Questions 7, 8 and 9 are Higher tier only. C 7 Neil bought a watch for 60 and sold it a week later for 2. Work out his percentage loss. Write your answer correct to 2 significant figures. (2) C AO2/ 8 Here are the details of how income tax is calculated for the tax year : The first 647 is free of income tax. The next 0 92 is charged at %. Any further income up to is taxed at 40%. John has a taxable income of Calculate how much tax John will pay. (4) C AO2/ 9 Stephen invested 000 for three years at % compound interest. His sister Millie invested 000. The value of Millie s investment increased by 9.2% over the three years. Who made the better investment? You must show all your calculations. () (Total = 0 marks) 6
By the end of the year the value of the car has gone down by 40%. How much is the car now worth?
3 3.1 Finding the new amount after a percentage increase or decrease Questions are targeted at the grades indicated To work out a multiplier for a percentage increase (e.g. 140 increase of 40%) 100% +
More information14 PERCENTAGES. Before you start. Objectives
14 PERCENTAGES One of the most common percentages used to compare schools is the number of students getting five GCSEs grade A* C. Percentages can also be used to compare results across the sexes; traditionally,
More informationDistance Learning Pack for: Unit 2: Working with fractions, decimals and percentages. Targets:
Distance Learning Pack for: Unit 2: Working with fractions, decimals and percentages. Targets: 1. Types of fractions. 2. Fractions of quantities. 3. One number as a fraction of another. 4. Adding and subtracting
More informationPercentages. Examination Question: A car was bought for It depreciated in value by 25% each year. What was the value of the car after 3 years?
Percentages Percentages Multipliers The multiplier for an increase of 6% is 1.06 (100% + 6% = 106% or 1.06). To increase an amount by 6%, multiply it by 10.06. The multiplier for a decrease of 12% is 0.88
More informationOil prices rise by 4% The numerator is 45 and the denominator is 100
2 CHAPTER 3. 3 A head Scatter graphs CHAPTER 3 Percentages CHAPTER 2. Percentages ALL PRICES REDUCED BY % DAILY BLAH Oil prices rise by 4% thank you for your contribution this year. Your salary will increase
More informationIn order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature.
Percentages In this unit we shall look at the meaning of percentages and carry out calculations involving percentages. We will also look at the use of the percentage button on calculators. In order to
More informationPercentages. You will need a calculator 20% =
What is a percentage? Percentage just means parts per hundred, for example 20% stands for 20 parts per hundred. 20% is a short way of writing 20 over a hundred. When using a percentage in a calculation
More informationBasic Calculations and Percentages
Saturday Xtra XSheet: 1 Basic Calculations and Percentages Key Concepts In this session, we will focus on summarising what you need to know about:  Basic Calculations (revision of earlier work) o Scientific
More informationWorking with percentages. Introduction. Try these. Think about
Working with percentages Introduction You will have met percentages before. They are very useful because they are easier to work with than fractions and make it easy to compare things, for example, test
More informationPERCENTAGES M.K. HOME TUITION. Mathematics Revision Guides Level: GCSE Higher Tier
Mathematics Revision Guides ercentages age 1 of 14 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier ERCENTAGES Version: 2.3 Date: 01022014 Mathematics Revision Guides ercentages
More informationSection 1. Proportions
Worksheet.5 Percentages Section Proportions A pie is cut into twelve pieces. John eats five pieces, Peter eats one piece and Chris and Michael eat three pieces each. If we ask what proportion of the pie
More informationA percentage is a fraction with a denominator (bottom number) of % = 23
Chapter 5 Percentages We have all seen advertisements on television that use percentages. Shops selling items at a % discount or cereal boxes offering % more than usual for the same price. Percentages
More information2 Fractions, decimals and percentages
2 Fractions, decimals and percentages You can use fractions, decimals and percentages in many different practical problems. Fractions You need to know how to: Read, write and compare common fractions Example
More information2. In solving percent problems with a proportion, use the following pattern:
HFCC Learning Lab PERCENT WORD PROBLEMS Arithmetic  11 Many percent problems can be solved using a proportion. In order to use this method, you should be familiar with the following ideas about percent:
More informationLesson Plan  Simple and Compound Interest
Lesson Plan  Simple and Compound Interest Chapter Resources  Lesson 414 Simple Interest  Lesson 414 Simple Interest Answers  Lesson 415 Compound Interest  Lesson 415 Compound Interest Answers
More informationLesson Plan  Percent of a Number/Increase and Decrease
Lesson Plan  Percent of a Number/Increase and Decrease Chapter Resources  Lesson 411 Find a Percent of a Number  Lesson 411 Find a Percent of a Number Answers  Lesson 412 Percent of Increase and
More informationPercentages. It is quite straightforward to convert a percent into a fraction or decimal (and vice versa) using the following rules:
What do percentages mean? Percentages Academic Skills Advice Percent (%) means per hundred. e.g. 22% means 22 per 00, and can also be written as a fraction ( 22 00 ) or a decimal (0.22) It is quite straightforward
More informationMake the denominators the same, convert the numerators by multiplying, then add the numerators.
Experience & Outcome: MNU 207a I have investigated the everyday contexts in which simple fractions, percentages or decimal fractions are used and can carry out the necessary calculations to solve related
More informationTo Multiply Decimals
4.3 Multiplying Decimals 4.3 OBJECTIVES 1. Multiply two or more decimals 2. Use multiplication of decimals to solve application problems 3. Multiply a decimal by a power of ten 4. Use multiplication by
More informationFractions, decimals and percentages
Fractions, decimals and percentages Some notes for the lesson. Extra practice questions available. A. Quick quiz on units Some of the exam questions will have units in them, and you may have to convert
More informationTeens version. Instructor guide. 2003, 2012 Wells Fargo Bank, N.A. All rights reserved. Member FDIC. ECG714394
Teens version Instructor guide 2003, 2012 Wells Fargo Bank, N.A. All rights reserved. Member FDIC. ECG714394 Budgeting Unit Overview In these lessons, middleschool students (grades 68) are introduced
More informationMaths 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 informationTHINGS TO REMEMBER CONSUMER MATHEMATICS
PREMIER CURRICULUM SERIES Based on the Sunshine State Standards for Secondary Education, established by the State of Florida, Department of Education THINGS TO REMEMBER CONSUMER MATHEMATICS Copyright 2009
More informationAll the examples in this worksheet and all the answers to questions are available as answer sheets or videos.
BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com Numbers 3 In this section we will look at  improper fractions and mixed fractions  multiplying and dividing fractions  what decimals mean and exponents
More information% of a number: 1) find 10%, 2) then by 2.
Math 6/7 NOTES (8.1a) Name Calculating Percentages of Numbers Mental Computations: To find 10% of a number mentally, move the one place to the left. 10% of 30 10% of 270 10% of $53 To find of a number,
More informationFINANCE m e p STRAND: FINANCE Unit 2 Simple and Compound Interest TEXT Section
CMM Subject Support Strand: FINANCE Unit 2 Simple and Compound Interest: Text m e p STRAND: FINANCE Unit 2 Simple and Compound Interest TEXT Contents Section 2.1 Simple Interest 2.2 Compound Interest 2.3
More informationCalculate the amount if you know the total and percentage
Calculate the amount if you know the total and percentage For example, if you purchase a computer for $800 and there is an 8.9% sales tax, how much do you have to pay for the sales tax? In this example,
More informationCONVERTING PERCENTS TO DECIMALS a) replace the % with x0.01 b) multiply by 0.01, i.e., move decimal point TWO PLACES TO LEFT
Chapter 6 Percents and Their Fraction and Decimal Forms N% = N per hundred Ratio = (this form I use most of the time) 70% 23.4%. 00% CONVERTING PERCENTS TO FRACTIONS 32% 90% 75% 0.06%.. 75% 50% 66 % CONVERTING
More informationTeaching & Learning Plans. Applications of Geometric Sequences and Series. Junior Certificate Syllabus Leaving Certificate Syllabus
Teaching & Learning Plans Applications of Geometric Sequences and Series Junior Certificate Syllabus Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what
More informationcount up and down in tenths count up and down in hundredths
Number: Fractions (including Decimals and Percentages COUNTING IN FRACTIONAL STEPS Pupils should count in fractions up to 10, starting from any number and using the1/2 and 2/4 equivalence on the number
More informationDecimals 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 informationPERCENTS  compliments of Dan Mosenkis
PERCENTS  compliments of Dan Mosenkis Percent Basics: Percents are connected to many ideas: fractions, decimals, proportions, relative amounts, and multiplicative change. You could say they are like the
More informationH.C.C.T.P. Highway Construction Careers Training Program. Entrance Exam. Study Guide
H.C.C.T.P. Highway Construction Careers Training Program Entrance Exam Study Guide Entrance Exam Study Guide How to use this study guide: This study guide is to prepare you for the math section on your
More information1 Financial mathematics
E 1A Review of percentages 1E Understanding compound interest 1B Financial applications of percentages 1F Working with the compound interest formula SA M PL NUMBER AND ALGEBRA 1 Financial mathematics 1C
More informationFinancial Maths Investing Money
Financial Maths Investing Money PD General Maths Name: C:\Documents and Settings\tracey_hbutters\Desktop\mathematics\year_levels\math_stage6\General\preliminary\notes\financial_maths\financia 1 CAPACITY
More informationPreAlgebra Lecture 6
PreAlgebra Lecture 6 Today we will discuss Decimals and Percentages. Outline: 1. Decimals 2. Ordering Decimals 3. Rounding Decimals 4. Adding and subtracting Decimals 5. Multiplying and Dividing Decimals
More information1 of 56. Percentages
1 of 56 Percentages 2 of 56 Convert a percentage to a decimal Copy into your notes 3 of 56 Converting a Percentage to a Decimals Before we use percentages in calculation we need to learn how to convert
More informationThe Box Method. part % whole 100
The Box Method There are different methods for solving problems involving percents. An easy and dependable method is The Box Method. When you can analyze which number is missing from the problem, then
More informationCONNECT: Percentages. Phrase % Phrase % Practically all
CONNECT: Percentages If you haven t done maths for a while, it might be best for you to start with CONNECT: Fractions FRACTIONS 4; FRACTIONS, DECIMALS, PERCENTAGES how do they relate? Percentages occur
More informationChapter 4. Fractions, Decimals, Percent s Worksheets. Name: Class::
Chapter 4 Fractions, Decimals, Percent s Worksheets Name: Class:: Rounding Worksheet NAME: Thousands Hundreds Tens Units Decimal. Tenths Hundredths Thousandths Use the table provided to help you round
More informationPercents. Writing percents as decimals. How to change a percent to a decimal.
Percents Introduction: Percent (%) means per hundred or hundredths. When you read in the newspaper that 80% of the voters voted, it means that 80 out of 100 eligible citizens voted. A percent can be considered
More information2 Fractions, decimals and percentages
2 Fractions, decimals and percentages You can use fractions, decimals and percentages to help you solve everyday practical problems. Fractions Write fractions in their simplest form. Do this by dividing
More informationGrade 6 Math Circles Fall 2012 Applications of Percent
1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 6 Math Circles Fall 2012 Applications of Percent A percentage is a way of expressing a number as
More informationRich Kid Smart Kid Games Game Three: Ima s Dream Topic: Pay Yourself First Grade Level: 912
Rich Kid Smart Kid Games Game Three: Ima s Dream Topic: Pay Yourself First Grade Level: 912 Interactive Internet Game Activity Bill and Penny are just like the young people we all know. Some have the
More information7.1 Percent, Decimal and Fractions
Chapter 7. Percent 7.1 Percent, Decimal and Fractions 7.2 Solving Percent Problems Using Percent Equations and Proportions 7.3 Application of Percent 7.4 Estimation with Percent 7.5 Interest 1 7.1 Percent,
More informationDIVISION OF DECIMALS. 1503 9. We then we multiply by the
Tallahassee Community College 0 DIVISION OF DECIMALS To divide 9, we write these fractions: reciprocal of the divisor 0 9. We then we multiply by the 0 67 67 = = 9 67 67 The decimal equivalent of is. 67.
More informationSection 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 informationPercentages  quiz. Level A. 1. What percentage of this grid of squares is shaded? (There are 100 squares in this 10 10 grid.
Level A 1. What percentage of this grid of squares is shaded? (There are 100 squares in this 10 10 grid.) A) 30% B) 70% 2. Which is the smaller percentage? A) 20% B) 25% 3. Approximately 80% of households
More informationThese sample questions, selected from state endofcourse exams, cover the same algebraic concepts explored in the Math in Fashion lesson.
Math in Fashion: Sample Related EndofCourse (EOC) Questions These sample questions, selected from state endofcourse exams, cover the same algebraic concepts explored in the Math in Fashion lesson.
More informationKey Stage 2 SATs. A School Presentation to Parents. Information and Guidance on the Changes and Expectations for 2015/16
Key Stage 2 SATs A School Presentation to Parents Information and Guidance on the Changes and Expectations for 2015/16 Chapters Key Stage 2 SATs Changes Assessment and Reporting Scaled Scores Scaled Score
More informationFive daily lessons. Page 23. Page 25. Page 29. Pages 31
Unit 4 Fractions and decimals Five daily lessons Year 5 Spring term Unit Objectives Year 5 Order a set of fractions, such as 2, 2¾, 1¾, 1½, and position them on a number line. Relate fractions to division
More informationUnit 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 informationSelfDirected 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 informationUnit 5 Length. Year 4. Five daily lessons. Autumn term Unit Objectives. Link Objectives
Unit 5 Length Five daily lessons Year 4 Autumn term Unit Objectives Year 4 Suggest suitable units and measuring equipment to Page 92 estimate or measure length. Use read and write standard metric units
More informationGrade 7 Maths Term 1. MATHS Grade 7 RATIO AND RATE A. DEFINITIONS
1 Grade 7 Maths Term 1 MATHS Grade 7 RATIO AND RATE A. DEFINITIONS 1. RATIO A ratio is used to compare the sizes of two or more quantities that use the same unit of measurement. A ratio of 5 : 6 means
More information7. [Decimals / Fractions / Percentages]
7. [Decimals / Fractions / Percentages] Skill 7. Ordering decimal numbers. MM. MM. Line up the decimal numbers at their decimal points. Compare digits in the same places, starting from the left, until
More informationUnit 4 Number and Operations in Base Ten: Multiplying and Dividing Decimals
Unit 4 Number and Operations in Base Ten: Multiplying and Dividing Decimals Introduction In this unit, students will learn how to multiply and divide decimals, and learn the algorithm for dividing whole
More informationMath 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
More informationPractice Problems to Prepare for Trades Math Assessment Test Form A (Answers are located at the end of this practice exam)
Practice Problems to Prepare for Trades Math Assessment Test Form A (Answers are located at the end of this practice exam) The actual Trades Math Assessment Test will have 0 questions few multiple choice
More informationRound 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 informationIntroduction to fractions A fraction is the ratio of two whole numbers, i.e. one whole number divided by another whole number:
Fractions & Percentages Topics Covered: Fractions Simplifying fractions Equivalent fractions Improper fractions & mixed numers Operations with Fractions (addition, sutraction, multiplication, division)
More informationKey stage one end of year assessment. May 2016
Key stage one end of year assessment May 2016 New curriculum In 2014/15 a new national curriculum framework was introduced by the Government for Years 1, 3, 4 and 5. However, Years 2 and 6 (due to statutory
More informationNumber: Fractions (including Decimals and Percentages) COUNTING IN FRACTIONAL STEPS Year 1 Year 2 Year 3 Year 4 Year 5 Year 6
Pupils should begin to count in halves, using practical resources to support Number: Fractions (including Decimals and Percentages COUNTING IN FRACTIONAL STEPS Pupils should count in count up and down
More informationAdding and Subtracting
Positive and Negative Integers 1 A 7 th Grade Unit on Adding and Subtracting Positive and Negative Integers Developed by: Nicole Getman December 1, 2006 Buffalo State: I 2 T 2 Positive and Negative Integers
More informationeday 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 informationGrade 7 & 8 Math Circles October 13, 2010 Percents and Ratios
1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 7 & 8 Math Circles October 13, 2010 Percents and Ratios Definition Percent: a way of expressing a
More informationChapter. Percentage. Contents:
Chapter 3 Percentage Contents: A B C D E F G H Percentage The unitary method in percentage Finding a percentage of a quantity Percentage increase and decrease Percentage change using a multiplier Finding
More informationFundamentals of accounting
Fundamentals of accounting About this free course This free course is an adapted extract from the Open University course B124 Fundamentals of accounting www.open.ac.uk/courses/modules/b124. This version
More informationPercent, Sales Tax, & Discounts
Percent, Sales Tax, & Discounts Many applications involving percent are based on the following formula: Note that of implies multiplication. Suppose that the local sales tax rate is 7.5% and you purchase
More informationEquivalent Conversions
Grades 6 8 Part 1 of 2 Poster/Teaching Guide Math Lessons & Worksheets to Build Skills in Equivalent Conversions Aligned with NCTM Standards Math Grants Available (details inside) Dear Teacher: Welcome
More informationLESSON SUMMARY. Mathematics for Buying, Selling, Borrowing and Investing
LESSON SUMMARY CXC CSEC MATHEMATICS UNIT Four: Consumer Arithmetic Lesson 5 Mathematics for Buying, Selling, Borrowing and Investing Textbook: Mathematics, A Complete Course by Raymond Toolsie, Volume
More information11 Fractions and Percentages
MEP Practice Book SA Fractions and Percentages. Fractions, Decimals and Percentages. Express each of the following percentages as a fraction in its lowest terms. 0% % % (d) 0% (e) 60% (f) 0% (g) % (h)
More informationUsing Proportions to Solve Percent Problems I
RP71 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
More information5 Decimal numbers. 1 Decimal numbers. 2 How to read decimal numbers.
5 Decimal numbers 1 Decimal numbers Decimal numbers such as 3.762 are used in situations in which we look for more precision than whole numbers provide. As with whole numbers, a digit in a decimal number
More informationWootton Wawen C.E. Primary School. A Guide to Mental Maths
Wootton Wawen C.E. Primary School A Guide to Mental Maths Why is it important that children recall maths facts? Calculators should not be used as a substitute for good written and mental arithmetic. (National
More informationFinancial 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
More informationChapter 7Growth Rates and Percentages
Chapter 7Growth Rates and Percentages Percentages 7.1 The danger with using percentages is that the percentage sign is easily detached from the percentage value leading to incorrect statements. For example
More informationAddition 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
More informationSimply 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 informationGCSE 185/02. MATHEMATICS (2 Tier) FOUNDATION TIER PAPER 2. P.M. MONDAY, 2 June hours. Candidate Name. Candidate Number.
Candidate Name Centre Number 0 Candidate Number GCSE 185/02 MATHEMATICS (2 Tier) FOUNDATION TIER PAPER 2 P.M. MONDAY, 2 June 2008 2 hours ADDITIONAL MATERIALS A calculator will be required for this paper.
More informationMaths GCSE Higher Tier Unit 2. Revision Booklet. Name: This booklet contains past paper questions by topic. 1. Integers and Decimals
Maths GCSE Higher Tier Unit 2 Revision Booklet Name: This booklet contains past paper questions by topic 1. Integers and Decimals 2. Factors and Multiples 3. Laws of Indices 4. Standard Form 5. Fractions
More informationContents. 3 Introduction. 4 Basic Operations. 6 Order of Operations. 8 Basic operations with fractions. 16 Introduction to decimals
Judyth Hayne 0 Contents Introduction Basic Operations 6 Order of Operations 8 Basic operations with fractions 6 Introduction to decimals 0 Basic operations with decimals Significant figures and rounding
More informationMaths Targets  Year 5
Maths Targets  Year 5 By the end of this year most children should be able to Multiply and divide any whole number up to 10000 by 10 or 100. Know what the digits in a decimal number stand for, e.g. the
More informationEDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES. Maths Level 2. Chapter 2. Working with fractions, decimals and percentages
EDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES Maths Level 2 Chapter 2 Working with fractions, decimals and percentages SECTION B Types of fraction 5 2 Using a calculator for fractions 7 Fractions of
More informationChapter 4  Decimals
Chapter 4  Decimals $34.99 decimal notation ex. The cost of an object. ex. The balance of your bank account ex The amount owed ex. The tax on a purchase. Just like Whole Numbers Place Value  1.23456789
More informationAlgebra 1 Topic 8: Solving linear equations and inequalities Student Activity Sheet 1; use with Overview
Algebra 1 Topic 8: Student Activity Sheet 1; use with Overview 1. A car rental company charges $29.95 plus 16 cents per mile for each mile driven. The cost in dollars of renting a car, r, is a function
More informationFractions 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 informationYEAR 6 BLOCK 2 ASSESSMENT
WIGAN LEA NUMERACY STRATEGY YEAR 6 BLOCK ASSESSMENT 6 Name: Date: KEY OBJECTIVES ASSESSED Question Order a mixed set of numbers with up to three decimal places. 3 Reduce a fraction to its simplest form
More informationDirectorate Curriculum: FET SCHOOLS GRADE 12 TEST 1, 2014 MATHEMATICAL LITERACY MARKS: 70. Time: 2 hours. Page 1 of 13
Directorate Curriculum: FET SCHOOLS GRADE 12 TEST 1, 2014 MATHEMATICAL LITERACY MARKS: 70 Time: 2 hours Page 1 of 13 Instructions 1. This test consists of 5 questions and 2 annexures 2. Answer ALL the
More informationWord 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 informationProblem Solving Competency 9
Name: Class: _ Date: _ ID: A Problem Solving Competency 9 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Steven wants to buy a $565 bicycle. Steven has
More informationShawlands Academy. Intermediate 1. Homework Unit 3
Shawlands Academy Intermediate 1 Homework Unit 3 Intermediate1 Homework 1 Unit 3 Non 1. Calculate: (a) 10.2 + 0.5 35 x 420 (c) 2 / 3 of 108 2. A washing machine can be bought by paying a deposit of 74
More informationDecimal 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 information100 40 5 4 = 149. how many left? what s the difference? 5 60 80 4 = 149. take away. Maths in School. minus. Subtraction in School.
100 40 5 4 = 149 0 635 735 775 780 784 1000 8 5 2 1 5 3 how many left? what s the difference? 5 60 80 4 = 149 take away 0 635 640 700 780 784 1000 Maths in School minus Subtraction in School by Kate Robinson
More informationPercents applications.notebook April 07, 2016
Applications with Percents Working with percents is something that people do all the time. The goal for the next few days is to identify how/where we encounter percents in our every day lives and learn
More informationName Date. 2. Belinda jogged 1.5 km, then walked 500 m. Write the ratio of distance jogged to distance walked in simplest form.
Extra Practice 1 Lesson 2.1: Using Proportions to Solve Ratio Problems 1. Find each missing term. a) x:8 = 9:24 b) y:15 = 7:3 c) a:8 = 9:4 d) p 12 = 15 10 e) b 5 = 18 6 f) t 11 = 6 33 2. Belinda jogged
More informationConsolidation of Grade 6 EQAO Questions Number Sense and Numeration
Consolidation of Grade 6 EQAO Questions Number Sense and Numeration Compiled by Devika WilliamYu (SE2 Math Coach) Overall Expectations NV1 Read, represent, compare, and order whole numbers to 1 000 000,
More information7 th Accelerated Chapter 3 Review
Name Period score = Notes c/b 10 50 7 th Accelerated Chapter 3 Review Part IWrite the best answer. Estimate a 20% tip for each of the bills shown. 1. $57.80 2. $122.46 Estimate a 15% tip for each of the
More informationDIAMOND PROBLEMS 1.1.1
DIAMOND PROBLEMS 1.1.1 In every Diamond Problem, the product of the two side numbers (left and right) is the top number and their sum is the bottom number. Diamond Problems are an excellent way of practicing
More informationUnit 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
More information